",mF e 3 iiii O'^^ Digitized by the Internet Archive in 2008 with funding from IVIicrosoft Corporation http://www.archive.org/details/arteducationforhOOpranrich ART EDUCATION FOR HIGH SCHOOLS A COA\PREHEKSIVE TEXT BOOk ON ART EDUCATION FOR HIGH SCHOOLS TREATING PICTORIAL, DECORATIVE AND CONSTRUCTIVE ART, HISTORIC ORNAMENT AND ART HISTORY. THE PRAMG COMPANY NEW YORK CHICAGO BOSTON ATLANTA DALLAS Copyright, 1908, By THE PRANG EDUCATIONAL COMPANY '/? Acknowledgment In presenting "Art Education for High Schools" to the pubhc, grateful acknowledgment is made to the many educators and teachers of art who have assisted in the undertaking. Without the inspiration, suggestion and the direct help received from these sources, this book could not have been written. While it is impossible to make individual mention of those who have contributed in various ways to the preparation of these pages, the publishers desire, by this means, to express their sincere appreciation to all, with the hope that this volume will repay, in service to the cause of Art Education, the efforts put forth by so many earnest workers. / 2586?! Preface "Art Education for High Schools " is planned upon the basic idea that the teaching of art is vastly more important than the teaching- of draw-^ ing. It is believed that the study of art can be presented in the light of certain governing principles, which can be developed in such a way as to equip the high school student at the end ■ of his four years' course not only with a knowledge of material things in the world about him, seen under various aspects and in various relationships, but with such a knowledge of art principles as will give him a better appreciation of the good work of all ages and a fuller understanding of art in its relation to his own life. This book is not a course of study, but its scope is so broad and so comprehensive that many courses of study may be based upon it. The aim has been to provide in the several chapters a clear and definite presentation of each important division of the subject, and to suggest exercises which, if worked out, will assist the student in his understanding of the topic treated. These problems in themselves form an outline of work that might be taken as a course of study. The exercises given in Chapter VI stand as an illus- tration of this feature of the book. The marvellous development of art education in public schools that has taken place in the last quarter of a century has manifested itself more par- ticularly in the elementary grades. As a result of this interest there is no lack of literature on this phase of the subject. There are now available various published systems of art education for elementary schools, with text- books, drawing-books and a large amount of material constituting a full equipment for work. But when we look for similar aids to the further development of this work in high schools, academies and colleges, we find almost nothing of an organized nature. The teacher of art in a secondary school must plan his own course from a confused mass of material found in various places, and must transmit as much as he can of necessary informa- tion to the individuals or classes under his instruction. To furnish the same kind of help to high school students and teachers as is now available to the pupils and teachers in elementary schools the present volume has been prepared. That it may fulfil in some measure this purpose, and that it may be of substantial aid in establishing art education as an indispensable factor in the higher education of the American people, is the earnest wish of those who have directed the preparation of this work. Contents PAGE ACKNOWLEDGMENT Ill PREFACE V CONTENTS VII CHAPTER I Pictorial Representation ...... i II Perspective Drawing ....... 34 III Figure and Animal Drawing . ( . . . . • 71 IV Constructive Drawing . . . . . . .103 V Architectural Drawing . . . . . . -1/9 VI Design 222 VII Historic Ornament . , . . , , . . 277 VIII Art History 303 Index . . . . . . • . . . -341 .';,i':U'\ CHAPTER I PICTORIAL REPRESENTATION Modes of Expression. In pictorial representation there are three distinct forms or modes of expression. We can represent objects in color masses, in neutral values of light and dark, or in outline. Of these three modes, perhaps the most important is the problem of representation by means of light and dark masses. As this involves a knowledge of color masses, the student will soon find that outlines or contours can be satisfac- torily drawn only when the masses themselves are understood. Impressions Formed by Shapes and Values of Masses. Our ■•!>. ART EDUCATION— HIGH SCHOOL first impression of a tree, a person, a landscape, a house, an animal, or of any object is of a mass of color, seen either alone or in relation to other masses of lighter or darker color. We recognize objects by the shapes of their masses more readily than by their color or their details. An ink silhouette of the form of a tree brings to our mind the image of the tree just as directly as does a picture in color. By the character- istic masses of an oak, a maple or an elm, we are able to recognize the particular kind of tree that we see. We do not recognize the tree at a distance by its color, or by the shape of its leaves. A person approach- ing in the twilight is readily recog- nized, not only as a person, but as old or young, as a laborer or a professional man, or as possessing certain other qualities, even when no details whatever are seen (Fig. i). Our im- pression is based upon the characteristic forms of the color masses, or values, and by values is meant the degree of light and dark that a color expresses. Pictures of twilight or moonlight owe their effect of restf ulness and repose to Jfch^elimination of detail and to an emphasis of mass which permits the eye to rest undisturbed upon large essentials. This is illustrated in Fig. 2 . Minor details, it is true, enable us to verify a first impression, as in the case of the tree, but they are subordinate to those things from which we obtain our first or general impression. Study of Masses. The study of pictorial representation, then, should begin with a consideration of the characteristics of objects as expressed by their principal masses, — the size, shape, and values of these masses. Such consideration may be followed by a study of conditions that may furthe- affect the appearance of these masses, such as sunlight and shadow, texture, PICTORIAL REPRESENTA TION w^^\ *;»' o. &^ 1^ ^< "i^^S^ J ^ ART EDUCATION— HIGH SCHOOL perspective, or the effect of distance and atmospheric conditions upon the local color of objects. Pictorial Quality. Pictorial quality depends mainly upon the shape, arrange- ment and values of the masses of color within a given space ; for example, opposing light and dark values contribute to pictorial effect, as in the placing of dark trees against a light sky, a dark figure against a light background, or a light figure against a dark background. We soon find that we cannot disassociate an object from its surroundings. The environment, the background, or the masses against which objects are seen are as much to be considered in picture-making as the shapes of the principal masses themselves, and although they occupy a subordinate place, they are important elements, and must be duly related to the whole. For example, Fig. 3 shows a pencil sketch of a tree, rendered in values of gray, but the effect obtained depends very largely on the contrast made by these values with the light paper. If this same drawing were made upon dark paper we can see that its beauty would have been lost. If we arrange any dark object against a light background and closely observe its appearance we shall see, essentially, a spot of dark color which we might recognize as the object simply by the shape of the mass. The object in Fig. 4 is easily represented by a simple pencil drawing of its dark mass with no con- sideration of background other than that afforded by the light paper. If, however, the object we select has also a mass of light, we must then arrange a sufficiently dark surface against which the light mass may be opposed. Fig. 5 shows a simple object drawn m PICTORIAL REPRESENTATION ART EDUCATION— HIGH SCHOOL against a background chosen to provide contrast for each of the two vakies found in the object itself. Comparative Values. Let it be understood, then, that rep- resentation is a matter of com- parative vakies, and that the surroundings of an object are important in the consideration of pictorial effect. It does not follow, however, that we must give the surroundings of an ob- ject equal importance with the object we have chosen for the main interest. Suppose, for ex- ample, that we are to draw from still-life, or from the human fig- ure, or from some selected portion of the landscape, and that we do not wish the surrounding objects to appear prominent, or to appear at all ; we must then reduce these surrounding objects to simple tones of color of the value necessary to bring out the quality, form and character of the object we have selected for our picture. This point is illustrated in Figs. 6 and 7. In our sketch of the vase of flowers we do not wish to show the books, which may be on the same table. We simply leave them out, substituting for them the tone or values we de- sire as a background for our study. Exercises. Many exercises in illustration of this process of elimination PICTORIAL REPRESENTA TION should be drawn by the student, and for such exercises arrangements of still-Ufe will be found convenient, since we can adjust backgrounds or other surroundings as we may desire. For first exercises, select, arrange and draw objects of one color, then try those having more than one color mass, ART EDUCATION— HIGH SCHOOL selecting backgrounds whose values will best bring out the quality and character of the objects chosen, as illustrated in Figs. 4, 5, 8 and 9. Contrasting Forms, Sizes and Color Values. When a reasonable degree of facility in rendering is acquired the student will be ready to under- take the drawing of groups composed of objects having contrasting forms, sizes and color values. This involves a more difficult problem, since, instead of the simple elements supplied by one object, the background and the sur- face upon which the object rests, we now have several masses of different shapes, sizes and colors, which must be considered first with relation to one another, and finally with relation to the background, or surrounding masses. Fig. 10 shows how one problem of this kind has been worked out. Principal Masses and Masses of Lesser Interest. In drawing PICTORIAL REPRESENTATIOIV from the landscape we should select and draw carefully the elements upon which the in- terest centers, merely sug- gesting the elements of less importance, or substituting color values for them. Fig. 1 1 shows a photograph of a group of trees, in which there are many other things that do not improve the pictorial effect, but divert the interest, and thus detract from the effect of the trees of which a picture is desired. Fig. 1 2 shows a pictorial rendering of the same scene. Color Values. In the study of pictorial representa- tion the question of color values becomes of immediate interest. If we observe the landscape in early autumn for instance, we may see a ^''^- ^^ blue sky with light clouds, a hazy blue or purple color in the distance, and in the foreground, greens, reds, yellows and browns, — some bright in color and some grayed. If we photograph this landscape we reduce everything to values which are all gray or all brown, according to the color of the photo- graphic paper. The only difference we can then see in the color of the trees, grass, sky and distant hills is in their light and dark quahties. We know that some colors photograph lighter than others, but we know also that an ordinary camera will not give us a translation of the true color values of all colors, for those hues which contain reds or yellows will photograph darker than their true values, and those dominated by blue will photograph lighter than their true values. By means of an isochromatic plate, however, this 10 ART ED UCA TIO IV — HIGH SCH O OL photographic defect is overcome, and it is possible to obtain true color values, as shown in Fig. 13. It is by this process that all paintings are photographed. In representing the landscape with charcoal or pencil we try to do what the isochromatic plate does in photography, — to reduce all colors to their true light and dark qualities, without regard to what is generally meant by color or hue. Color Quality. In painting from the landscape or from other sub- jects, we must determine not only the value of a color, but we must know that the local or individual color of an object is affected by distance and by conditions of the atmosphere, or by both. We know that objects are affected by perspective, — that distant objects appear much smaller in pro- portion than those near by, — but we do not always appreciate that they PICTORIAL REPRESENTATION 11 are also changed in color. Between us and the distant hills, for example, / is interposed a body of air that acts like a veil, and, as we look through it, ' distant local colors are rendered dimmer and grayer. Again, if on a clear day we look into the cloudless sky, we see that the color effect of the air is blue, but under different conditions this body of air may take on different colors, such as a tender violet, a faint yellow-green, a delicate rose-color or a subtle gray. Between the observer and a distant object is always interposed this body of colored air, which, as we look through it, affects the local color of all objects in greater or less degree, according to their distances. As distance increases, forms seem to grow smaller, and the shape and local color less distinct. As distance decreases, forms appear larger and more distinct, and the local color grows stronger and less gray, until, when the object is near the eye, its real local color may be determined. In a fertile, cultivated country, where a moist atmosphere prevails, the color of objects at a distance is more affected than in a dry, desert country, where there is little or no moisture in the air. The dryer the atmosphere, the thinner the interposing veil, and the more distinct and local in their coloring are distant objects. For this reason, distances in a very dry climate are deceptive to one who is accustomed to the moist atmosphere of a fertile country. But in any country atmospheric conditions vary. On a bright day we see objects more nearly in their local color than we do on a gray day. Under ordinary conditions we can see, when we are close to a tree, that its mass of foliage is green, the local color. As we go from the tree we see the green through the atmospheric veil, and it is gradually grayed. At a great distance the line of houses, trees and hills is all merged into one mass of gray, and this gray may take on different hues, according to different conditions of the atmosphere. This is well illus- trated in the four sketches on the plate facing page 256, showing the same landscape under four different conditions of the atmosphere. In the study of objects that are close to us the atmospheric effect is not so pronounced, yet it is a matter of sufficient importance to warrant our consideration. Light and Shade. Another modification of the appearance of an object is the effect of sunlight and shadow, or, as it is termed, of light and shade. An object when exposed to a bright light presents a light surface on the side near the light, and a darker surface on the side away from the 12 ART EDUCATION— HIGH SCHOOL light. Whatever the local color of an object may be, it is always influenced by this effect of light. Any object seen indoors, or where there is compara- tively little light, appears much darker than it does when seen under direct sun- light. The real local color of an object is determined when it is seen under diffused light, — that is, under light that does not strike the object from some direct center, like a lamp or candle, or in the form of direct sunshine. In arranging still-life objects or groups for the study of light and shade, we should avoid the extremes of too much or too little light. The diffused light o± a room is best for the drawing of still-life, and by means of a shadow-box we can control the light effects upon a group. By fastening PICTORIAL REPRESENTATION 13 together two pieces of board (Fig. 14) and placing them in such a way as to exclude the light from all or a part of our group we can soften the effect of the bright light from the windows. The shadow- box, too, helps us to overcome the intermingled lights and shadows, or cross-lights, that proceed from several windows, or from several sources of light in a room. In elementary exercises it is best for us to work from light effects that show one light side, one dark side and one shadow onl}'. In a bright light, the contrast between the light side and the shaded side of the object will be strong, — we know that the bright light of noon- day, for instance, casts the darkest shadows. The dimmer the light, as at evening, the less contrast there is between the light and shaded sides of any object — the less distinct is the difference between the shaded side and the shadow. We can easily demonstrate this if we observe objects in a room that is lighted by gas. If the gaslight is gradually turned off, we can see that the shadows become less strong as the light grows dimmer. . The length of shadows is determined by the position of the light, — the higher the light, the shorter the shadow. This, again, is illustrated in the com- parison of shadows seen at midday with those seen in the late afternoon. Shadows also soften and become less clearly defined as they recede from the object that casts them, and in the same proportion that dark masses grow lighter, so light masses grow darker as they recede, or as distance affects them. Reflections. Polished surfaces reflect, more or less perfectly, the images of objects placed upon them. A quiet pool of water, for example, will reflect the trees upon its banks with the fidelity of a mirror, but the slightest movement of the surface of the water will produce lines in the reflection which add to its artistic quality, even though they distort the per- fect image. Colors, also, are influenced in reflections by the quality of the light overhead, and by the color of the water in the pool or stream, which varies from time to time, according to prevailing conditions. In arranging still-life studies, objects made of glass or of polished metal, such as brass or copper, are often used in order to gain, through reflections, added variety and interest in foregrounds. Landscape painting, also, offers opportunity for the use of reflections, as the paintings of Corot, Inness, Turner, and of many other artists so well illustrate. 14 ART EDUCATION— HIGH SCHOOL Outline Drawing. Although it is true that we see objects in color masses, and that we are able to distinguish one object from another by means of the size, shape and character of the various color masses pre- sented, we know that rep- resentation is not confined to mass drawing or paint- ing. Objects may be represented by outline drawing also, and although this method is more or less abstract, it is possible to express in outline all the characteristics of an object except its color. Textures, even, of various kinds, such as the hard surface of stone or of pot- tery, the woody quality of a tree-trunk or twig, the ^'*'' ^^ delicate petal of a flower, or the fur or hair of some animal, may all be expressed by means of outline drawing. To be able to so qualify a line as to make it express these char- acteristics requires skill and experience, and a knowledge of the characteris- tics of the mass which such an outline limits or bounds. We could not, for example, draw a map in outline unless we had a knowledge of the size, shape and topography of the area of country which the map was intended to repre- sent. Sometimes, it is true, outline drawings are purely symbolic, as in the drawings of little children or of savage tribes, but in all technical and artistic work, outline drawing aims to express every quality of an object except its color. PICTORIAL REPRESENTATION Blocking in. In outline drawing, and some- times in mass drawing as well, we often "block in " or sketch with light lines the general proportion and shape of objects. This enables us to make several estimates before placing the final line, and in this way we avoid the errors that result from the at- FiG. 17 tempt to complete one part of the drawing before another part is studied or begun. If a drawing is faulty in its proportions, or in the relative positions of its various parts, no amount of careful finishing can correct the mistake. It is therefore best to sketch very simply, or block in, lines that will indicate the size, shape and position of parts, before spending any effort on technique of line, or upon the careful drawing of any one part. Fig. 1 5 shows a drawing which might easily result if we should begin our study of a dog, for example, by drawing the nose first, and continue to the line of the head, back, etc. Our attention would probably be fixed on the line, rather than upon the general proportion, and the result would be a distortion. Fig. i6 shows a better way of beginning all studies of this nature. Fig. 17 shows the vigorous lines that are put in, with the lighter, block lines used as a guide. When a careful drawing of an object is to be made in charcoal the form should be suggested by loose, light lines, drawn with a sharpened stick of hard charcoal. Hold the charcoal loosely, and "feel" for the form in a series of light lines, correcting, changing and redrawing without eras- ing until the right line is obtained. If erasures are made the tendency will be to repeat the error in a new line, but if all tentative or trial lines are kept, the error will be seen, and that error, at least, will not be repeated. In the finished drawing, all lines may be erased except those expressing the correct drawing of the form under consideration. Fig. 18 shows an outline 16 ART EDUCATION— HIGH SCHOOL drawing of a group studied in this way, before the trial Hnes are erased. Fig. 19 shows a similar group with the trial lines erased. Composition. In every picture there should be a spot or center of particular interest, — a place where the eye pauses or rests. This center may be simply a combination of colors, or it may consist of some object, as a tree, a house, or the face in a portrait. If we wish to paint a picture of a tree we should first consider the placing of the sketch upon our canvas. There would be, also, various masses or shapes against which the tree would be seen, such as the mass of the sky, the mass of the distance, the mass of a hillside, or a barn, or of other trees, and the mass of the fore- ground. The right selection of all these shapes, the adjustment of their sizes, positions, proportions and color values is what is meant by composi- tion. This adjustment can be determined only by much practice and expe- rience, combined with a knowledge of the principles of design. PIC TORI A I REPRESENTA TION 17 ^■\ \ i V A finder (Fig. 20) is a device that enables us to exercise our judgment ' in selecting a composition. If we look through the opening, changing its size and shape as we move the finder about, a variety of arrangements can be seen, and we can select and control the shapes which make up our picture. Sometimes the elements we wish to use will look better in a hori- zontal enclosure, as, for instance, in painting a broad expanse of the sea; and sometimes a vertical enclosure seems best, as when a ship with a mast or when tall trees or buildings are the important elements. The comparison 18 ART EDUCATION— HIGH SCHOOL r X I 4 -' ■ ^-- / -^ .^..J^ '^^. 4^ ^'^ 5^ PICTORIAL REPRESENTA TIOiV 19 ? I 1 W* of these effects and the effort to select the best of several arrangements develop artistic taste and judgment. Exercises with the Finder. To test the efficacy of the finder as an aid to good composition, select some object around which you wish the interest of a sketch to center. Adjust the opening until you have obtained a good relationship of all shapes enclosed, considering not only the shapes in the object itself, but also the shapes made by the background, foreground and by all other elements included. The center of interest should not occupy the exact center of the composition, as such a position is apt to divide the background spaces evenly, and our picture would lack what is known as variet)- ; the arrangement would be monotonous, as Fig. 2 1 illustrates. It is safe to avoid any arrangement that divides the back- ground into equal right and left spaces, or into equal upper and lower spaces. Neither should the center of interest be placed too far at one side, as in Fig. 22. Interest, variety and balance are all secured by the arrange- ment shown in Fig. 23. A little practice will enable the student to select with the finder good arrangements from the landscape. In still-life composition, also, may be found very interesting arrangements of shapes, of light and dark effects and of color. In arranging groups of objects we must remember that 20 ART EDUCATION— HIGH SCHOOL OO^' interest depends largely upon variety in the objects chosen, in their relative positions, and in the unity or com- pleteness of the group as a whole. After the objects are selected and placed, the group should be studied through a finder for the purpose of determining defi- nitely the size of the back- ground spaces, and of re- viewing critically the whole arrangement before begin- ning to draw. The finder helps us to shut out sur- rounding and conflicting elements, and centers our attention and judgment upon the shapes seen through the opening. Its use in select- ing and studying composi- tions is similar to the use made of a finder by the photographer, who studies the picture seen upon his ground glass, or finder, Fig. 26 Fig. 27 bcforc his negative is ex- posed. The student should practise making several arrangements of the same group, studying the different effects through the finder and trying to decide as to the best composition. Practise, also, from groups of different objects, changing the members of a group or rearranging them until good composi- tions are obtained. Such exercises will probably result in many deductions such as the following : — ■ PICTORIAL KEPRESENTA TION ' Too many objects of equal importance in size, shape, color, character, etc., scatter the interest (Fig. 24). Objects placed beside each other in a row give an arrangement that lacks unity (Fig. 25). Equal divisions of space render the arrange- ment monotonous (Figs. 26 and 27). Too great a difference in the areas gives an effect of unbalanced arrangement (Fig. 28). One object placed directly in front of another gives an unpleasant effect of massing (Fig. 29). There must be some relationship or har- mony between the various objects in a picture. Although the objects in Fig. 30 make a good composition, so far as shape, arrangement, and values are concerned, the group is not harmoni- ous because its members are incongruous. This is corrected in Fig. 3 1 . Landscape Drawing. Up to this point, what has been said in this chapter refers to the representation of all kinds of objects, as the illus- trations indicate. After establishing these general principles, it will be well to consider some points bearing on the representation of particular classes of objects with which the student will be con- cerned. The landscape immediately suggests itself as a source to which we turn more fre- quently than to any other. The best possible conditions under which to study the landscape are reached when we go directly to it for this purpose. If we can look through a finder at actual trees, hills, houses, water and sky and find beautiful compositions of line, light and dark, and color, we may quickly gain both appreciation 22 ART EDUCATION— HIGH SCHOOL of the beauty of nature and the abihty to select a portion of that beauty for a picture. If these ideal conditions are not possible, however, we can use photographs of nature as a substitute, and it is to the photograph we must resort in the majority of schools. When this is done, every opportunity for out-of-door sketching should be grasped as an aid to the development of this preliminary study, based upon pictures. Whether we work from nature or from pictures, the fundamental principles and the method of following them will be the same. We have spoken of the parts of the landscape as the distance (meaning the part farthest away), X^o. foreground (meaning the part nearest;, and the middle distance (meaning the part midway between distance and foreground). These are only relative terms, however, and must not be understood as meaning a definite, measurable portion of the landscape or picture space. But the student must understand how to locate masses or shapes in the several places indicated. How to Begin a Study of the Landscape. Look through your finder and select an arrangement of light and dark shapes in the landscape, showing hills, trees and sky, or any other landscape elements. In first prac- tice, work only for values, leaving out all details. With brush, charcoal or soft pencil put in the masses, keeping the composition very simple. Draw or paint in this way until you are able to produce from the landscape before you, or from a photograph of the landscape, a composition that is interesting in the selection of shapes, balanced in arrangement, and rendered in a few simple values, as illustrated in Fig. 32. Continue to make in this way arrangements from the landscape, keeping your rendering in flat tones, in a few values. Either color values or neutral grays may be used, with any medium preferred. Color Added to a Pencil Sketch of the Landscape. Attractive compositions may be made with pencil on tinted paper, applying thin color washes over the pencil work. Fig. 33 shows a pencil drawing on tinted paper of some fishermen's huts, built upon posts or piles over the water. Notice the interesting treatment of the reflections, and the slight but telling suggestion of distance. The pencil sketch is a complete thing in itself ; but the few strokes of water-color added in the plate facing page 24 open up a world of color possibilities which the pencil sketch can but faintly suggest. I PICTORIAL REPRESENTA TIOM Details of the Landscape. Follow this practice by a careful study of individual objects, such as trees, clouds, fences, houses, etc. Make care- ful, suggestive sketches of such objects, treating them as notes or studies to be used in landscape painting or drawing, as occasion offers. Artists fill many note-books or portfolios with studies like those shown in Fig. 34. How to best use these notes is a matter requiring judgment and skill. Too much detail will render a picture photographic in effect, ^nd this is not desirable ; too little will show a lack of structural knowledge and of texture. We must know how to suggest that rocks are hard, that clouds are soft, that hills are solid and that water may show movement or present a 24 ART EDUCAT/OA^—N/GH SCHOOL PICTORIAL REPRESENTA HON 25 J^S ^<|fc^ 'XW* 26 ART EDUCATION— HIGH SCHOOL mirror-like surface. We wish to show as much of texture and of the char- acteristics of the landscape elements as will add to the interest, variety, and * beauty of our picture. A knowledge of the structural quality of the landscape is valuable, and necessary in the same way that a knowledge of the anatomy of the human figure is essential to good drawing from life. Accents. In the studies shown in Fig. 34 you will notice sharp, black touches called accents, which are made with the full strength of the pencil and are placed wherever they seem needed. These are important in lending brilliancy and sparkle to the sketch, and they give, besides, a certain quality to any characteristics that an object may present. This is shown in the treatment of roof edges, openings in the foliage, undercuts in branches, or in the irregular depths of shade in doors and windows. When used without discrimination accents injure a sketch, but when skilfully placed they are indispensable. Figures in the Landscape. If the student is able to use human figures or animals in landscape compositions he will find his resources for interesting material much extended. All such elements of interest must be treated as part of the composition, and not as something added or thrown in after the composition is complete. The mass or shape of a man or a cow must be related to the other shapes of the picture, just as the mass or shape of a hillside or a house is related, and its size, position, value or color must be analyzed and made to take its place in the whole scheme. In • using figures or animals, however, we shall have to decide whether the landscape interest or the figure interest is to predominate. If the former, we must reduce the size of the figures and give them secondary treatment, as in Fig. 35. If the latter, we use the landscape as an accessor)^, and give the figures prominence, as in Fig. 36. But in both cases the figures are treated as a part of the composition, and in neither case would the picture be complete without them. Still-life Drawing. The class of material for art study known as still- \ life includes pottery, flowers, fruits, vegetables, utensils of various kinds, or any other objects selected for use because of some interesting problem which they may present or suggest. When we speak of a still-life study we mean an arrangement of objects that we can control, some group whose members we can select or combine to suit our purpose, and which, with PICTORIAL KEPRESENTA TION 27 some exceptions, can be kept for study for an indefinite time. In the landscape we know that conditions change, often very rapidly, and in drawing from the figure or from animals we are again limited in time by the endurance or by the mood or whim of our subject. Because of the stability of still-life mate- rial and because we can govern so directly its choice and arrangement, it offers the very best opportunity for thorough practice in drawing and for the study of the general principles which have been explained in this chapter. In this material we miss, it is p^^ 35 true, some of the de- hghtful effects of distance, atmosphere, and of certain kinds of perspective, but the student that is well grounded in still-life practice will be able to apply what he has learned in any direction that he may select. Still-life practice is to the artist what 4aily physical exercise is to the athlete ; it gives greater power, and this insures better results. Still-life Studies with Charcoal. It will be found that all kinds of paper do not take charcoal equally well, and a rough, unglazed paper espe- cially prepared for this work, called charcoal paper, should be procured. For certain effects, cartridge paper or butcher's wrapping-paper is often used to good advantage. ART EDUCATION— HIGH SCHOOL After carefully re- viewing what has been said regarding masses, values, effects of light and shade, and composi- tion, arrange a simple group of still-life objects and study it through a finder. When satisfied that your group answers the requirements, block in the main shapes, using a sharpened stick of charcoal of medium hardness. Then lay in the large masses, trying to express at once their true shapes and values (Fig. 37). After these masses are applied freely with the charcoal point, they may be rubbed lightly with the finger ends in order to distrib- FiG. 36 ute the charcoal evenly over the surface of the paper (Fig. 38). If the charcoal is rubbed too heavily the paper will present a smudged or smeared appearance, which of course should be avoided. After the surface has been lightly rubbed the masses that need strengthening should be gone, over again and the necessary lights taken out with kneaded rubber. Tones that seem too dark or too f aggressive may be wiped off or softened with a chamois skin or soft cloth, j After the larger values are laid in, the smaller lights and darks, the reflections and other secondary elements should be studied, the student working with charcoal, chamois skin and eraser until the desired effect is obtained. Fig. 39 shows such a drawing completed. To preserve a drawing of this PICTORIAL REPRESEXTA TION kind, it should be sprayed with a thin solution of white shellac and alcohol, called fixative. This makes a thin varnish which causes the particles of charcoal to adhere to the paper. Pencil Studies. Any good drawing-paper with a hard surface will answer for pencil work, and interesting studies may be obtained from the use of the tinted pencil papers now so generally supplied. A soft pencil I that gives a broad definite line at one stroke is best for general use. A \ pencil drawing must never be rubbed, as is permissible in charcoal rendering. The attempt should be to gain the desired value by direct strokes, instead of by working over a mass more than once. Before attempting to apply a tone or value, study it carefully and practise with your pencil on an extra piece of paper until you are able to produce the full strength of the value by going over the surface of the paper but once. Then apply it freely to the desired area of your composition. Figs. 3, 4, 5, 14, 20, 33, 34 and 35 all show examples of pencil rendering. Study good pencil drawings, notice the kinds ART EDUCATION— HIGH SCHOOL PICTORIAL REPRESENTATION 31 of lines used, and try for this quality in your practice. Pencil studies, also, should be well sprayed with fixative, to prevent them from rubbing. The plate facing page 22 shows a pencil sketch on tinted paper. The pose was chosen for the subject of the sketch, the letter-box on the lamp- post being drawn from memory, as well as the few touches that suggest the street. After the figure with these environments had been blocked in, the dark values of the cap, coat, etc. were laid on with definite, vigorous strokes. The lighter values in the pose were expressed by the color of the paper. The pencil sketch appeared quite finished before the water-color touches, which were tints rather than washes of full strength, were added. Water-Color Handling. There are many different methods of handling water-colors, each sanctioned by artistic authority. As the best method is largely a matter of individual choice, it will be wiser for the student to learn one method, and after he has become familiar with that, he can, by experimenting, and by study and practice, find out how the method he has learned may be modified or adapted to suit his particular needs. Some successful artists prefer to work upon paper that is previously made moist, while others, equally successful, prefer to work directly on dry paper. In good results of either method we would hardly be able to tell which one was used. It is the quality of the result that is important, not the method by which such a result is obtained. Whatman's hand-made paper is best for water-color work. This is somewhat expensive for beginners, however, and many other cheaper papers will answer. Good pencil paper of sufficient tooth will generally take water-color quite satisfactorily. One Way of Using the Wet Method. Dip in water a piece of blotting-paper (cut slightly larger than the paper which is to receive your painting), and lay it upon your drawing-board. Upon this lay the water-color paper, which has also been dipped in water. With a dry blotting-paper of the same size as the water-color paper remove any superfluous moisture that may rest upon the paper. Then wuth a brush full of wet color (not too much water) lay in the masses, working with great directness. As long as the paper remains m^oist changes can be made, other colors or masses added, or lights removed by a dry brush, a soft sponge or a cloth. The plate facing page 12 shows a sketch made on moist paper. The Dry Method. In the dry method of working, the color is ART EDUCATION— HIGH SCHOOL '^^ '^.' applied directly to the dry surface of the paper, the brush being used wetter than it is when the paper is moist. In the wet method the water PICTORIAL REPRESENTATION 83 already on the paper helps to carry the color, and in the dry method more water is needed in the brush to sufficiently dissolve or thin the color. In working "dry," changes are not easily made, and should be avoided. Generally speaking, the wet method gives softer and more melting effects, while crisp and snappy effects are more easily obtained by the dry method. It is usually found that the beginner succeeds better when he works upon wet paper until he feels some confidence in his use of color. He must learn by experience when the paper and colors are wet enough, yet not too wet, to produce the desired result. The more practice he has the more he will feel like making a combination of both methods in his work. Color Added to Charcoal Drawings. Very interesting effects are obtained by applying water-colors to a charcoal or pencil drawing. Fig. 40 shows a charcoal study which is finished^ values and in light and shade, and has been sprayed with fixative. Light washes of water-color were 1 then added. (See plate facing page i.) Try this with some of the sketches you have saved from former practice. If you begin a study with the idea of finishing it in color, it will be well to keep the lights very light in the '' charcoal work, or the color will darken them too much. The Use of Colored Chalks, or Crayons. The plate facing this page shows another interesting method of securing good color effects. Tinted paper of good color and quality is taken as a foundation or background. The position and forms of the objects are blocked in lightly and the color masses are then laid on in a loose, free way, allowing the tint or color of the paper to shimmer through. The full force of color, laid on with bold strokes, is reserved for a few accents and high lights. Drawings of this character should be sprayed with fixative. With colored chalks (which are opaque), either dark or light tinted papers can be used, but when water-color washes are to be applied, it is best to choose light tints of paper, owing to the transparent nature of the medium. In all your practice, whether from still-life, from plant growth, from the landscape or the human figure, and in whatever medium you work, try to express simply and truthfully the character and spirit of your study. CHAPTER II PERSPECTIVE Perspective is the art of representing upon a plane surface the appear- ance of any object, without regard to the facts of its form and size. A per- spective drawing generally shows the effect of a third dimension upon a surface, such as a sheet of paper, which has but two dimensions. Although 'perspective is an exact science and is governed by principles that can be demonstrated, a working Icnowledge of its laws may best be gained by observation from nature and from objects. The knowledge gained by such observation and by practice is often spoken of as free-hand perspective, while the study of the mathematical laws which govern the appearance of objects is called scientijc or mechanical per- spective. In practising free-hand perspective the student strives to express what he sees or feels, and he is not restricted by attention to exact formulas and measurements. In scientific perspective he assumes a picture plane, a horizon or eye-level, a point of distance, vanishing points and distance points, and then proceeds upon a purely scientific basis. This process results in a technically correct representation of the object as it would appear under the assumed conditions. Free-Hand Perspective. Perspective affects nearly everything that we see. If we look across a field, as illustrated in the color plate opposite, we observe that objects in the distance appear much smaller than they really are.' The trees that are shown in the sketch, for instance, might all have been of the same size, but as they recede or are seen farther and farther away, they apparently diminish in size, and the tree in the foreground appears higher than the top of the distant mountain, although we know that in reality the mountain towers high above the tree which is near us. In the picture we notice, also, that colors are dimmer and grayer in the distance, and that the ^^ iym **^4 PERSPECTIVE 35 light and dark masses are less strong in contrast as they are seen farther away. These changes in values and in colors are due to what is called aerial perspective, — the combined effect of distance and of the atmosphere. Again, ' in our picture we notice that the shapes of the boats and the sails are not alike, although for our purpose the sketch was planned to show several sail- boats which in reality were exactly alike. The difference in their shapes, as shown in the sketch, is due to the different positions in which they are . placed with relation to the observer. We see, then, that in making a draw- ing in perspective, we must consider both the distances of objects from us and their positions in relation to us. Another very noticeable effect of per- spective is shown, in the direction of the rails in the railroad. These are parallel in reality, but they do not appear so in our sketch. The rails seem to approach one another as they recede from the eye, until finally they con- verge at one point. In our picture the stretch of land and the surface of the lake represent a horizontal plane, which, when seen at the oblique angle which its position in relation to the eye establishes, appears less wide than it really is. When I a surface, because of its position, appears narrower than it really is, it is said to hQ.foresJiortcned. The principle of foreshortening is the simplest and most obvious principle of perspective, for we see surfaces foreshortened more fre- quently than we see them in their true shape. Deductions. From the study of a scene such as that represented we are able to make the following deductions, which are governing principles in the representation of objects : — a. Surfaces wJieii viewed obliquely appear foreshortened. b. Distance affects the apparent sice of objects. c. Distance affects the apparent color of objects. d. Position affects the apparent form of objects. e. Parallel Tines, receding from the eye, appear to converge. The Foreshortened Circle. A circular face or shape, when held in different positions, illustrates the effect of perspective in a very clear and interesting way. Fig. i shows a hoop which is held or suspended directly in front of the observer, giving a full-face view of its outline. The shape of the view is, of course, a circle. If the hoop is held in a vertical plane so that its rim or edge is exactly opposite the eye-level, its appearance will ART EDUCATION-^ HIGH SCHOOL be represented by a vertical line (Fig. 2). (The thick- ness of the rim of the hoop does not affect the prin- ciple illustrated.) If the hoop is held in a horizontal plane opposite the eye-level, its appearance is a hori- zontal line (Fig. 3). If the hoop is raised or lowered slightly the appearance is an ellipse (Figs. 4 and 5), and the width of the ellipse from front to back appar- ently increases as the hoop is moved farther above or farther below the eye. If the hoop is suspended in a vertical plane, and placed at the right or left of the eye, its outline appears as an ellipse whose long axis is vertical, and the width of the ellipse, measured by the short axis, increases with the distance of the hoop to the right or left (Fig. 6). When objects whose bases are circles, such as cylindric objects, bowls, jars, vases, etc., are seen below the eye, so that the circular faces are neither directly under nor directly opposite the eye, the lower ellipse appears wider than the upper one, for the reason already explained. In preliminary practice it is well to sketch in light line the whole curve of an ellipse when but half of its outline is seen (Figs. 7 and 8). The student should become thoroughly familiar with the principle of the foreshortened circle, and should draw many objects illustrating it, working both from the object and from memory or imagination. Exercise I. Draw, from the object, a glass half filled with water, placed so that the upper edge is slightly below the level of the eye. Exercise II. Draw, from the object, a lamp- shade above the level of the eye. Exercise III. Draw, from the object, a cup and saucer in their usual positions. Exercise IV. (a) Draw, without the object, a vertical cylinder with the lower face on a level with PERSPECTIVE 37 the eye ; (b) with the upper face on a level with the eye; {c) with the lower face held slightly above the level of the eye ; (d) with the middle of the curved face on a level with the eye. From the study of the foreshortened circle we are able to make the following deductions : — a. A face view of a circle is ahvays a circle. b. An edge vieiv of a circle is always a straight line. c. A circle seen obliquely always ap- pears as an ellipse. d. The more obliquely the circle is see?t the narrozver the ellipse appears, — the more nearly it approaches a straight like. e. The less obliquely the circle is seen the wider the ellipse appears, — tJie moi'e nearly it approaches a circle. The Effect of Distance. The farther an object is placed from the observer the smaller it appears. This is easily discerned when we look at objects in the landscape, where the distance is great enough to make the difference in size very apparent. The law holds good, however, when the distance is slight, and it may be easily demonstrated : hold two 12" rulers in a vertical position, directly in front of you, so that their, edges touch throughout their entire length. The rulers in this position, and at the same dis- tance from the eye, appear to be the same size. Now move the right ruler slowly away from you, keeping the ruler at the left iscr— IT:)! ART EDUCATION— HIGH SCHOOL Stationary. The difference in the appar- ent length will be readily seen, and can be measured upon the nearer ruler (Figs. 9 and 10). To demonstrate this principle in another way, place two objects of the same size on a table or shelf in front of you, so that either the tops or the bottoms of the objects are on the level of the eye. Move one object twice as far from you as the other. Test the apparent height of both, and you will find that the farther one appears one-half the height and width of the nearer object. If one object is four times as far away as another, it appear- but one-fourth as high and wide ; if teii times as far away, it appears but one- tenth the height and width of the nearer object (Figs. 11 and 12). Place objects against or partly be- hind each other, and testing with the pencil held at arm's length, compare the apparent size of objects placed at different distances from the eye. Notice how the apparent difference in size is demonstrated in the photograph of the corn-shocks (Fig. 13)- The device of the rulers serves also to illustrate the principle of foreshorten- ing. Place the two rulers together in a horizontal position on a level with the eye and directly in front of you. Hold the left ends together with the left hand, and with the right hand swing the upper ruler away from you, keeping the under ruler stationary. The apparent decrease in the length of the upper ruler, as measured on the under ruler, proves that lines and surfaces are foreshortened as they are turned away from the eye (Figs. 14 and 15). PERSPECTIVE 39 The Horizon Line, or Eye-Level. If you stand upon the shore of the sea or of a large lake and look across the surface of the water it appears to rise as it recedes, until it reaches, in the distance, the level of the eye. If you should climb to the top of a cliff and look again across the water, its surface would still appear to rise until it reached the higher level which your eyes had attained in that elevated position. This distant level, where the earth and sky seem to meet, is called the line of the horizon, or the eye- level, and upon this level all horizontal planes or lines vanish. The floor and the ceiling of a room are horizontal planes receding from the eye, and if extended, they would vanish in the horizon line. Note : The horizon line must not be confused with the sky-line, which is the line made by masses, such as hills, trees, houses, etc., cutting against the sky. Except on a level plane the horizon line is not visible ; the sky-line is always visible. As all horizontal lines receding from the eye must vanish in the horizon line, those below the eye appear to slant upward as they recede, and those above the eye seem to slant downward, and if these receding lines are parallel they will seem to converge to a point upon the horizon line. Convergence. No line can appear longer 40 ART EDUCATION— HIGH SCHOOL than it really is, but under certain conditions it appears shorter, as has-been demonstrated. A verti- cal line may be seen directly in front of the eye, or it may be seen above, below, to the right or to the left of the eye, but its apparent length depends upon its distance from the observer, and its per- spective representation, for all artistic or pictorial work, is always vertical. All other straight lines may, under certain conditions, appear as "retreating" or "van- ishing" lines. In the colored sketch already referred to, the railroad tracks are receding from us, and, although we know that in reality they are par- allel, they appear to converge, and if they were extended over a level plane we would see that they would con. verge to a point on the horizon line and would vanish in that point. This princi- ple is demonstrated in the horizontal lines of buildings, in street scenes, in room interiors and in roadways and PERSPECTIVE sidewalks. In small objects the con- vergence of lines is not so apparent, but we can establish proof that it exists. Lay a book upon a table, with the back directly in front of you. Under the cover of the book place a string long enough so that both its ends may be held in one hand so as to hide from your vision the retreating horizontal edges of the cover (Fig. i6). The two ends of the string are seen to converge, thus indicating the true appearance of the ends of the book in this position. In Fig. i6 two of the four horizontal edges in the top of the book are parallel to the horizon line of the observer and do not seem to change their direction. It is only receding horizontal lines that seem to con- verge, and which, if extended, would meet in a point upon the horizon line.. The student should draw from many objects illustrating the convergence 42 ART EDUCATION— HIGH SCHOOL A 2 B.' ^>' ,' ^\ \E , r 1 .... , , K \\ t .' 1 // \ 8 of retreating horizontal edges. Two rulers or two strips of stiff paper may- be used to test angles after the sketch is made, as shown in Fig. 17. Parallel Perspec- tive. When rectilinear objects are placed so that one set of lines is vertical, another set is parallel with the observer's horizon, and another set is horizontal and receding, converging to a point upon the hori- zon directly opposite the eye, as in Figs. 16, 17 and 18, they are said to be in parallel, or one point perspective. In Fig. 18, which is a photograph of a railway station, it is seen that the vertical lines of all the buildings, of the telegraph pole, and of the freight cars remain vertical ; all horizontal lines that are parallel ^vith the horizon remain hori- zontal ; while the receding horizontal lines, such as the rails, the ridge and eaves of the roofs, etc., all tend toward the same point in the horizon line. To Determine the Vanishing Point in Parallel Perspective. The vanishing point for converging Hues may be determined by simply producing the lines until they meet. An interesting device for demonstrating this is illustrated in Fig. 19, and is worked out as follows : Sit in front of a table or desk, and at the two nearer corners hold two rulers in a vertical position, as at A and A, Fig. 19. Observe the top of the table as seen between the rulers, and then incHne them until they hide from your sight the ends of the table, as at B and B. If the rulers, in this position, could be extended, they would meet at a point opposite and on a level with the eye. If you should imagine this done, and should fix a point on the wall beyond the table, locat- ing the point at which they would meet, as at VP, you would find the van- ishing point for all of the receding horizontal lines in the table. A ruler PERSPECTIVE 43 held so that it hides from your sight a line connecting the bottom of the legs, as at C, will slant toward the vanishing point, VP, as shown in the sketch. Again : Stand with your back against the wall of a long, narrow room and look toward the opposite wall, assuming a point on the wall exactly opposite your eye. With the thumb and finger of the left hand hold a string in a vertical position so that the thumb that holds it hides the assumed vanishing point. The string in this position hides from your sight the crack in the floor upon which you are standing ; that is, the crack, which is a hori- zontal line receding from the eye, appears as a vertical line. Holding the thumb in the same position, take the other end of the string in the right hand and swing it to the right. You can then hide with the string the lower line of the base-board (Fig. 20), and by moving the string you can cover the upper and lower lines of windows, doors, blackboards, picture frames, the upper line of the wall, or any horizontal edge or line that is receding from you. The upper end of the string may be held in place with the right 44 ART EDUCATION— HIGH SCHOOL IB ^^z^^i ^ ii ^^/^^^/ i ^^^^Jli -'■■%. ■pK^^y^ / 'A ^^^S fe^^^i Bridge across the Mississippi River at Thebes, III. Fig. 21 hand and the same experiments made with the hnes at the left. An interest- ing illustration of parallel perspective is shown in the photograph of the bridge (Fig. 21). Exercise V. Find the vanishing point in the picture (Fig. 22). Exercise VI. Draw in parallel perspective an outline sketch of a book ; a checker-board ; a table ; a chair ; a strawberry box ; a bookcase. Note. If the student will place any object behind a vertical pane of glass or a fine wire screen and trace upon this plane the outlines of the object, he will have a correct drawing of its appearance, which will help him to understand the principles of perspective. Exercise VII. Make a sketch similar in character to Fig. 22, from your observation of a street or railroad. Deductions. From the foregoing the following deductions are made : — a. All parallel Jiorizontal edges receding from tlie eye appear to converge. b. All receding Jiorizontal edges appear to incline toivard the level of the eye. PERSPECTIVE 46 ■^ fF -«^ the door a little more and study the effect upon the inclination of the top and bottom edges. It will be found that the vanishing point changes according to the angle at which the door stands, and that the degree of inclination changes in like proportion. , Make a similar test with the door nearly closed. The nearer shut the door, the less will be the inclination of the top and bottom edges, and the farther away will be the vanishing point, biit this point will always be on the eye-level. Make a similar study from a door opening toward you (Fig. 30). It will be well to sketch the same door several times, until you can make an 60 ART EDUCATION— HIGH SCHOOL accurate drawing of its appearance without testing, depending upon your eyes, your sense of proportion, and your knowledge of perspective principles. Turned Cylindric and Conical Objects. The principles of fore- shortening and convergence enter into the representation of objects based in their construction upon the cylinder and the cone. In Fig.. 31 the cylinders are represented as lying in a horizontal plane and turned at an angle, so that the near end appears as a foreshortened circle, or ellipse. The outlines of the curved surface become retreating horizontal lines and show convergence, as the lines of a rectangular box would do in a similar position. In drawing an upright cylinder, the straight lines of the sides seem to pass into the curve of the ellipse at the ends of its long diameter, forming a tangential union, (When a straight line passes without any perceptible change into a curve, the union is called tangential.) The axis of a right cylinder or a cone is always at right angles to the long diameter of the base, and this is true when the object is turned as well as when it is upright, or when its axis is parallel with the horizon line. When the cone is seen below the eye, as in PERSPECTIVE 51 Fig. 32, the straight hnes (which are obhque) appear to form a tangential union with the curve of the elHpse, not at the ends of its long diameter, but a little farther back, and this is true of the turned horizontal cylinder as well, as shown in Fig. 31. The fuller or broader the elHpse of the base of 52 ART EDUCATION— HIGH SCHOOL \X ^ _ _ _ !^ the cone, the farther back from the ends of the long diameter will this union seem to be. Fig. 33 makes this clear. Exercise VIII. D r a w a flower-pot lying on its side and turned at an angle. Sketch its axis and both diameters of both ellipses. Exercise IX. Draw a music roll turned at an angle, lying on a horizontal surface. Exercise X. Sketch lightly one or two parsnips or carrots turned at an angle, and lying on a horizontal surface. Oblique Perspective. When an object is in such a posi- tion that all or a part of its hori- zontal edges are oblique to the ground, as illustrated in the cover of the box shown in Fig. 34, it is said to be in oblique v^ perspective. In the box cover, the retreating edges are slanting and parallel, and they seem to converge and to vanish in points above or below the eye-level at a distance proportionate to the inclination of the edges. The exact location of such points may be found, if desired, by the following procedure: Place a large box with a hinged cover directly in front of you, below your horizon line. Draw it first PERSPECTIVE 53 in parallel perspective with the hinged edge toward you and the cover shut (Fig. 35). As you know, the retreating horizontal edges will appear to vanish in the horizon line. Raise the cover at an oblique angle (Fig. 36) atid again draw the box. You will find that the vanishing point for the retreating edges is directly above the vanishing point for the same lines when they were horizontal (O.V.P., Fig. 36). Turn the box so that the hinged edge is at the back, and slightly raise the cover (Fig. 37). Sketch the box in this position, and you will see that the vanishing point for the oblique lines is directly below the vanishing point for the same edges in a horizontal position. Now turn the box at an angle and slightly raise 54 ART EDUCA7 ION— HIGH SCHOOL the cover, as shown in Fig. 38. The retreating //^r/^^w/rt/ edges appear to vanish in the horizon line, and the retreat- ing oblique edges at the ends of the cover appear to vanish in a point directly above the vanishing point for the hori- zontal edges with which these oblique edges were parallel before the cover was raised. The short oblique edges that show the thickness of the cover seem to vanish in a point directly below in O.V.P.^. The reason for this will be clear, when you remember the principle already established — that receding parallel planes vanish in a line. V.V.L., Fig. 38, is the vanishing line for the vertical planes in which the ends of the box cover lie. Therefore, all lines lying in those planes will vanish in that line. We often find parts of buildings, .such as slanting roofs and dormer windows, in oblique perspec.tive. In Fig. 39, the ends of the barn and the ends of the house are in vertical planes which are par- allel to each other. These planes vanish in a vertical 66 :U-^x^^A>^fg.ipb--:. -^^ / I _ / vanishing line (V. V. L). All lines lying in these planes will vanish in certain points on the vertical vanishing line. Figs. 40, 41, 42 and 43 illus- trate how vanishing points for various parallel oblique edges may be located. ART EDUCATION — HIGH SCHOOL Deductions. From the fore- going, these additional deductions may be made : a. Parallel horizontal edges receding to the left appear to con- verge to a point on the eye-level at the left of the object ; those receding to the right appear to converge to the rig Jit of the object. b. When rectangular objects are standing with their side faces turned equally away, the vanishing points are equidistant from the object; but zuhcn their side faces are tjirned unequally aivay, the two vanishing points are unequally dis- tant from the object, according to the angle at zvhich the object stands. c. Farther vertical edges ap- pear shorter than nearer vertical edges, although in reality they may all be of equal length. d. Receding parallel planes, if produced, appear to vanish in a line. e. Receding horizontal planes vanish in a Jiorizo^ital line on a leugl with the eye, called the eye- level {E. L.), the horizontal line {H. L.), or the horizontal vanishing line {H. V. L.). f. All lines lying in the same plane, or in parallel planes, vanish in the same straight line. To Find Perspective Centers. As objects or parts of objects appear smaller in proportion to their distance from the eye, the perspective centers .^^ /i\ mm ] i PERSPECTIVE of the foreshortened planes will appear a little beyond the geo- metric centers. In Fig. 44 the top of the gable and the center of the door or the window are a little beyond the center of the end and side of the barn. To test this, draw the diagonals of the rectangles as shown in the illustration. The altitude of a pyramid is obtained in the same way (Fig. 45). The apex will be directly over the perspective center of the base. The long diameters of two concentric circles will not appear in the same line. The long diameter of the inner ellipse is a little above the diameter of the outer ellipse, as shown in Fig. 46, which was photographed from a drawing of two concentric circles. The diameters ab and cd were drawn on the photograph. Because the farther half of a sur- face seen obliquely ap- pears shorter than the 68 ART EDUCATION— HIGH SCHOOL nearer half, it is sometimes thought that the farther half of an ellipse (the appearance of a circle seen obliquely) should be drawn narrower than the nearer half. That a circle seen obliquely appears as a perfect ellipse is shown by the photographs (Figs. 46 and 47), which were taken from draw- ings of circles. It will be seen in Fig. 47 that the diameter ef, of the circle, which is also the diameter of the square, does not remain the long diameter of the ellipse. The line gh, which is the long diameter of the ellipse, was drawn through the exact center of the ellipse on the photograph. The two halves are exactly alike. PERSPECTIVE 59 Mechanical Perspective We have seen that freehand perspective is largely a matter of the close observation of objects as they appear under different aspects and conditions. We come now to the study of the theory of perspective, in which the prin- ciples deduced from our study of objects are proved by scientific methods. In mechanical perspective certain conventions are assumed which must first be explained. Conventions. Imagine a sheet of glass to be standing in an upright position before you, through which you can see the various objects in the room. This glass extends, in imagination, from the floor to the ceiling, and from side to side of the room. A plane such as the glass represents is called the Picture Plane (P.P.). The edge that rests on the floor represents the Ground Line (G.L.). The position of your eye represents the Station Point (S.P.), and is always located at a given distance from the Picture Plane. The direction in which you are looking, represented by an imaginary line drawn from your eye to a point on the Picture Plane exactly opposite your eye, is called the Line of Direction (L.D.). The point opposite your eye, on the Picture Plane, is called the Center of Vision (C.V.), A horizontal line passing through the Center of Vision is called the Horizon Line (H.L.). When we look at a fixed point before us, our vision is not limited to the point alone, but we see, more or less clearly, a certain field or area sur- rounding the point. This area is the field of vision, and its extent may be illustrated as follows : place the palms of your hands together and extend your arms directly before you. Look fixedly at some point opposite your eyes. Con- tinuing to gaze at this point, slowly open your extended arms. You will observe ■ that you can see your hands less and less distinctly as they move away from the point upon which your gaze is fixed, until finally the hands disappear from sight. The points at which your hands disappear mark the limits of your field of ART EDUCATION— HIGH SCHOOL vision and these points are reached when the arms are at an angle of 90° to each other, or at 45® with your Line of Direction. The field of vision, then, is the area measured by lines drawn from the Station Point at an angle of 45° with the Line of Direction. The points at which these lines meet the Horizon Line are called Distance Points (D.P.). These Fi«- *^ Distance Points are used as meas- uring points for certain lines, as will be shown later. (Fig. 48.) The Relationship of Planes. In mechanical perspective we find that the two most important planes are the Picture Plane (the vertical plane upon which the picture is drawn) and the Ground Plane (an imaginary level plane of infinite extent, some distance below the level of the eye, upon which the object to be represented and the observer are supposed to stand). In Fig. 49, Plane A is the Picture Plane ; C and B represent the Ground Plane ; the observer stands on one side of the Picture Plane, at S.P., and E repre- sents the position of the eye. The province of mechanical perspective is to project from plans or views of an object a mathematically correct perspective representation of that object. Part C of the Ground Plane (Fig, 49), which is behind the Picture Plane, is used to draw plans upon, and from these plans the perspective representation is projected upon the Picture Plane. It is, therefore, necessary for this part of the Ground Plane to be brought into the same plane with the Picture Plane, and so we must revolve it through a quadrant until it lies over or above the Picture Plane. For the same reason. Part B of the Ground Plane must be revolved through a quadrant until it lies below the Picture Plane. The path of these revolutions is shown in Fig. 50. Fig. 5 I shows the arrangement of these planes as they must appear upon our paper, which is the plane upon which all these plans, views and projec- tions must be drawn. Fig. 52 shows a perspective diagram, and Fig. 53 shows how a drawing in parallel perspective is made upon the diagram. In all problems in mechanical perspective there is one invariable rule which PERSPECTIVE 61 .^^^J^^ . / .f : . ■ PLAN RP H.L. GL. c.v. S.R pp H.L. « j -grr Fig. 52 must be followed : A II vicas7ireincnts iniist be viadc upon the Picture Plane. Parallel Perspec- tive. Parallel or one- point perspective refers to that position of the object which makes use of only one Vanishing Point, and this Vanish- ing Point is also the Center of Vision. In parallel perspective, the object stands parallel to the Picture Plane, as illustrated in Fig. 53. Here, two cubes of the same size are placed so that their faces are either parallel with or perpendicular to the Picture Plane. They are both at the left of the ART EDUCATION— HIGH SCHOOL S.P Fig. 53 really is. The vertical lines remain Line of Direc- tion (L.D.). One is placed against the Picture Plane and the other is some distance behind it. In order to make a perspec- tive drawing that is mechanically accurate, it is necessary to pro- ject all points from the plan to the Picture Plane. In this case A and B are; the respective plans of the cubes. The nearest face of the cube is against or in the Picture Plane, and will be shown in its actual size and shape. The farther face of the cube will appear in the Picture Plane in its true shape, vertical and the but smaller than it horizontal lines that are parallel with the Picture Plane remain horizontal. PERSPECTIVE 6ii The other faces of the cube are seen obliquely and will not appear in their true shape but will be foreshortened, and their horizontal retreating lines will vanish in the Center of Vision, The apparent width of the faces is deter- mined by drawing lines from points on the plans to the Station Point. Where these lines pierce the Picture Plane will be found on the Picture Plane the apparent width of the foreshortened faces of the cube. Projecting these points downward gives us intersections with the vanishing lines that converge to the C.V. For example : lines from D and C drawn to S.P. pierce the P.P. at points E and F. From points E and F, lines projected downward until they intersect the Vanishing Lines from L and M, locate points H, I, J, and K, determining the foreshortened face G, of the second cube. The other foreshortened faces are located in a similar way. In order to make a correct perspective drawing of an object, it is necessary to know the following facts : — • a. The actual sice and shape of the object. b. Its distance from, and relative position to, the Picture Plane. c. Its distajice from, and relative position to, the Line of Direction. ' d. Its distance from, and relative position to, the Ground Litie. e. The height of the eye above the Ground Line ; this height also fixes the Horizon Line. f. The distance of the spectator from the Picture Plane ; this distance determines the Station Point. g. The scale of ineasurem,ents used. Angular Perspective. Angular, or two-point, perspective refers to that position of the object which makes use of two vanishing points, located upon the Horizon Line. All lines parallel with the Ground Plane, but at any other angle than 90° to the Picture Plane, are in angular perspective, and their vanishing points will be on the Horizon Line, but not in the Center of Vision. An object in angular perspective is illustrated in Fig. 54. A square prism is placed at an angle of 45° to the Picture Plane, some distance behind it and some distance to the right of the Line of Direction, its top view or plan being represented by A. In drawing the diagram, the P.P., H.L., and G.L. must be parallel. The L.D. must be perpendicular to these lines. The distance between the P.P. and the H.L. may be assumed, and the S.P. 64 ART EDUCATION— HIGH SCHOOL PERSPECTIVE 65 must be located on the L.D. at an assumed distance below the G.L. The steps in working out the problem are as follows : — 1. Through S.P. draw a line parallel to 1-4, cutting P.P. in D.P.i. 2. Drop a perpendicular from D.P. i to H.L. establishing the point V.P.I. This is the vanishing point for the perspective of the line 1-4, and for all lines parallel with it, as 2-3. 3. Extend 1-4 to meet P.P. at B. 4. Drop a perpendicular from B to G.L., establishing point B'. 5. Draw a line from B' to V.P.i. The perspective of Hne 1-4 will be somewhere in this line. To find the perspective of point i, the extremity of line I -4, proceed as follows : — 6. Through S.P. draw a line parallel to 1-2, cutting P.P. in D.P. 2. 7. Drop a perpendicular from D.P. 2, meeting H.L. in V.P.2. 8. Extend 1-2 to meet P.P. in D. 9. Drop a perpendicular from D to G.L. establishing the point D'. 10. Draw the line D'-V.P.2. The perspective of point i lies in this line, D'-V.P.2, — and also in the line B'-V.P.i ; therefore, it must be at their intersection, i '. 11. As this prism is assumed to stand upon the Ground Plane, at some distance behind the P.P., and as we have learned that all measure- ments must be made upon the P.P., we must measure the height of the prism (assumed to be 4 inches) up from B', establishing point E. 12. Draw E-V.P.i. The perspective of the line 1-4 will be some- where in the line E-V.P.i. 13. To find point i ", measure 4 inches from D' on the line D-D', estab- lishing point F Draw F-V.P.2. The intersection of E-V.P.i and F-V.P.2 locates i", the perspective position of point i . 14. Draw I'-i", the perspective of the nearer edge of the prism. 1 5 . The apparent width of the faces of the prism is determined by drawing lines from the points in the object, as 2, 3 and 4, to the S.P. Where these converging lines pierce the P.P., as in points G, H, and I, will be found the apparent widths. From these points drop perpendiculars to G.L. At the intersection of these lines with the vanishing lines already found, locate G', H' and I', and below G", H" and I". 66 ART EDUCATION— HIGH SCHOOL PERSPECTIVE 67 i6. Draw the necessary verticals connecting these points. After a careful study of the foregoing explanation of Fig. 54, the student should work out simple problems, such as the following : — Exercise XI. Draw a square plinth measuring i foot X 4 feet X 4 feet, placed at an angle of 30° to the P.P., 2 feet behind the P.P. and 2 feet 6 inches to the right of the L.D. S.P. is 10 feet in front of P.P., and 2 feet 3 inches in front of G.L. H.L. is 5 feet above G.L. Scale ^ inch= i foot. Exercise XII. A square pyramid measuring 2 inches X 2 inches at the base, altitude 3^ inches, is placed at an angle of 45° to the P.P. It is \ inch behind the P.P. and i inch to the right of L.D, S.P. is 5 inches from P.P., and H.L. is 3!^ inches above S.P. G.L. is i inch above S.P. Scale, full size. This problem is worked out in the same manner as the problem of the square prism (Fig. 54) with the exception of the location of the apex of the pyramid in the perspective view. To find the perspective of the apex, draw A-A', parallel to 1-4 (Fig. 55). From A' drop a perpendicular to G.L., establishing A". Measure 2^ inches up from A", establishing point D. A"-D is the altitude of the pyramid, measured on P.P. Draw D-V.P.i. The per- spective apex will be at some point on this line. Draw A-S.P., establishing point E on P.P. From E drop a perpendicular intersecting D-V.P.i in E'. E' is the perspective apex. A Building in Angular Perspective. Fig. 56 shows a perspective view of a simple country church, and illustrates the process usually followed by architects in projecting measurements from plans and elevations. In order to obtain all the measurements necessary in making the perspective drawing, we need the side elevation A and the roof-plan B. The roof-plan is drawn at the angle assumed as the point of view of the observer. (In choosing a point of view for a perspective drawing select an angle that will show the building in as comprehensive and advantageous a position as possible.) In this case, the roof-plan is placed a short distance behind the P.P. The S.P. is assumed to be in front of the near corner of the building. D.P.I and D.P.2, and V.P.i and V.P.2 were established as in previous examples, already explained. All points from the roof-plan were projected to the P.P., and perpendiculars were dropped from the intersection of these points with the P.P., as in the preceding problems. All vertical dimensions ART EDUCATION— HIGH SCHOOL PERSPECTIVE needed were projected from the side view. For instance, the perspective height of the steeple was found by projecting point C in the roof-plan to the P.P., establishing C. From C a perpendicular was dropped to the G.L., establishing C". C" ' in the side view was projected to intersect C-C\ in C" ". Then the line C" "-V.P.I was drawn. The perspective of the apex of the steeple was at F, the intersection of the line C" "-V.P.i with the line D-E. The other points needed were found by a similar process, as shown in the drawing. Oblique Perspective. All lines that are neither parallel nor perpen- dicular to the G.L. nor to the P.P. are in obhque perspective. (See " Oblique Perspective," pages 52 to 5^.) 70 ART EDUCATIOX—HIGH SCHOOL Oblique perspective is used mainly in getting the perspective of gables, hip-lines and roof valleys in architectural drawing. Fig. 57 shows how a box whose cover is in oblique perspective may be drawn with mechanical accuracy, by means of the projection of dimensions and angles from a plan and a side view. i A Pen-and-Ink Sketch of a Building Drawn in Mechanical Perspective FROM AN Architect's Plans CHAPTER III FIGURE AND ANIMAL DRA\A/'ING Knowledge of Anatomy. In the anatomy of the human figure, as well as in the anatomy of animals, there are a few fundamental facts that may be gained through a brief study of the subject, the possession of which will enable the student to approach the problems of figure and animal draw- ing with a better understanding of its essentials than art knowledge alone can give him. Painters, sculptors and illustrators find that an extensive knowledge of the location and function of bones and muscles in the human figure is indispensable ; for the high school student, however, such exhaust- ive study is not possible, nor is it necessary to the development of general art knowledge. Such acquaintance with the general proportions, construc- tion and articulation of the human figure should be gained as will enable the student to draw the human form and the forms of familiar animals with intelligence and considerable accuracy. General Proportions. The head is the basis of measurement and proportion in either the male or the female figure, and the average man measures y\ heads in height. Fig. i shows the general measurements of an average figure as to the heights of the various parts. The upper meas- urements are : from the top of the head to the base of the chin, i head ; to the deepest part of the chest, 2 heads ; to the rim of the pelvis, 3 heads ; to the base of the torso, 4 heads. (In the female figure the base of the torso is a little lower than this measurement.) The lower measurements are : from the foot to the lower edge of the knee-pan, 2 heads ; to the head of the thigh-bone, 4 heads ; from the head of the thigh-bone to the base of the torso, i head. Adding these proportions, we find the sum to be 7 ^ heads, the height of the average human figure. 72 ART EDUCATION— HIGH SCHOOL In the upper half of the figure the dis- tance between the top of the head and the base of the torso may be divided into thirds, giving us the following points : From the top of the head to the shoulder, \\ to the waist, I; to the base of the torso, f . From the arm-pit to the elbow-joint is equal to the length of the forearm from the elbow to the wrist. The arm when dropped from the shoulder and extended at full length brings the tips of the fingers approximately to the middle of the thigh-bone. I FIGURE AND ANIMAL DRAWING 73 74 ART EDUCATION— HIGH SCHOOL Proportionate Widths. Fig. 2 shows a few of the important propor- tionate widths of the figure. The width of the head at the level of the eyes is f of a head. The width of the shoulders at their widest point (slightly below the joints) is 2 heads. The width of the hips at the head of the thigh-bone in the male figure is i^ heads; in the female figure it is if heads. Proportionate Depths. Fig. 3 shows the human figure in profile, and gives a few of its proportionate depths. From the lips to the back of the neck measures f of a head. The chest at its greatest depth measures 1 1 heads. The depth of the loins at the rim of the pelvis measures | of a head. Proportions Vary with Age. The proportions of the human figure vary greatly according to age, the measurements already given being the average in the adult. In childhood, we find that the head is much larger, in FIGURE AND ANIMAL DRAWING 75 76 ART EDUCATION— HIGH SCHOOL proportion, than it is when the figure is full grown. Fig. 4 shows the relative proportions of the head to the body at the ages of six months, five years, nine years, and in the adult. Exercise I. Make sketches from grown people, at home or in school, as shown in Figs. 5, 6 and 7. Begin by making dashes to locate the top of the head and the level of the feet, as A and B in Fig. 5. Lo- cate some very apparent line, such as a waist-line, a vest-line, or the line of a coat or jacket, about midway between the dashes A and B. (See C, in Fig. 5.) Block in the main masses of the head, torso, skirt, etc. Verify these shapes and measurements by refer- ring to the diagrams given in Figs. I, 2 and 3. Show only proportions of the figure, not details. Exercise II. From one of your schoolmates posed in profile make a FIGURE AND ANIMAL DRAWING 77 L ,.*^" 78 ART EDUCATION— HIGH SCHOOL similar study, as shown in Figs. 8 and 9. Remember that when the figure is not full grown, the head is larger in proportion to the body. The sketch shown in Fig. 8 represents a boy that was seven heads high. Proportions of the Head and Features. The general shape of the head is like an ovoid with the greatest width at the top. The eyes are located half way between the top of the head and the chin. The nostrils are half-way between the eyebrows and the chin. Dividing the distance between the nostrils and the base of the chin into thirds locates the opening of the mouth and the upper limit of the chin. (See Fig. 10.) The space between the eyes is equal to the width of an eye, which is also the width across the lobes of the nose. The top of the ear is about on a level with the eyebrow, and the lower edge of the ear is about on a level with the end of the nose. All these measurements must be considered as approximate only, but they are of great service as aids to accurate observation. In Fig. 1 1 the lines that are drawn to locate the features may be con- sidered as circles extending around the ovoid form of the head. When the head is tipped back, these circles become, in perspective, ellipses, and it is interesting to note that they still locate the features, and give us a correct idea of foreshortening. Fig. 12 shows the head tipped forward, and the lines of the ellipses take the opposite curve. FIGURE AND ANIMAL DRAWING 79 Exercise III. In order to become familiar with measurements given above, make enlarged copies of Figs. lo, ii and 12. Exercise IV. From the pose, make a drawing of the head, verifying the measurements given' in Fig. 10. In finishing the sketch, the lines locating the features may be erased. Action. When the figure is seen in different positions, such as in bending, kneeling, etc., the measurements and proportions of the different parts seem to be changed. This is because of the effect of perspective. The real proportions do not change. The human figure, in its various posi- tions is affected by perspective in the same way that any other object is affected, and in sketching an attitude that brings foreshortening into the question we must remember that appearances are often very different from facts. In the statue shown in Fig. 13, all parts impress us as being in correct proportion, yet we could apply the unit of measurement (the head) only to the legs from the knee down, and to the upper part of the left arm, because all the other parts are turned, and are foreshortened. The head itself is bent forward, and does not appear in its true height. The torso is also inclined. The upper part of the right leg, the lower right forearm, the hands and the left foot are greatly foreshortened and are not measurable by ordinary means. Yet we know that the parts have not actually changed their proportions or measurements ; — they only appear to have done so, in the same way that the faces of a cube retain their true measurements, although, in perspective their appearance is so much changed. The side view of a sitting figure is not difficult to draw, as in this posi- tion there is little foreshortening, and most of the parts appear in their true length (See Fig. 14). Exercise V. From the side view of a boy, sitting, and engaged in some action, such as whittling, hammering, fishing, reading or writing, make a sketch. Draw first light lines that will indicate the swing or direction of the figure, as shown by the lines A, B and C in Fig. 15. Upon these lines, block in the head, and the general shapes of the waist, the trousers, the legs, etc. Test the measurements, make the necessary corrections, and lay in the values, somewhat as indicated in Fig. 16. Balance. In all standing figures the center of gravity should pass through the supporting foot, or between the feet, if they support equally. 80 ART EDUCATION— HIGH SCHOOL FIGURE AND ANIMAL DRAWING 81 ART EDUCATION-HIGH SCHOOL FIGURE AND ANIMAL DRAWING 84 ART EDUCATION— HIGH SCHOOL In a figure that is merely supporting its own weight this point is immediately below the pit of the neck (Figs. 17 and 18). The extent to which a figure is thrown forward, back, or to one side does not alter this rule, so long as the figure is stationary (see the Hne AB in Fig. 19). When a figure is carrying a weight, the line that indicates the center of gravity is shifted in a direction opposed to the force of the weight. For example, in Fig. 20 the weight on the back throws the line AB (which marks the center of gravity) to the right, and it falls outside the foot-base; in Fig. 21, the weight of the dumb-bells is held in front of the figure, and the center of gravity falls behind the feet; in Fig. 22 the weight is carried in the left hand, conse- quently the center of gravity is found at the right. If the weight in the left hand were increased, the center of gravity would fall still further to the right. We see that the figure is thrown out of normal balance in proportion to the force opposed to that balance. FIGURE AND ANIMAL DRAWING 85 A loss of balance creates motion ; this may be voluntary, as in walking or running, or involuntary, as in falling. The extent to which a figure is thrown out of balance indicates the rapidity of the motion. This is shown in Figs. 23 and 24, where the motions of walking and running are illustrated. By comparing these two sketches it will be seen that the difference between these actions is not alone in the position of the legs, but that other parts of the body are affected as well. In running, the more intense action is shown in the forward thrust of the head, the stiffening of the muscles of the neck and back, and in the increased action of the arms. When a man throws a ball it is not alone by the position of his arms that the action is expressed, but by the position and action of the head, torso and legs ; the torso is bent back and turned, the left leg is raised from the ground in the effort to balance the torso, and there is a combined action of all the muscles in the body, in the effort to hurl the ball (Fig. 25). Exercise VI. Draw one of the school-boys in the act of carrying a 86 ART EDUCATIOX—HIGH SCHOOL pail of water or a valiser Note the location of the center of gra\-ity, and the position of the head, torso, opposite arm, etc. Exercise VII. Draw from the pose a girl sweep- ing or writing upon the blackboard. Sketch the action lines, and block in the main shapes, compar- ing one part with another, as you work. Finish the sketch in values. Bone Construction. When we attempt to draw the figure in action, we find that a knowledge of the skeleton and its construc- tion is essential, in order that we may know where and to what extent action may take place. Bones, we know, are rigid, and have of themselves no power to move. Action is produced when bones articulate with one another by means of muscular con- traction. This articulation is much more pronounced in some parts of the body, as, for instance, in the arms, legs and neck, than it is in others. FIGURE AND ANIMAL DRAIVING 87 • Beginning with the skull, we find that it meas- ures about \ of the height of the figure. The differ- ence between this measure- ment and the measurement of the head, previously given, is accounted for by the allowance made for muscle and hair. With this exception, the meas- urements of the figure as before stated apply also to the measurements of the skeleton. Figs. 26, 27 and 28 show the front, side and back views. The skull is placed at the top of the spinal column or backbone, which is composed of bony rings, each capable of slight movement, one upon the other. It runs a little below the middle of the figure, and is slightly cur\'ed, as shown in Fig. 27. The spine is the supporting column of the figure, and to it the ribs are attached at the back (Fig. 28). With the exception of the two lower pairs, the ribs are attached in front to the breast-bone, or sternum (see A Fig. 26). The collar-bone, or clavicle (B, Figs. 26 and 28), is attached to the top of the breast-bone and reaches to the shoulder, where it forms a socket with an extension of the shoulder- blade, called the scapula (C, Figs. 27 and 28). The shoulder has no other articulation with the skeleton, its further attachment being by muscles only. ART EDUCATION— HIGH SCHOOL The spine extends be- low the casing of the ribs, and is finally consolidated and joined to the pelvis (D, Figs. 26, 27 and 28), which is a basin-shaped bone supporting the spinal column. At its lower out- side margin is a deep socket into which the thigh- bone, or femur (E, Figs. 26, 27 and 28), is inserted. Both the arm and the leg have one bone in the upper portions and two bones in the lower portions, as shown in the drawings already referred to. In looking at these sketches of the skeleton, it is not difficult to see in what places motion is pos- sible and in what places it is impossible. The two upper vertebrae of the spinal column are so constructed Fig. 27 . , as to give unusual move- ment to the neck. The upper vertebra, called the atlas (F, Fig. 27), allows the head to move forward and back, while the second vertebra (G, Fig. 27), called the axis, forms a pivot-like joint, around which the head may rotate. The shoulders have great freedom of movement and can be raised to the level of the jaw, thrown forward or pushed back and depressed. In the ribbed portion of the trunk there is little motion, but at the waist the figure can bend forward and back, it can incline to either side, or it can partly turn with a rotary movement. The pelvis itself has no motion. FIGURE AND ANIMAL DRAWING In the arms there is far more freedom of move- ment than in the legs, be- cause of the free articula- tion of the shoulder socket. The arms and legs articu- late at the elbows and the knees. The upper bone of the arm is called the humerus (H, Figs. 26, 27 and 28). As has been said, in the lower portion of each is introduced a second bone, giving a rotary- motion, and allowing the wrist and ankle to turn from side to side. In the arm, this second bone, the radius (I, Figs. 26, 27 and 28), rotates around the head of the ulna (J, Figs. 26 and 28), the bone that makes a hinge-joint with the h u- merus, and forms at the wrist a pivot, around which the radius rotates. This t'IG. 28 construction enables the hand to twist and turn. In the ankle there is less freedom of movement, as the bone tibia (K, Figs. 26, 27 and 28) makes both the knee-joint and the ankle-joint, and the second bone, called the fibula (L, Figs. 26, 27 and 28), while it permits some freedom of movement, is not able to communicate its action to the foot. In the front of the knee-joint is a small, flat, round bone called the tympanum (M, Figs. 26 and 27), which is attached by tendons to the leg bones. This forms the prominent part of the knee. 90 ART EDUCATION— HIGH SCHOOL Muscles. We have now a general idea of the human skeleton and of its capacity for action. The bones themselves, we have seen, have no capacity for action but depend for movement on muscular contraction. A student who desires to make a serious study of the figure should become familiar with at least as many of the ^ muscles as are shown in R. Figs. 29, 30 and 3 1 . Figs. 29, 30 and 31 show the front, back and side views of the muscular system. A, Figs. 29, 30 and 31, is the sterno-mastoid muscle, which draws the head forward. B, Figs. 30 and 31, is the trapezius, which draws the head back. C, Figs. 29, 30 and 31, is the deltoid, which lifts the arm. D, Figs. 29, 30 and 31, is the latissimus dorsi, which draws the arm down and back. E, Figs. 29 and 31, is the pectoral, which draws I FIGURE AND ANIMAL DRAWING the arm and shoulder forward. F, Fig. 29, is the rectus abdominis, which draws the body forward. G, Figs, 29, 30 and 31, is the external oblique, which draws the body- laterally and assists in the expiration of the breath. H, and I, Figs. 30 and 31, are the gluteus and tensor muscles, which, when acting together, hold the body erect. When the gluteus acts alone, the thigh ^ is drawn backward; when the tensor acts alone, the thigh is drawn forward. J, Figs. 29 and 30, is the gracilis muscle, which helps to bend the leg, and assists in bringing it and the thigh inward. K, Figs. 29 and 31, is the rectus femoris, which straightens and extends the leg. L, Fig. 30, is the semi-tendinosus, which helps to bend the leg. M, Figs. 30 and 31, is the biceps femoris, which also helps to bend the leg and assists in turning the 90 ART EDUCATION— HIGH SCHOOL leg and foot out- ward, when the figure takes a sit- ting position. N, Figs. 29, 30 and 31, is the g ^ s txoc ji e m i us^ which ends in the' t £.pxl^ jji achilles , and raises the heel, as in walking, running or stand- ing on tiptoe. O, Figs. 29 and 31, is the tib- ialis anticus, which raises the front of the foot, P, Figs. 29, 30 and 31, is the bi- ceps, which raises the lower arm. O is the tri- ceps, which straightens the forearm and op- poses the action of the biceps. R, Figs. 29 and 30, is the supi- nator 1 o n g u s , which rolls the ra- dius bone outward and the palm of the hand upward. FIGURE AND ANIMAL DRAWING 93 S, Fio-s. 29 and 31, is the flexor carpi ulnaris, which extends the wrist and hand. In applying the knowledge we have gained of the proportion, action, ' balance and construction of the human figure to drawing from the pose, we are often perplexed because the clothing obscures many of the principal joints and qualifies to some extent the ratio of proportions. The uncertainty of measurement in the clothed figure is, however, only additional proof that the student needs some definite knowledge of anatomy to keep him from making absurd blunders in locating or indicating important joints, etc. If we possess even a limited amount of scientific knowledge of the points covered in this chapter, we will look at the pose, not as a mass of unintel- ligible lines and uncertain proportions, but with an effort to locate the essential features of construction and action that every figure must contain. When we know where to look for these points we shall find that much of the construction of the figure is apparent through the clothing, and is often measurable. Exercise VIII. On tinted paper make a pencil sketch from the pose of a boy sawing a board. The pose may appear with shirt sleeves rolled up, with a soft hat, and with some note of color, as for instance in the necktie. Sketch in the figure as heretofore directed, getting the action lines first, then blocking in proportions. Finish in values, adding suggestive touches of white chalk and color as the costume demands (see color plate facing page 22). Exercise IX. On tinted paper sketch from the pose of a boy at a manual training bench. The pose should be in the act of planing, using chisel and mallet, boring a hole with brace and bit, etc. Use charcoal for this sketch. After the work has been sprayed with fixative, color effects may be added with thin washes of water-color (see " Color added to Char- coal Drawings," page 33). Exercise X. Sketch from the pose of a girl drinking tea from a cup, holding the saucer in the left hand. The girl should be dressed in white, with a note of color, such as a tie, a bow in the hair, etc. (The cup and saucer might carry a note of blue color.) Sketch the outlines in pencil, and put in the mass of the costume in white chalk, modelling the waist, the sleeves and the skirt the same as in pencil rendering, instead of laying the chalk on in a flat tone. 94 ART EDUCATIO.Y — HIGH SCHOOL Exercise XI. Sketch from the pose of a child pulhng a toy horse, wagon, etc. Use tinted paper as before, and show a color note in the toy or in some part of the costume. E X c r ci s e XII, Sketch from the pose of a child sitting or kneel- ing. (Marbles, building blocks, boat-sailing and looking at picture-books are suggested as interest- ing occupations.) Use tinted paper, pencil, chalk or color to gain effects. Other suggestions for figure drawing are : Draw from the pose of the teacher at her desk ; from the teacher standing; from the teacher bending over an easel or desk ; from the teacher arranging a group of still-life ; from the janitor using his brushes and brooms ; from the engineer at the furnace ; from workmen about the building ; from a boy playing hockey ; from a girl stirring cake in a large yellow bowl with one or two blue bands ; from a man reading a newspaper ; from a woman sewing, or hanging up clothes, etc., etc. All of these suggestions are capable of interesting manipulation, if done on tinted or bogus papers, with charcoal, pencil, white chalk, colored crayons or water-colors. Anatomy of Animals. If we are familiar with the bone construction FIGURE AND ANIMAL DRAWING 95 and the muscular system of man, we shall find that we have a general idea, also, of the skeletons and muscles of the verte- brate animals, for be- tween the anatomy of man and that of the ani- mals there is much in common. Owing to the difference in posture and to the different habits of life, there is necessary in the animals some re- adjustment and modifica- tion of the parts, but the general plan we shall find to be the same. Fig. 32 is the skel- eton of a man in the position of a quadruped. By comparing this figure with Fig. 33, which is the skeleton of a cat; with Fig. 34, the skele- ton of a dog ; with Fig. 35, the skeleton of a horse ; and with Fig. 36, the skeleton of a cow, we see at once the general similarity of plan. Each has a skull, backbone, ribs, pelvis and limbs. There are, of course, great differences in the shapes, sizes and proportions of the individual bones, for the habits and necessities of different animals vary greatly. The skull of man, for instance, has a larger brain capacity than we find in the animals, while the other parts of the skull, such as the jaws, the nose, etc., are much smaller in proportion. In the elongation of the spines of the vertebrae, ART EDUCATION— HIGH SCHOOL shown at A, in Figs. 33 to 36, we see the pro- visions made for the attachment of tlie large muscles that are neces- sary to hold the head in a horizontal position. We note, also, a differ- ence in the slant of the scapula, B, in Figs. 33 Fig. 36 a. ^: Ti. to 36. Its position IS more nearly vertical than in man (Fig. 32), where the same bone is nearly horizontal, producing an effect of squareness in the shoulders. Again, animals have a larger ribbed portion than man, and this makes possible an increased lung capacity. The pelvis in animals (C, Figs. 33 to 36) is much smaller in proportion than is the corresponding bone in man. The large protuberances at the back of this bone (D) are for the attachment of the large muscles of the leg. The greatest difference between the skeletons of man and the animals is seen in the legs, although when we make a careful comparison we find, even in the limbs, a great similarity of construction. The arms in man may be said to correspond with the fore-legs of animals. While it is true that the bones in the upper leg of the animals (see E in Figs. 33 to 36) are much shorter than the corresponding bones in man, they closely resemble the human bones in other respects. In the bones marked F in the animal skeletons, corresponding to the two lower bones of the human arm and leg, there is a greater difference, and this variation continues in the animals themselves. The carnivorous animals, which are digitigrades (that is, animals with paws, and that walk upon their toes), still have the two bones in the lower leg, as will be seen in the bones marked F in Figs. 33 and 34. The herbivorous animals, which are ungulates (animals having hoofs) have the two bones in the fore-legs, although the second bone is somewhat rudi- mentary, while in the hind-legs the bones F are fused into one (Figs. 35 and 36). In Figs. 33 to 36 there is a group of bones marked G, corresponding to the human wrist and ankle bones. The bones marked H correspond to the tarsal and metatarsal bones — the bones of the human hands and feet. FIGURE AND ANIMAL DRAWING 97 In these last bones there is much variation among the animals. In the hoofed animals, they are fused into one, and are very much elongated ; in the animals with paws they are still elongated, but remain separate. The bones marked I in the animal skeletons cor- respond to the finger bones in man. We have thus seen how closely the animal skeleton resembles the skeleton of man. We have found that it has a corresponding bone, or its modification, for each bone in the human skele- ton, with the single ex- ception, in some cases, of the collar-bone. The cat has a collar-bone, and the dog a rudimentary one, but the cow and the horse have none. The absence of this bone accounts for the restricted lateral move- ment of the animals' fore-legs. Comparison of Muscles. As we have ART EDUCATION— HIGH SCHOOL D is the latissimus dorsi muscle. E is the pectoral muscle. F is the rectus abdominis muscle. G is the external oblique muscle. H is the gluteus maximus muscle. I is the tensor muscle. K is the rectus femoris muscle. compared the human and animal skeletons and have found great similar- ity, let us now consider the muscular arrange- ment in man and the animals. Fig. 37 repre- sents man in the position of an animal. Fig. 38 is the cat ; Fig. 39, the dog; Fig. 40, the cow; and Fig. 41, the horse. As each muscle in these five figures is indicated with the same letter, we may readily compare and name them, and by re- ferring to the paragraph on Muscles, page 90, we may review the attach- ment and action of these same muscles in man. A is the sterno-mas- toid muscle. B is the trapezius muscle. C is the deltoid muscle. FIGURE AND ANIMAL DRAWING 99 L is the semi-tendinosus muscle. M is the biceps femoris muscle. N is the gastrocnemius muscle. O is the tibialis anticus muscle. P is the biceps muscle. O is the triceps muscle. R is the supinator longus muscle. S is the flexor carpi ulnaris muscle. We find in the muscles of animals, as in their skeletons, a construction similar to the human construction, with similar action ; but the extent to which action is possible is greatly affected by the differences already men- tioned^ — in the length and shape of the bones and in the size, shape and strength of the muscles. For example, in the animals the additional number of vertebrae in the neck and the length and strength of the neck muscles enable the animal to turn the head directly backward, or to lower the head to the ground, as in grazing. Again, the elongation of the tarsal bones makes it possible for the animal to reach its head with its hind hoof or paw. There are many other actions possible with animals which are traceable to structural differences. Balance in Animals. The balance of animals is easily discernible, as the weight of the animal, when standing still, is borne at the four extremities of the trunk. When action occurs, either in locomotion, or to oppose some force, this balance is necessarily disturbed. In Fig. 42, the balance of the dog is destroyed, — that is, the dog could not stand in this position without the opposing force AB. In Fig. 43, the horse, pulling against the force AB, 100 ART EDUCATIO.Y~ HIGH SCHOOL \ Fig. 44 must throw his body forward to sustain equilibrium. The loss, regaining and changing of balance causes locomotion. Locomotion. In walking, an animal has always two or more feet on the ground, and when two feet are suspended between the supporting legs, the suspended feet are laterals, that is, they are on the same side of the body (Fig. 44). When the suspended feet are one forward and one back of the supporting legs, the suspended feet are diagonals (Fig. 45). In trotting, FIGURE AND ANIMAL DRAWING 101 the diagonal feet move together, as in Figs. 46 and 47. In a gallop, the animal throws itself forward with a fore-foot, lands upon the diagonal hind- foot, places next on the ground the other hind-foot and lastly the remaining fore-foot. These movements are illustrated in the eight sketches shown in Fig. 48. The student should make a number of drawings, copying in pencil Figs. 44, 45, 46 and 47, until he is familiar with these various actions. He y "y "^ 'ffC should then verify his sketches by a close observation of animals, when he can see them in similar action. With this knowledge at his command, he can sketch animals from life without stopping to study the complicated actions involved in the walking, trotting and galloping common to all animals. When sketching from life this definite knowledge of the universal actions of animals can be used unconsciously, and attention can be given to those 102 ART EDUCATION— HIGH SCHOOL actions which are individual, or which are characteristic of the particular animal under observation. The more we gain of general knowledge in draw- ing, and the greater masters we become of certain universal laws of propor- tion, action, balance and construction, the freer we are to observe and express individuality, or that which is not universal. While we must have definite knowledge of the type, it is a certain departure from the type that makes a sketch interesting. The object, then, of this definite and scientific study is not to lead us away from nature, but rather to bring us back to nature, with keener appreciation and with a better understanding of the great simplicity of her universal laws. J CHAPTER IV CONSTRUCTIVE DRAWING Introduction In carrying on the work of the world it is necessary that there should be a division of labor. The hardships of pioneer life are due very largely to the separation of man from his fellows. In building his shelter, for instance, the early settler must cut down his own trees, and, instead of the timbers which the saw-mill and the planing-mill could prepare for him, he must resort to logs laid one upon the other for the walls of his dwelling. He cannot develop the resources of the new country without the assistance of his fellow-man, and when more people are attracted to the locality he has chosen, there arises the demand for the architect, the carpenter, the mason, the plasterer, the plumber, the machinist and for all the other work- men which the building up of a community makes necessary. In order that all this constructive work may be carried on without confusion or loss of time, some definite and accurate means of conveying ideas is needed. Even if all men spoke a universal language, words would fail to convey with clearness and accuracy all the information that a body of workmen must possess in order to build a house, a bridge, or a piece of machinery. A drawing or picture is a language which men of all nations understand, but a picture of the appearance of an object, while it may give a general idea of that object, does not furnish all the facts of- form, size, and structure which a workman must have if he is to construct that object. Hence there has been developed another kind of drawing, called constructive or me- chanical drawing, which deals with the facts of an object, and not with its appearance. Mechanical drawing has certain methods peculiar to itself; and its symbols and conventions constitute a language for the transmission 104 ART EDUCATION— HIGH SCHOOL of ideas relating to construction. In order to acquire this language the student will need the following equipment : — Materials and Instruments ^ Drawing-board Emery pad or sand -paper Ink eraser Paper Compasses India-ink Thumb tacks T square Ruling pen Scale Triangles French curves Pencils Pencil eraser Penholder and pen Drawing-Board. A drawing-board may be procured of any school- supply house. Paper. The paper should be of good quality, and sufficiently heavy to stand the eraser. It may be either white or manila. Two good sizes for ordinary school use are 9" x 12" and 12" x 18". Thumb Tacks. These are tacks with large, flat heads, used for fastening the paper to the drawing-board. Four tacks are sufficient for a sheet of paper of ordinary size. Scale. For elementary work, a ruler marked off in inches, halves, quarters, eighths and sixteenths will answer ; but for more advanced work l"l I I I I I ' I I I I I I I ' I I I ' I ^ |iii|iii|iii|iii| ^ %, Fig. 1 v\^\»^\^^{\^\\i\ \ \ ^ ,\ ^ ,\ ^ ,\ ^ ,\ ^ >\ ^ .\ \ .\ \ \ ^ \. ^'^"^'^'^'^\ L^\.^.\^\A^\^\^\A^\^\^\AA^\^\^\A^\^\^\^\■A\ \AA^\^\^\^\^\^\^\AA^\^\^\\\\\^\^\^\\\^\\\^\^\^\.\^\ Fig. 2 where scale drawings are required, an instrument called a scale is neces- sary. Two scales used in ordinary practice are shown in Figs, i and 2. Pencils. Two pencils, one medium hard and one hard, are necessary. The hard pencil, which is used for making fine lines, should be sharpened to a "wedge" point, as shown in Fig. 3. The medium-hard pencil, lln elementary work, where inking is not required, the student will not need the last five items on this list. CONSTRUCTIVE DRAWING 105 Figs. 3 and -1 which is used for Hning in, for figures, for letters and for free-hand lines, should be sharpened to a conical point, as shown in Fig. 4. In both pencils the lead should be kept sharp by rheans of emery cloth or sand-paper, which may be glued or otherwise fastened to a thin strip of wood. Compasses. Compasses are used for drawing circles and parts of circles, and are provided with a needle point for fixing centers, a detachable pencil point, an inking pen, and a lengthening-bar, used for draw- ing curves of large circles (Fig. 5). Good compasses are jointed, thus allowing the legs to be bent in order that both blades of the pen may be perpendicular to the paper when in use. The lead in the compasses should be hard and sharpened to a wedge point, the flat face being set to coincide with the circle which it draws. In ad- U justing the lead, be careful not to set the thumb-screw too tight, as there is danger of " stripping " the thread. T Square. The T square is an important instrument, used in draw- ing horizontal lines and in supplying an edge against which the triangles are placed in drawing vertical and oblique lines. It is made of two pieces, the head and the blade (Fig. 6). Triangles. Two triangles are necessary: one called the 45° triangle, having angles of 45° and 90° (Fig. 7), and one called the 30° and 60° triangle, having angles of 30° and 60° (Fig. 8). Triangles made of transparent material, such as celluloid, are preferable. Erasers, The pencil eraser should 106 ART ED UCA TION— HIGH SCHO OL be soft and pliable. The ink eraser or sand-rubber is needed for erasing inked lines. Ink. Waterproof India-ink should be used for "inking in" mechanical drawings. Ruling Pen. A ruling pen is used for inking in all lines. It has a thumb-screw adjustment by which the width of the line is regu- lated (Fig. 9). Arrow- heads, figures and let- ters are inked with a common pen ;^a No. 303 Fig. 9 /--ii i-i-' • 1 f iG. 10 FIG. 11 *'*'• ^ Gillott s pen is good. Irregular or French Curves. These are made in various forms. The illustrations show some common examples (Figs. 10, 11 and 20). Directions for Using Materials and Instruments The drawing-board when in use should lie flat upon the desk, or it may be slightly inclined. Generally, the board should be placed with the long edges running from left to right. To fasten the paper upon the board, place it about in the center, and fix a thumb tack in the upper left corner. Set the head of the T square against the left edge of the board so that the upper edge of the blade coincides with the upper edge of the paper. Fix a second thumb tack in the lower right corner. Then fix tacks in the other two corners. In ruling lines, use the T-square blade, the edge of a triangle or a ruler. The scale should be used for marking distances, and not for ruling lines. If a line of a certain length is desired, it is best to draw a fine pencil line longer than the line required, and to mark off the exact distance on that line, rather than to try to make it the right length at the first trial. To mark off the exact distance, lay the scale on the line, and set the point of the pencil at the marks measuring the distance on the scale, making small pencil points on the line. When two equal distances are to be measured from a central point, or when several equal distances are to be set off on a line, it is better to use the dividers. Spread the points of the dividers until they measure on the scale the required distance. "Step off" these distances on the line, thus making COXSTRUCTIVE DRAWING at each point a slight puncture on the surface of the paper. To draw circles with the compasses, take the head of the compasses between the thumb and forefinger, or between the thumb, forefinger and middle finger, as shown in Fig. 12. The instru- ment should be placed so that the pencil point is \^ at the left of \ \^ and below the center, and held so that the pressure on the fixed ^^^ ^^ point is very slight. In describing the circle, turn the hand to the right, so that the pen- cil point will take the same movement as the hands on a clock-face. The ^'''" ^^ compass should be held at a slight in- clination to the right and the pressure on the pencil point should be even throughout. In ruling straight lines from one point to another, as from point A to point B in Fig. 13, first place the pencil on one of the points, as B; slide the edge of the ruler up until it touches the pencil and also coincides with the other point, as A. Draw the line. Lines are usually drawn from left to right. When the T square is in use, the head should be held against the left edge of the drawing-board. The upper edge of the blade should be used for ruling horizontal lines (Fig. 14). Vertical lines should be drawn against the edge of a triangle whose base is resting against the upper edge of the T-scjuare blade 108 ART EDUCATIOX— HIGH SCHOOL (Fig. 15), To draw lines at 45, 30 or 60 degrees, use the triangles as shown in Fig. 16. For oblique lines at other angles, use the triangles as shown in Fig. 17. The placing of marginal lines on a sheet of paper is important, and should be systematically done. Place the paper on the board, as previously explained. Decide on the width of the margin, as three quarters of an inch. Measure this distance in from each edge of the paper, placing the dot near the middle of the proposed line. Place the pencil point on the lower dot, and slide the T square up to meet it. Using the upper edge of the T square as a ruler, draw a fine line the whole length of the paper. Draw the upper marginal line in the same way. Make the side lines by using the T square and a triangle. Line in or strengthen the lines forming the rectangle, and erase the ends that fall outside. All drawings should be done first with fine pencil lines, so that cor- rections can easily be made. When the drawing is to be finished in pencil, Fig. 17 the lines not wanted should be erased, and the others lined in with a medium-hard pencil, taking care to make all corresponding lines of uniform width. When a line that is to be erased is near another line, the line to be retained may be covered with a piece of paper, so as to protect it while the other is being removed. If the line to be erased is between two other CONSTRUCTIVE DRAWING 109 lines, use, as a protector, two pieces of paper or cut a narrow slit in one piece. The ruling- pen,^ used for inking in drawings, should be filled from the quill attached to the stopper of the bottle. The column of ink in the pen should not be more than a quarter of an inch high. All lines of the same width and kind on a sheet should be inked in with the same setting of the pen, and the pen points then changed for the next width of line by adjusting the screw. Try fig. is the lines on a waste piece of paper before inking the drawing. In ruling lines, the pen should be held nearly perpendicu- lar to the paper, inclined to the right, with the pen pressed slightly against the edge of the ruler (Fig. i8). Curved lines should be inked first. In using the compass pen, the joints in the legs should be adjusted so that the lower parts of the legs are perpendicular to the paper (Fig. 19). Try the pen on waste paper before making the line on the sheet. If both points are not touching ^'^' ^^ the paper, the line will be ragged on the side of the short point. In case a very fine line cannot be made with the pen, it is probably dull. To sharpen it, screw the points together and sharpen on the outside only, using a fine oil-stone. For inking curves that are not circular it is necessary \ j to use the instrument known ^^-^ } ^'' as the irregular or French ""''■-----_.!._------'''' curve. The desired curve Fig. 20 should be first drawn free hand, with a light pencil line. This must be 1 Inking is sometimes omitted in the first year or in the first two years of high school work, for the sake of devoting more time to learning the principles of mechanical drawing, and to giving practice in pencil drawing. 110 ART EDUCATION— HIGH SCHOOL done very carefully, as any error in the pencilling is emphasized in the ink- ing. Lay the French curve on the line, so that it fits as large a portion as possible, as at A B (Fig. 20). Do not ink in quite as much of the line as coincides with the curve. Move the curve along, matching it with another portion of the line, as at B C and continue this process until the curve is accurately inked. Geometric Problems Geometry is the basis of accurate constructive drawing, and is fre- quently used in design ; therefore the student should become familiar with those geometric constructions that are ordinarily employed. The work- ing out of the problems that follow will prove a means of gaining this knowledge, and will provide opportunity for practice in .the use of instru- ments. All geometric problems should be worked with the ruler and compasses, and every point found by geometric methods. The use of the T square and triangles follows later, when practical constructive methods are considered. A problem in geometric drawii>g may be divided into three parts : first, that which is given ; second, the construction ; third, that which is required; and to distinguish these separate features, three kinds of lines are used. If the work is in pencil, make the given lines medium width (Fig. 21), the working lines very fine (Fig, 22), and the required or result lines strong and dark (Fig. 23), If the problem is to be inked in, draw all . lines in fine, full pencil lines, then ink in as indicated Fig. 21 abovc. Working or construction lines may be inked ~' ; with fine, short dash lines (Fig. 24). In working !__: the problems, mark the given lines and points with F'«- 23 capital letters, and the constructive steps with nu- -- merals, in the order of procedure, thus: i will indi- FiG. 24 ' J^ ' cate the first step taken ; 2, the second step, and so X\X on. A problem thus worked will show at a glance N what was given, the method of working, and the result (Fig. 27). In working geometric problems the student should at first make large drawings, not more than CONSTRUCTIVE DRAWING 111 one on a sheet, or one problem worked two or three times, placed in various positions (Fig. 25). Later, the space within the margin may be divided into four equal parts, and a problem or exercise placed in each space (Fig. 26). Problem I — To draw a perpendicular to a line AB at a given point C in the line. (Fig. 27.) With C as center and any radius less than CB or CA, set off equal distances, Ci and C2, from C. With points i and 2 as centers, and with a radius greater than half the distance 1-2, describe arcs intersecting at 3. Draw the line 3C, which is the required perpendicular. Problem II — To draw a perpendicular to a line AB from a point C outside the line. (Fig. 28.) W^ith C as center and any radius, draw arcs cutting the line AB in two points, i and 2. With i and 2 as centers and any radius, draw arcs intersecting at 3. Draw C3, the re- quired line. Note. It must be remembered that a perpendicular line is not necessarily a vertical line. Problem III — To draw a perpendicular to a given line AB, at or near its extremity. (Fig. 29.) With A or B as center and any radius, draw an arc (nearly a semicircle) cutting the line AB in I. With i as center and with the same radius, cut this arc at 2. With 2 as center and with the same radius, describe the arc 3-4. With 3 as center and same radius, intersect 3-4 in 4. Draw 4A, the required perpendicular. Problem IV — To bisect a given straight line AB or an arc of a circle ACB. (Fig. 30.) With A and B as centers and any radius greater than half of AB, describe arcs intersecting at i ^^ c Fig. 27 -B 112 X ART EDUCATION— HIGH SCHOOL and 2. Draw the line 1-2, which bisects the given line AB, the arc ACB, and is perpendicular to the line AB at its center. Exercise I. Bisect lines and arcs in the positions given in Fig. 31: — Exercise II. Construct a square on its diag- onals (Fig. 32). Problem V — To draw a line parallel to a given straight line, at a given distance from it. (Figs. 33 and 34.) Let AB be the given line and CD the required distance. Place two points in the given line AB, and from these points erect perpendiculars by Problem I.' With i and 2 as centers and a radius equal to the required dis- tance, CD, draw arcs cutting the perpendiculars in points 3 and 4. Draw 3-4, the required line. In practice, the perpendiculars are sometimes omitted (Fig. 34). Problem VI — To construct a square upon a given side, AB. (Fig. 35.) At A or B erect a perpendicular by Problem III. With A as center and AB as radius, describe an arc cut- ting the perpendicular, in i. With B and i as centers and AB as radius, describe arcs intersect- ing in 2. Draw 1-2 and 2B, Exercise: Construct an oblong, the sides be- ing given; length, 3", width, 2". Problem VII — To construct an equilat- eral triangle upon a given base AB. (Fig. 36.) With A and B as centers and AB as radius, describe arcs which intersect at i. Draw lA and iB. 1 If, in working out a problem, it becomes necessary to repeat a former problem, the steps of the problem referred to are not numbered. CONSTRUCTIVE DRAWING 113 Exercise I. Construct an isosceles tri- angle, the base and sides being given ; base, 2" ; sides, 3". Exercise II. Construct a scalene triangle, the sides being given; sides, 2", 3" and 4", respectively. Problem VIII — To bisect a given angle ABC. (Fig. 37.) With B as center, describe an arc intersecting AB and BC in i and 2. With I and 2 as centers and any radius, describe arcs intersecting in 3. Draw the line 3B, which bisects the angle ABC. Exercise: Bisect an acute angle and an obtuse angle. Problem IX — To trisect a right angle ABC. (Fig. 38.) With B as center and any radius, describe an arc intersecting AB and BC in I and 2. With i and 2 as centers and the same radius, cut the arc in 3 and 4. Draw 3B and 4B, trisecting the angle. Problem X — At a point A in a given line AB to draw an angle equal to a given angle CDE. (Fig. 39.) With D as center and any radius, describe an arc cutting the lines DC and DE in i and 2. With A as center and the same radius, describe an arc cutting the line AB in 3. With 3 as center and radius equal to 1-2, intersect the arc in 4. Draw 4A, the required angle. Problem XI — To construct an angle of 60° at a given point A on the line AB. (Fig. 40.) With A as center and any radius, describe an arc cutting the line AB in i. With i as center >< Fig. 40 114 ART EDUCATION— HIGH SCHOOL and the same radius, intersect the arc in 2. Draw A2, making an angle of 60°. Problem XII — To construct an angle of go°, 60°, 45°, 30", 15°, or of any other given magnitude. (Fig. 41.) The circumference of a circle contains 360°. Any diameter, as 1-2, divides the circle into two equal parts, each containing 180°. Two diam- eters at right angles to each other, as 1-2, and 3-4, divide the circle into four equal angles of 90° each. Trisect one of these, as 4C2, by Problem IX, obtain- ing angles of 30°, 2C5, and 60°, 5C4. Bisect 2C5 (an angle of 30°) and angles of 15°, 2C7 and 7C5 are obtained. Bisect an angle of 90° (Problem VIII) and obtain angles of 45 °. Trisect, by spacing with the dividers, an angle of 15° and angles of 5 ° are ob- tained. Divide one of these into five equal parts and single degrees are obtained. Note. Any angle cannot be trisected geometii- it must be spaced with the dividers. Problem XIII — To divide a given line into any number of equal parts. (Fig. 42.) Let AB be the given line, to be divided into five equal parts. At A draw a line making any acute angle as BAC, with AB. At B draw a line making the same angle as DBA, with AB (by Problem X), but on the oppo- site side of the line. Beginning at A and B set off on the lines AC and BD as many equal parts, less one, as the given line is to be divided into, — in this case, four. Connect the first point, i, with the last point, 8. Draw parallels to the line 1-8, connecting the other points. These parallels divide the given line AB into five equal parts. Problem XIV — To inscribe a regular hexagon within a given circle. (Fig. 43.) Draw a diameter cally : CONSTRUCTIVE DRAWING 115 of the circle, 1-2. With i as center and the radius of the circle as radius, intersect the cir- cumference at points 3 and 4. With 2 as center and the same radius intersect the circumference at points 5 and 6. Draw 1-3, 3-5, 5-2, 2-6, 6-4 and 4-1. The inscribed figure is the re- quired hexagon. Note I. By joining alternate points an inscribed equi- lateral triangle is obtained. Note 2. The radius of a circle spaced off on the cir- cumference divides the circumference into six equal parts. Problem XV — To construct a regular hexagon upon a given base. (Fig. 44.) Let AB be the given base. With A and B as cen- ters and a radius equal to AB describe arcs intersecting at i . With i as center and the same radius describe a circle. Set off the radius six times upon the circumference, and draw A2, 2-3, 3-4, 4-5 and 5-B, making the required hexagon. Problem XVI — ^Vithin a given circle to inscribe a square. (Fig. 45.) Draw a diam- eter of the circle, as 1-2. Bisect 1-2 by- Problem IV, and continue the bisector until it intersects the circle in points 3 and 4. Draw 1-3, 3-2, 2-4, 4-1, thus obtaining the required inscribed square. Exercise : Within a given circle to inscribe a regular octagon (Fig. 46). Problem XVII — To construct a regular octagon upon a given side. (Fig. 47.) Let AB be the given side. With A and B as cen- ters, and a radius equal to AB, describe two semicircles. At A and B erect perpendiculars by Problem II L Extend the line AB in both IW ART EDUCATTOISr— HTGH SCHOOL directions until it meets the arcs in points i and 2. Bisect the right angles 1A3 and 2B4, by Problem VIII. Produce the bisectors until they meet the arcs in points 5 and 6. Draw the line 5-6, cutting the perpendiculars in 7 and 8. From 7 and 8 set off the distance y-Z on the perpendiculars, in points 9 and 10. Draw- through 9 and 10 a straight line, indefinite in length. Set off from 9 and 10 distances 9-1 1, 9-12, 10-13 ai^d 10-14 equal to 5-7. Draw 5-1 1, 11-12, 12-13, 13-14 and 14-6, making the required octagon. Problem XVIII — To construct a regular octagon within a given square. (Fig. 48.) Let ABCD be the given square. Draw its diag. onals, intersecting at the center, i. With A, B, C and D as centers, and Ai as radius, draw arcs intersecting the sides of the square in points 2, 3, 8, 9,6, 7, 4 and 5. Draw 9-6, 7-4, 5-2 and 3-8, making the required octagon. Problem XIX — To inscribe a regular pentagon within a given circle. (Fig. 49.) Draw a diameter, 1-2, and a radius, 3-4, perpen- dicular to it. Bisect 1-3 in 5. With 5 as center and radius 5-4, intersect 1-2 in 6. With 4 as center and radius 4-6, intersect the circle in 7. 4-7 is the side of the required pentagon. Set off this distance five times on the circumference, and draw 4-7, 7-8, 8-9, 9-10, and 10-4. Problem XX — To construct a regular pentagon upon a given side. (Fig. 50.) Let AB be the given side. With A and B as centers and radius AB describe circles intersect- ing in points i and 2. With 2 as center, and the same radius, obtain the intersecting CONSTRUCTIVE DRA WING 117 points 3, 5 and 4. Through 3-5 and 4-5 draw lines, producing them to points 6 and 7. With 6 and 7 as centers and radius AB de- scribe arcs intersecting at 8. Draw A7, 7-8, %-6, and 6-B. Problem XXI — To inscribe a regular polygon of any number of sides within a given circle. (Approximate method.) (Fig. 51.) Suppose we wish to inscribe a polygon of five sides within a given circle. Draw a diameter, AB, and divide it by Problem XIII into as many equal parts as the polygon is to have sides, — in this case five. With A and B as centers, and radius AB, describe arcs inter- secting in 5. From 5, draw a straight line through the second point 2, to intersect the circle in 6. A6 is a side of the required polygon. Beginning at 6, set off A6 upon the circle to obtain 7, 8 and 9. Draw A-6, 6-7, 7-8, 8-9 and 9A. Problem XXII — To c'rcumscribe a circle about a given triangle. (Fig. 52.) Let ABC be the given triangle. Bisect any two of its sides by Problem IV. Produce the bisectors until they meet at i. With i as center, and radius lA, iB or iC, describe the circle. Exercise I. To draw a circle through three given points, not in the same straight line, construct a triangle by connecting the given points with straight lines, and proceed as in Problem XXII. Exercise II. To find the radius of a given arc, or the center of any circle, assume any three points in the curve and proceed as above. 113 ART EDUCATION— HIGH SCHOOL \y Exercise III. To find the radius of the arch for a window, the width of the window and the rise of the arch being given (Fig. 53). Let the width of the window AB be 4" and the rise of the arch 1-2 be f ". Find the center for the arcs. Problem XXIII — To inscribe a circle within a given triangle. (Fig. 54.) Let ABC be the given triangle. Bisect any two of the angles by Problem VI IL The bisectors will intersect at i. From point I draw a perpendicular to any one of the sides, by Problem II, obtaining point 2. With i as center, and 1-2 as radius, draw the required circle. Problem XXIV — To inscribe three equal tangential circles within an equilateral triangle. (Fig. 55.) Let ABC be the given triangle. Bisect the angles A, B and C by lines meeting at i. Bisect the right angle 1-2-B, obtaining the point 3, the center of one of the required circles. With i as center, and radius equal to 1-3, describe a circle, obtaining the points 4 and 5, which are the centers of the other two circles. The shortest distance, as 3-6, from the center 3 to a side of the triangle is the radius of the required circles. Exercise I. Inscribe six equal tangential circles within a regular hexagon (Fig. 56). Exercises: Construct Trefoils, Quatrefoils and Cinquefoils (Figs. 57, 58, 59, 60 and 61). Problem XXV — To draw a tangent to a given circle at a point A in the circumference. (Fig. 62.) Draw a radius, Ai, and extend the line beyond the circumference. Erect a perpendicular at A by Prob- lem I. BC is the required tangent. Problem XXVI — To draw an arc of a given radius tangent to two lines forming a right angle. (Fig. 63.) With B as center and any radius, draw I COXSTRUCTIVE DRAWING 119 arcs cutting the sides of the right angle in I and 2. With i and 2 as centers, and the same radius, draw arcs intersecting in 3. With 3 as center, and the same radius, draw the required arc. Exercise: Round off the corners of a given figure (Fig. 64) with curves of f" radius, as in Fig. 64^. Problem XXVII — To draw an arc of a given radius, tangent to two straight lines forming an oblique angle. (Fig. 65.) Let AB be the given radius, and CDE the given angle. Bisect the angle CDE by- Problem VIII, and draw a line FG parallel to DE, at a distance equal to the given radius AB. The intersection of FG with the bisector of the angle will be the center of the required arc. From point i draw lines perpendicular to the lines DC and DE, in points 2 and 3. These are the points of tangency. With i as center, and a radius equal to AB, draw the required curve. Exercise: Draw a curve of i" radius, tangent to two lines forming an obtuse angle. Problem XXVIII — To draw an arc of a given radius, tangent to a given line and a given circle. (Fig. 66) Let AB be the given line, C the given circle, and DE the given radius. Draw a line EF parallel to AB at a distance DE. Draw any radius of the circle C, as 1-2, and produce it to make the distance 2-3 equal to DE. With I as center, and 1-3 as radius, describe an arc intersecting the line EF in point 4. From 4 draw a perpendicular to the line AB -P ART EDUCATION— HIGH SCHOOL in point 5, which is the point of tan- gency on the line AB. With 4 as center, and radius 4-5, draw the re- quired tangential arc. Exercise: Describe arcs of |" radius, tangent to the circle E and the straight lines AB and CD (Fig. Gy. Figs. 67a and 68 are applications of this problem). Problem XXIX — To draw an arc of a given radius, tangent to two given circles. (Fig. 69.) Let A and B be the given circles, and CD the given radius. With the center of the circle A as center and radius 1-2, equal to the radius of A plus CD, describe the arc 2-3. With the center of circle B as center and radius 4-5, equal to the radius of B plus CD, draw the arc 6-5 intersecting the arc 2-3 in 7. With 7 as center and radius equal to CD, draw the required tangential arc. Exercise: The centers of two circles whose diameters are I "and 2", respectively, are 3" apart. Draw a curve having a radius of 2", tangent to the two circles. Problem XXX — To construct an ellipse, its major and minor axes being given. (Fig. 70.) Place the axes AB and CD at right angles to each other at their centers, obtaining point I. With i as center, describe circles upon the axes as diameters. Divide each circumference into the CONSTRUCTIVE DRA WING same number of equal parts, say twelve (Problem IX). Draw lines through the points in the large circle parallel to CD. Draw lines through points in the small circle paral- lel to AB. The points of intersection in these parallels, as 3, 4, are points in the curve of the ellipse. Draw a free-hand ellipse through these points, correcting it by means of the French curve. ' Problem XXXI — To draw with a trammel an ellipse when the axes are given. (Fig. 71.) Draw the two axes at right angles to each other at their centers. Lay off on the straight edge of a strip of paper the length of one half of each diame- ter. Thus, 1-2 is equal to half of the short diameter, and 1-3 to half of the long diame- ter. Adjust the paper in relation to the diameters so that point 2 is on the long diameter, and point 3 on the short diameter. Place a point at the end of the paper at 4. Move the paper so that point 2 will move in on the long diameter and point 3 will move out on the short diameter. Mark another point 5 at the end of the trammel. Repeat this at frequent intervals on each quarter of the ellipse. Draw a free-hand cur\'e through these points. Correct by use of the French curve. Problem XXXII — To draw upon given axes an approximate ellipse. (Fig. A 72.) Draw the two axes AB and CD per- pendicular to each other at their centers. With I as center, and half the short axis, iC as radius, describe an arc C2. Draw CB. 122 ART EDUCATION— HIGH SCHOOL From C set off C3 equal to 2B, which is the difference between half the short and half the long axis. Bisect B3, and continue the bisector until it intersects AB in 4, and CD in 5. With 4 as center, and radius 4B, describe an arc B6. With 5 as center, and radius 5-6, describe an arc that will pass through C, completing one quarter of the curve. From i set off 1-7 equal to 1-4, and 1-8 equal to 1-5. Draw lines connecting 5-7, 8-7 and 8-4, extending them as indicated in the figure. With points 4, 5, 7 and 8 as centers, complete the ellipse as already explained. Geometrical Definitions A Point is that which has position without extension (Fig. 73). A Point is formed when two lines intersect (Fig. 74). A Line is that which has length without breadth or thick- ness (Fig. 75). Lines are either vertical, horizontal or oblique. A Vertical Line is a line perpendicular to the plane of the horizon (Fig. J 6). A Horizontal Line is a level line parallel to the horizon (Fig. 75). An Oblique Line is a slanting line, neither upright nor level (Fig. 77). Parallel Lines are lines CONSTRUCTIVE DRA WING 123 running in the same direction, which, if produced, will never meet (Figs. 78 and 79). Two straight lines are said to be perpendicular to each other when they meet at right angles (Figs. 80 and 81). (Perpendicular and vertical are not synonymous terms.) A Surface is that which has length and breadth without thickness (Fig. 82). A Plane is a surface such that if any two points in it are joined by a straight line the line will lie wholly on the surface (Fig. 83). A Solid is that which has length, breadth and thickness (Figs. 84 and 85). An Angle is the difference in the direction of two straight lines which meet at a point, or would meet if ex- tended (Fig. "^6 a and b). The point where the lines meet is called the ver- tex of the angle (plural vertices). A Right Angle is formed by the meeting of two lines that are per- pendicular to each other (Fig. ^j a and b). An Acute Angle is an angle which is less than a right angle (Fig. 88). An Obtuse Angle is an angle which is greater than a right angle (Fig. 89). A Right-angled Triangle is a triangle which has a right angle (Fig. 90). Fig. 87 124 ART EDUCATION— HIGH SCHOOL An Acute-angled Triangle is a triangle which has three acute angles (Fig. 91). An Obtuse-angled Triangle is a triangle which has one obtuse angle (Fig. 92). An Equilateral Triangle is a triangle which has three equal sides (Fig. 93). An Isosceles Triangle is a tri- angle which has two of its sides equal (Fig. 94 a and b). A Scalene Triangle is a triangle which has no two of its sides equal (Fig. 95). A Quadrilateral is a plane figure bounded by four straight lines (Figs. 96, 97, 98, 99, 100 and 10 1). A Square is a quadrilateral hav- ing four equal sides and four right angles (Fig. 96). A Rectangle is a quadrilateral whose opposite sides are equal and parallel and whose angles are right angles (Fig. 97). A Rhombus is a quadrilateral whose sides are equal but whose angles are not right angles (Fig. 98). A Rhomboid is a quadrilateral whose opposite sides are equal and parallel and whose angles are not right angles (Fig. 99). A Trapezium is a quadrilateral which has no two sides parallel (Fig. 100). CONSTRUCTIVE DRAWING 125 A Trapezoid is a quadrilateral which has two sides parallel (Fig. loi). A Polygon is a plane figure having any number of sides (Fig. 102). A Regular Polygon is a plane figure having any number of equal sides and equal angles (Fig. 103). A Polygon of three sides is called a triangle (Fig. 104); of four sides, a quadrilateral (Fig. 105) ; of five sides, a pentagon (Fig. 106) ; of six sides, a hexa- gon (Fig. 107) ; of seven sides, a heptagon (Fig. 108); of eight sides, an octagon (Fig. 109) ; of nine sides, a nonogon (Fig. 1 10) ; of ten sides, a decagon (Fig. in). A Perimeter is the boundary of a plane figure (Figs. 96 to 1 1 1). A Diagonal is a straight line in any polygon which connects angles not adjacent (Figs. 1 12 and 1 13). In regular polygons, diagonals are called long when they pass through the center, as AB in Fig. 112, and short when they connect angles and do not pass through the center, as CD in Fig. 112. In a regular polygon with an even number of sides a line joining the centers of two opposite sides is often called a diameter (Fig. 1 14). A Circle is a plane figure bounded by a curved line called the Circumference, all points of which are equally distant from a point within called the center (Fig. 115). A Diameter of a circle is any straight line passing through the center 126 ART EDUCATION— HIGH SCHOOL and terminating in both directions in the cir- cumference (Fig. 115). A Radius (plural radii) of a circle is any- straight line extending from the center to the circumference (Fig. 115). An Arc of a circle is any part of the cir- cumference (Fig. 116). A Chord is a straight line joining the extremities of an arc (Fig. 1 16). A Semicircle is half of a circle (Fig. 1 1 5). A Quadrant is a quarter of a circle (Fig. 115). A Sector is a part of a circle bounded by two radii and the included arc (Fig. 116). A Segment is a part of a circle included between an arc and its chord (Fig. 1 16). A Tangent to a circle is a straight line which touches the circumference but does not cut it, however far produced (Fig. 116). An Ellipse is a plane figure 'bounded by a curve, every point of which is at the same combined distance from the two points within, called the foci (Fig. 117). A Sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center (Fig. 118). A Cube is a solid bounded by six equal square faces (Fig. 119). A Cylinder is a solid bounded by a curved surface and by two opposite faces called bases. A cylinder is named from the shape of its bases, which may be circular, elliptical or other curved shapes. The circular cylinder is the one ordinarily used (Fig. 120). CONSTRUCTIVE DRA WING 127 A Prism is a solid whose bases are similar, equal and parallel polygons, and whose sides are parallelograms. Prisms are named from the shape of their ends, as tri- angular, square, pentagonal, etc. (Figs. 121, 122 and 123). A Pyramid is a solid of which one face, the base, is a polygon, and the lateral faces are triangles, having a com- mon vertex called the vertex or apex of the pyramid (Figs. 124, 125 and 126). A Cone is a solid bounded by a plane surface called the base (which is a circle, ellipse or other curved shape), and by a lateral surface which is everywhere curved, and tapers to a point called the vertex or apex (Fig. 127). A cone is named from the shape of its base. A Truncated Cone or Pyramid is that portion in- cluded between the base and a cutting plane, which may be either parallel or oblique to the base (Fig. 1 28). When the cutting plane is parallel to the base the section between the cutting plane and the base is called a frustum (Fig. 1 29). I ^-■J-^ Fig. 121 Fig. 122 Fig. 124 Fig. 125 128 ART EDUCA TION— HIGH SCHOOL A Plinth is a cylinder or prism whose axis is its least diameter. Plinths are named from the shapes of their bases, as circular, square, triangular, etc. (Figs. 130, 131 and 132). An Ellipsoid is a solid, all plane sections of which are ellipses or circles (Fig- 133)- An Ovoid is an egg-shaped solid (Fig. 134). CONS TR UC TI VE DRA WING 129 Working Drawings Working drawings are drawings which deal not with the appearance of an object, but with its facts. They must furnish all that a workman needs to know in regard to its form, size, proportion, the material to be used and the method of manufacture or manner of construction, in order to make that object. In Fig. 135 is a perspective picture which gives a general idea of the three dimen- sions of a boat, but such a sketch would not furnish a builder with the necessary- facts which he must know if he wishes to make a boat like this. He must know its actual length, its actual width and its actual 1 , .-^, ^ , , -PIG. 130 depth. These facts cannot be accurately expressed in a perspective picture, but must be shown by means of geometric views — that is, views which would each give two of the actual dimensions of the object. These different views are named from the part represented. The front view is obtained by looking directly at the front of the object ; the top view, by looking directly at the top ; the end views, by looking directly at the ends, and the bottom view, when used, by looking directly at the bottom. In a working drawing, as these groups of views are called, the top view is placed above the front view ; the bottom view below the front view, and the end views at the right and left of the front view. Fig. 136 shows Top View ^ Mitch&d bonrds Front V/eur Fig. 136 i'/ End Vie xa/ 130 ART EDUCATION— HIGH SCHOOL Top VieiA} a working drawing of the boat. The front view shows the length and depth of the boat, the slant of the ends and the posi- tion of the rowlocks. The top view shows the width and length, the placing of the three seats and their dimensions, and the position of the rowlocks in relation to the middle seat. The end view shows the depth and the width of the boat and the angle which the sides make with the bot- tom, which in this case is a right angle. The separate views in a working drawing are also called projections, and whichever view is drawn first, forms the basis of pro- jection of all the other views. The terms "top view," "front view," "side view " and "end view " are only relative, for the same face may be a top view, a front view or an end view, according to the posi- tion of the object. For example, Fig. 137 shows three views of a square prism, standing vertically. The top view is a square, and the front and side views are oblongs. In Fig. 138 the position of the square prism is changed, and the front and top views are oblongs, while the end view becomes a square. In making a workim Front Mevo Side Vievo Fig. 137 drawing of an object the views should be placed in Top Vie to Top Vievo Front VieiAJ Side J/iew Front J/ievo Sida l^ew Fig. 138 Fig. 139 CONSTRUCTIVE DRAWING 131 their natural positions. For example, a brick usually rests on one of its largest faces, and to represent this, the views should be drawn as shown in Fig. 139. In drawing the views of a chimney, however, the front view should be expressed by the upright wide oblong, because that is its natural position (Fig. 140). In the representation of the different faces of objects, the eye is not supposed to be fixed at one point, as in perspective repre- sentation, but it is assumed to be opposite each point in the surface to be represented. When the faces are perpendicular to the line of sight, they are represented in their true shape, but when the faces are oblique to the line of sight, the oblique faces are represented as foreshortened. This is illustrated in Figs. 141, 142 and 143. Fig. 141 shows the top and front views of a cube placed directly in front of the observer. The two views are of the same shape, but they express different dimensions. The front view shows the height and the width from left to right, while the top view shows the width from left to right, and the width from front to back. These facts must always be shown by the front and top 1 |o^ View 1 Front Vieu) Side J/ievu Fig. 140 LIU front Mew front View 132 ART EDUCATION— HIGH SCHOOL Front yie-uj Front Vieiu Fig. 144 views of any object, in any position. Fig. 142 shows the front and top views of the cube placed at an angle of 45°. The front view shows the height, as before, and also, as before, the actual extension or width of t Ji e solid from left to right. This width is ex- pressed by horizontal lines, and the result is that the two oblique faces are foreshortened in the front view. The same point is illustrated by Fig. 143, which represents the front and top views of a cube turned at 60° and 30°. In drawing geometric views of objects showing oblique faces, the view that shows a true shape should be drawn first and the other views should be pro- jected from it. In Figs. 142 and 143 the top views were drawn, at the proper angle, first. The width of the front face was determined in both cases by lines projected from the angles of the top view. In the views of the hexagonal plinth (Fig. 144), the hexagon must be drawn first, as the faces in the top view are foreshortened and must be projected from points found in the view furnishing a true shape. In drawing views of cylindric objects, the circle should be drawn first (Fig. 145). Working drawings must be expressed by means of con- ventions that have been accepted for general use, because they are the most concise and accurate way of conveying certain facts. These conventions or symbols vary slightly in usage, but never to a degree that would make the meaning of the drawing unintelligible. The conventional lines and symbols used in mechanical drawing are shown in Fig. 146. Dimensioning. In working drawings, dimensions are I Fr^ont View Fig. 145 CONSTRUCTIVE DRAWING 133 very important. The size of each part must be indicated by plain figures, placed either outside or inside the drawing, wherever they will be most readily understood. Dimension lines are drawn light with a space left in the middle for the figures. Arrow- heads are placed at the ends of dimen- sion lines (Fig. 146). When there is not rpom enough for the arrow- heads to be drawn, they should be placed outside (Fig. 147). When the lines are too close together for the figures to be drawn, as in Fig. 148, they should be placed outside. They should read from left to right and from the bottom upward. If a dimen- sion is stated upon one view, it need not be repeated upon another view unless the drawing should be large and the views some distance apart. "Over all" dimensions should be shown in a separate line (Fig. 149). Drawing to Scale. Working drawings are seldom made the exact size of the object to be constructed. They are sometimes made larger, as in the drawings from which a watch is to be made, and, more frequently, smaller, as in draw- ings that show the plans and elevations of a house. The size Visible ed^es and contours Inx^zsible & d.^ e .s Wbr-Ain^ lines in /oencit Center' Lines WorAing or' jorojecting Hi Z 7' Di-mension lines /■ 134 ART EDUCATION— HIGH SCHOOL of the drawing is a matter of convenience, but it is necessary that a reduced or enlarged size be accurately drawn according to the proportion or scale chosen, and that all parts of a drawing be made to the same scale. Draw- ings of ordinary objects, if not made full size, are usually made \, \, \ or ~^^ the full size of the object, and these proportions can, with some calculation, be laid off with an ordinary ruler divided into inches, halves, quarters, eighths and sixteenths. If a working drawing of a box measuring i6" long, 8" wide and 4" high were to be made in a scale one-fourth full size, it would be easy to estimate the scale and make the drawings 4" x 2" x i". But in case fractions are involved in the measurements, or it is desired to make a drawing in some proportion not so easily determined, the problem would become involved. It is better, therefore, to be provided with a scale and to determine all reductions by its use. To make a full-sized drawing, a scale divided into inches and fractions of an inch is used. To make a half-sized drawing, a scale is used on which each six inches of its length is divided into twelve equal parts, each division standing for one inch. Following the same method, a quarter scale has each three inches divided into twelve equal parts, each part standing for an inch. To make a drawing in one-eighth full size, each inch and a half on the scale is divided into twelve equal parts, each part representing an inch. For a drawing one-sixteenth full size, each three fourths of an inch is divided into twelve equal parts, each part representing an inch. These proportions or reductions are indicated in the drawing thus : "Scale, Half-Size," or "Scale, 6' — i foot"; "Scale, Quarter-Size," or "Scale, 3' — I foot"; "Scale, Eighth Size," or "Scale, li' — i foot," etc. When a drawing is made full size, the statement would be : " Scale, Full Size," But sometimes it is necessary for drawings to be made even smaller than one-sixteenth actual size, as in drawings of houses, bridges, and of machinery. In these cases, we may take any measure as a unit. For instance, one inch may be taken to represent a foot, or one half, one fourth, or one eighth inches may represent a foot. The scale would then be stated: "Scale, i"=i'"; "Scale, i"=i'"; "Scale, i"=iV' etc. i CONSTRUCTIVE DRAWING 135 To Make Working Drawings with Instruments Exercise I. To draw three views of a square prism standing verti- cally (Fig. 150). First draw the top view, using the blade of the T square for the horizontal lines, and a vertical edge of one of the triangles set against the upper edge of the T square for the vertical lines. Measurements are set off with a scale or compasses. From the top view, project downward, ver- tical lines for the vertical lines of the front view. Measure off the proper length, and with the T square draw the horizontals, projecting them indefinitely for the side view. The distance between the front and top views should be sufficient to allow for the placing of any measure- ments without the appearance of crowding. In order to locate the side view, place the needle point of the compass at i, and with a radius equal to the dis- tance between the front and top views, as 1-2, draw an arc that will revolve point 2 in the top view to its position in the side view. With point i as center and a radius equal to 1-3, revolve point 3 in the top view to its position in the side view. 2-3 is the width of the side view. Complete the rectangle. Place the figures and dimension lines as indicated. ^—.. \ /hont Meto Sid^ 186 ART EDUCATION— HIGH SCHOOL Exercise II. To draw three views of a horizontal hexag- onal prism (Fig. 151). Draw the end view first by Problem XIV, page 114, or with the 30 and 60 degree triangle. Pro- ject the horizontal lines in the end view indefinitely, thus locating the horizontal edges of the front view. Locate the vertical edges of the front view. At i and 2 erect perpen- diculars to intersect the upper horizontal in A and D. With E as center, and with radii DE, CE, BE and AE, draw quarter circles to intersect pro- jected verticals from the front view. These points locate the edges for the top view. Finish as shown in Fig. 151. Exercise III. Draw three views of an upright, equilateral triangular prism, placed with one face in front. In this case, one edge is invisible and must be represented by a dash line. Exercise IV. Draw the same prism named in the previous problem, placed so that two oblique faces form the front view. Exercise V. Draw three views of an upright equilateral triangular prism, with the top view at the angle indicated in Fig. 152. Exercise VI. Draw the end and front views of a horizontal hollow cylinder. Indicate invisible edges. Note. In practical shop-work only as many viev>-s of an object are drawn as are necessary to show all the facts of the object. Two views are someiimes sufficient, but three or four views are often required to show the shape of all the parts. In the cylinder but two views are neces- sary, — the end and front views of a horizontal cylinder, or the top and front views of the upright cylinder. Other views would give no more information regarding the facts of the object. Exercise VII. Draw three views of the cylindric object shown in Fig. 153. On one end is a square projection and on the other end is a round projection. In this case three views are necessary, — the front and two end views, — as the front view would not show whether the projections at the ends are round or square. CONSTRUCTIVE DRA WING 137 Exercise VIII. Draw two views of a horizontal cylinder, in one end of which is a circular socket width and depth one eighth of the length of the cylin- der. In the other end is a square p^^ socket of the same dimensions. The end views in this case will be exactly the same as the end views in Fig. 153. Show invisible edges in front view. Exercise IX. Draw front, top, and two end views of the object repre- sented in Fig. 154. Exercise X. Make a working drawing showing three views of a wall bracket. Choose your own dimensions and draw to scale. Plates I and II show a number of joints used in wood-working. Working drawings may be made from these sketches or from actual joints found in the construction of furniture and in carpentry. On Plate III, page 140, is shown a working drawing of a library table, drawn to scale. Sketches showing the construction of the various parts are also given, drawn in a larger proportion. These sketches are not working drawings, and are not to be copied. But working drawings should be made of these parts, with the proper dimensions marked upon the drawings. A working drawing of a kitchen table may be made in a similar way, the student either design- ing the proportions or taking the measurements from the object. If all constructions are not made clear in the views, detail drawings should be made, giving the necessary information. Plates I, II, III and IV show sketches which may form the basis of working drawings. These drawings must show, either in views or by means of detail drawings, all the facts necessary for a workman to know in order to construct the object. Students may determine all measurements and proportions, stating them in their proper places on the drawings. Free-hand Constructive Drawing Although a finished working drawing Is almost invariably made with instruments, it is a mistake to suppose that free-hand drawing has no place in connection with construction. In practical life the valuable man is the 138 ART EDUCATION— HIGH SCHOOL Joints Co 72 nee ting Ends. JVtitr-e En d L ap End JVto-rtise and Tenon JVtortise and Tenon J^ouetail Jfeyed Mortise and Tenon Gained Joint} B-utt Joint Plain ButtJoint ^ Boxjoelled CONSTRUCTIVE DRAWING 139 Joints connectinj^ edgres Dovetailed CorneT Rabbet Joint Ton^e and Groove Xalf Blind Dovetailed Joint _ Co-rner man who can make a design or plan of some problem of construction. These initial ideas are nearly always set down on paper by means of free- hand sketches and working drawings, which may afterward be given to a draughtsman who can work them out carefully with instruments, thus ren- dering the drawing accurate, and furnishing all the detailed information that a workman must have. The free-hand sketch is the test of a student's understanding of the problem, and this understanding is even more impor- tant than the ability to use instruments with technical skill. Students should be able to sketch readily from any of the objects con- sidered in this chapter, making either pictorial representations or free-hand working drawings, as the problem demands. They should also be able to draw, with reasonable accuracy, circles, ellipses, spirals and other curves, rather than to depend upon compasses and the French curve. Free-hand ^Vorking Drawings Exercise I. Draw the front, top and end views of a pencil or chalk box. Exercise II. Draw the front and top views of a sphere. Exercise III. Draw the front, top and right end views of a horizontal cylinder. Exercise IV. Draw the front, top and left views of an equilateral triangular prism, placed with two oblique faces forming the front view. Exercise V. Draw the top and front views of a square pyramid, turned at 45°. ART EDUCATION— HIGH SCHOOL Scale J^"=f' -S-0' -^-J- 11= ^ ^ 1 1 1^ 1^ PI s 1 ■IJ — ^' ■*" '=- \^ __ -3^ Details of Library Table Drawer Corners Corner cons CructiorL End of Foot Rest or shelf 7~op ioZe screwed on. IroLhoer Pull ofj-fand J-faynmered Copper* End Rail CONSTRUCTIVE DRAWING 141 Exercises y^or* -LuoTOiing drau)ings Playit Stand Stool 142 ART EDUCATION— HIGH SCHOOL Exercise VI. Draw the front and top views of a hexagonal prism standing upright. Exercise VII. Make free-hand working drawings, showing as many views as are necessary, of the objects represented in Figures 155, 156, 157 and 158. Theory of Orthographic Projection Working drawings are usually based upon orthographic projection. Orthographic projection is the art of representing an object by means of projections or views made upon different planes at right angles to one another. In order that the student may understand the theory of the preced- ing working drawings, a demonstration should be made by means of the fol- lowing device : Take two panes of glass (the proportions suggested by the sketches that follow) and lay the long edges about a quarter inch apart upon a strip of cloth | of an inch wide. The cloth should have received pre- viously a coating of glue. To make the fastening more durable, glue another strip of cloth on top of the edges, so that the edges of the glass are between CONSTRUCTIVE DRA WING a double thickness of cloth, as shown in Fig. 159. If these pieces of glass are held so that one is vertical and the other horizontal, they will repre- sent the imaginary planes upon which the top and front views of an object are supposed to be projected or drawn. Call the vertical plane, V, and the hori- zontal plane, H. The lines of intersec- tion of these two planes is called the Ground Line (G. L.). Place some object, as a square plinth, behind V and below H, holding it so that the square faces are horizontal and paral- lel with H, and the front face parallel with V (Fig. 1 60) . By looking directly down from above it will be seen that if a tracing is made on the glass fol- lowing the outlines of the top surface of the plinth, the result will be a square. If the planes are held directly M 1 1 1 1 1 \ sv. II II II II 144 ART EDUCATION— HIGH SCHOOL in front, so that the center of the front face of the phnth is opposite the eye, a tracing of the outhnes of the phnth would be an oblong (Fig. 1 60). To demonstrate the theory of side views, fasten a piece of glass to the right edge and one to the left edge of the vertical plane, as shown in Fig. 161. Place these planes in the form of a box open at the back and at the bottom, as shown in Fig. 162. Within this box, hold the plinth as before, and, looking through each plane in turn, a face of the plinth will be seen on each of the four planes. If a tracing of a face were made on each plane, and the group of planes were then spread out on a fiat surface, as in Fig. 163, the arrangement of views used in working drawings would be seen. Eliminating the planes, the views appear as in Fig. 164. The projection of lines may be demonstrated in a similar way. Place the glass planes on a board in the position shown in Fig. 165. Procure a piece of wire, about the size of the lead in a pencil. Bend one inch of this wire over, to form a right angle. Bore a hole the size of the wire through the middle of a small smooth stick the size of a lead pencil, or / ' . I I \ I 1 j -j ^-j j I CONSTRUCTIVE DRAWING 145 smaller (Fig. i66). (The small wooden skewers used in meat shops are ex eel 1 e n t for this device). _^ Place the bent I 1 1 1 1 1 end of the wire through the hole in the stick (Fig. 167). Insert the straight end of the wire into a small hole in the center of the board under the glass (Fig. 165). This device will permit the stick to be turned at any desired angle. First place the stick in a horizontal position, parallel with both V and H. Look at it through the planes, and the stick, which stands for a line, will appear as represented in Fig. 168. It will be seen that when a line is parallel with either plane, it appears and would be drawn on that plane in its true length. It will also be seen that when a line is perpendicular to one of the planes (as the pencil is perpendicular to SV in Fig. 165), it appears as a point on that plane. Turn the stick on the wire so that, while it is still horizontal, it is perpendicular to V. It will appear as a point in V, and as a line on H and SV (Fig. 169). Fig. 166 146 ART EDUCATION— HIGH SCHOOL c — -}--, 1---, ^^B-\-^ B- \ .• -^ B- 1 S.Y. : / /; A 1 /'' i H A' s.v. j j»- - ' '^ 1 A' Fig. 171 Without regard to the glass planes, and in order to demonstrate this point still more clearly, hold a pencil in a horizontal position with the end facing you, and draw its top, front and side views. Turn the stick so that it will be parallel with V but will make an angle with H and SV, and draw the projections or views as they appear on the planes (Fig. 170). It will be seen that when a line is oblique to any one of the planes, the projection or view on that plane is foreshortened. Turn the stick so that it will still be horizontal but will make an angle of about 45° with V. Its projection or views will now be changed. The top view will be a line, show- ing its true length and the true angle it makes with V, The front view will be a horizontal line foreshortened, because it is seen obliquely. The side view will also be foreshortened into a horizontal line. Hold your pencil in this position and draw its different views. Turn the stick so that it will be parallel to SV and oblique to both the other planes. The stick will now appear in its true length on SV, and this view will show also the true angle the line makes with the other two planes (Figs. 171 and 172). In cases like this, the side view must be drawn first, because it is that view which shows the true length of the line. Draw the views of your pencil held so that it is parallel to SV and oblique to both the other planes. If the stick is placed so that it is oblique CONSTRUCTIVE DRAWING 147 to all of the planes, it will be seen that the line does not appear in its true length in any view, for all of its views would be foreshortened. Neither will a true angle be shown in any view (Fig- 173)- From the foregoing the following principles may be deduced : — 1. When a line is parallel with one of the planes, whether real or imaginary, it appears in its true length on that plane. 2. When a line is perpendicular to one of the planes, it appears as a point on that plane. 3. When a line forms an oblique angle with one of the planes, it appears foreshortened on that plane. 4. W^hen a line is oblique to all the planes, it is foreshortened, and does not appear in its true length on any plane. Let us review these lines as they occur in an object with which we are already familiar. In the prism shown in Y\g. 1 74, the line AE is parallel with both V and H, and perpendicu- lar to SV. Therefore, it appears in its true length in the top and front views, and as a point in the end view. The line CB is parallel with H and SV, and is perpendicular to V. It appears in its true length in the top and side views, and as a point in the front view. The lines AC and AB are parallel with SV, but make oblique angles with both V and H. They appear in their true length in the side view, and are foreshortened in both the other views (Fig. 175). The square pyramid (Fig. 176) offers another example of lines and faces 148 ART EDUCATION— HIGH SCHOOL u^" E' E X-'' x 1 ' '' - ■ ^ 1 ; a\e' \ }/^. c E V oblique to the planes upon which they must b e represented. T h e lines AB, AC, AD and AE are oblique to all the planes, and are therefore fore- shortened in all the views. To find the true length of a line in this position, the line must be revolved until it is parallel with one of the planes of projection. With A as center and AB as radius, revolve point B until the line used as radius is parallel with V, and the point B" is found. The point B" when projected to its position in the front view, will be B' ", and the line A' B' " will be the true length of the line AB, which is one of the long edges of the square pyramid. This process of revolving a point until the line is parallel with one of the planes is equivalent to turning the object one quarter around. When drawing the developed surface or pattern of a square pyramid, it is necessary to ascertain the true length of edges, as shown in Fig. 240. From the foregoing examples deductions may be made by which the true length of a line may be found when it makes angles with both V and H. With either end of the line in either view as center, and with the length of the projection or view of the line as radius, revolve the other end of the line until the line is parallel with the ground line. Draw the other view of the point revolved, and connect the points as shown CONSTRUCTIVE DRAWING in Figures 177, 178, 179 and 180. Exercise I. Find the true length of the Hnes ^~ shown in Figures 181, 182, 183 and 184. Exercise II. t;, ,0 Fig. 18 Find the true length of the line AB in Fig. 185. To draw oblique views of an object ; for example, the square pyramid, the base \ A/ 150 ART EDUCATION— HIGH SCHOOL inclined at 45°. Obtain the front and top views of the pyramid, as shown in I and 2, Fig. 186. Letter all points, bearing in mind that the letters in the front view must fall directly under the corresponding letters in the top view. At the right of the front view repeat the drawing at an angle of 45°, as shown in 3, Fig. 186. Place letters in 3 to correspond with the letters in 2. Project the points in i to the right, and project the points from 3 upward until they intersect the lines from i. For in- stance, the intersection of the lines projected from A in I with the line pro- jected from A" in 3 will give A' " in 4. Repeat with all other points, and finish the drawing. The student will be greatly assisted if he has the model and can hold it ^'°" ^^ in the position indicated. Exercise III. Draw corresponding views of a square prism. (Figs. 187 and 188.) Exercise IV. Draw the corresponding views of an equilateral COXS TR UC TIVE DRA WING 151 Draw the same views of a hexagonal prism, inclined at the triangular prism, inclined at 30° and 60°, and draw also the side view as shown in Fig. 189. (Not completed.) Exercise F. Draw the same views of a square pyramid, inclined at the same angle. Exercise VI. same angle. E X e rcise VII. Draw the ^ same views of a cylinder, in- clined at 30° and 60° (Fig. 190. Not com- pleted.) Note: In drawing oblique views of a circular surface it is neces- sary to establish certain points which may be projected 152 ART EDUCATION— HIGH SCHOOL /^'~'' : //^' '^:---1 / /■: ' ' ' '■ >_; -1 , \ VV' 1 ' 1;/' 7 ' > ii from one view to corresponding views. To do this, divide tlie circle into twelve (or more) equal parts, as shown in i, and project the points to the front view. Transfer the points to 3, and proceed as in the foregoing examples. Exercise VIIL Draw the same views of a cone. Notice that the contour lines from A'" (Fig. 191) are drawn tangent to the elHpse and not to the ends of the diameter. Exercise IX. Draw the top and side views of a circular plinth, whose circular faces are perpendicular to V, and at an angle of 30° with H (Fig. 192). Exercise X. Draw the front, top and side views of the objects repre- sented in Figures 193, 194 and 195. CONSTRUCTIVE DRAWING 1.-3 Cutting-planes, Intersections of Solids and Developments It is often necessary to show in a draw- ing some part of an object that cannot be seen on the outside of the object. In order that the interior construction may be seen, the object is supposed to be cut by a plane, called a cutting-plane, and one part removed. When the cutting-plane is parallel with the axis of the object the section found is called a longitudinal section. When it is perpen- dicular to the axis the section found is called a transverse section. When it is oblique to the axis the section is called an oblique sec- tion. These sections can be illustrated in a very simple way. If we cut an apple down through its center we pass a vertical plane through it. Removing one half, and looking directly at the part freshly cut, we see the longitudinal section, as represented in Fig. 196. If we cut an apple by a horizontal plane (using the knife at right angles to the axis) and remove the upper half, we find the transverse section, as represented in Fig. 197. If we pass the knife through an apple at an angle which is oblique to the axis we shall find an oblique section, as represented in Fig. 198. These sections show the true shape of the apple at the place where it is cut. They show also the arrangement of the seeds, and the growth of the core, and thus give a better idea of the structure of ^"^" ^^^ the apple than could have been gained by a study of the outside alone. Note: Sections that show the interior growth or construction of other objects, such as a seed-pod, any fruit or vegetable, a branch of a tree, etc., may be sketched, showing the result of longitudinal, transverse and oblique cutting -planes. The section in a drawing is indicated by covering the surface with light parallel lines, usually at an angle of 45°. 154 ART EDUCATION— HIGH SCHOOL A \ ; B A c 1 B' ^B The true shape of the section of a sphere cut by any plane, is a circle (Fig. 199). A cyhnder when cut parallel with its base, shows a section whose shape is a circle (Fig. 200). A cylinder when cut parallel with its axis, shows a section whose shape is a parallelogram (Fig. 201). A cylinder when cut oblique to its axis, shows a section whose shape is an ellipse (Fig. 202). An oblique sectional view is revolved 90° upon an axis parallel to the cutting-plane. This is done in order that the true shape of the section may be projected from the cutting-plane shown in Fig. 202. A cone when cut by a plane coinciding with its axis, shows a section whose shape is a triangle (Fig. 203), when cut parallel with its base, the section is a circle (Fig. 204), when cut oblique to its axis, so that all the elements^ of the cone are cut, the section is an ellipse (Fig. 205). When cut parallel with one of its elements, the section will, be bounded by a para- bola^ (Fig. 206). If a cone is intersected by a plane which makes a greater 1 Any straight line drawn on the surface of a cone and passing through the apex, as AB and AC (Fig. 205) is called an element. - The curve formed by the intersection of a cone by a plane, parallel to one of its elements is called a parabola, as the curve B" A" C" in Fig. 206. CONSTRUCTIVE DRAWING 155 156 ART EDUCATION— HIGH SCHOOL I angle with the base than do the elements, the section is bounded by a hyperbola 1 (Fig. 207). When a prism is cut by a plane parallel with its bases, the section is the same shape as the base (Fig. 208) ; when cut parallel with its axis, the section is a parallelogram (Fig. 209) ; when cut oblique to its axis, the section is an irregular polygon (Fig. 210). When a pyramid is cut by a plane coinciding with its axis, the section is a triangle (Fig. 211); when cut parallel with its base, the section is the same shape as the base (Fig. 212); when cut oblique to its axis, the section is an irregular polygon (Fig. 213). Sometimes a section shows two adjoining pieces of material, and when this is so, the different pieces are indicated by lines drawn at 45° in differ- ent directions, as in Fig. 214. If more than two pieces are shown in the section, lines drawn at other angles, as 30° and 60", may be used (Fig. 215). 'When the cutting-plane intersects the base of a cone and is not parallel to any element the curve of intersection is called a hyperbola, as the curve B" A" C" (Fig. 207). CONSTRUCTIVE DRAWING 157 Fig. 211 ^ :=!a!L Fig. 212 158 ART EDUCATION— HIGH SCHOOL Section lines representing the same piece, however, must always appear at the same angle in any part of that piece. Exercise I. Show a longitudinal section of a hol- low cylinder cut by a plane coinciding with its axis. Exercise II. Show a transverse section of a hol- low cylinder cut by a plane perpendicular to its axis. Exercise III. Show an oblique section of a cylinder cut by a plane at 30° with its axis. Fig. 202 shows the process of obtaining the sec- tion of a cylinder cut by a plane at 45°. Lines are drawn from points A, B and C perpendicular to the plane AC. A'C is drawn parallel to AC. B'D' is drawn equal to the diameter of the cylin- der. The ellipse may be drawn by Problem XXXI, or as shown in Fig. 236. Exercise IV. Fig. 216 shows the front and top views of a jack-plane with the longitudinal section. Draw a ie block-plane, showing similar ^'^- 218 views and sections. Note: Bolts and small round spindles are not usually sectioned. See Fig. 217 and the drawings on page 171. ^EE3 3 CONSTRUCTIVE DRA WING 159 M -^/^^ pai ^ Exercise V. Fig. 217 shows the front and end views of an ice-pick, with a longi- tudinal section. Draw similar views of a screw-driver. Exercise VI. Fig. 218 shows a side view of a spigot. Draw the sections as they would appear if cut on AB and on CD. Exercise VII. Draw the front and end views of the oil-stone shown in Fig. 219, and show a transverse section. Exercise VIII. Draw the front and end views of an ordinary tack-hammer and a transverse section of the handle at its greatest width. ^'«- 220 Note : Transverse sections are sometimes shown on one of tlie views, instead of appearing in a separate drawing (Fig. 220). The Development of Surfaces When objects are made of sheet material, such as paper, cloth, leather, tin, sheet iron, copper, etc., the entire surface has first to be laid out flat and then folded, rolled or moulded into the required form. The surfaces of objects whose faces are flat, such as prisms and pyramids, and of those that curve in but one direction, as the cylinder and cone, can be drawn in a flat pattern, or developed. When a surface is curved in more than one direc- tion, a pattern may be made that will approximate the surface, and may then be stretched or compressed into shape. A ball, for instance, may be covered with leather which may first be cut from a pattern and then, by wetting and shaping, be made to ft closely (Fig. 221). A bowl may be hammered into shape from a flat piece of copper (Fig. 222). The simplest forms from which -pio. 221 160 ART EDUCATIOX— HIGH SCHOOL \ \ 1 patterns may be developed are the geometric solids. The six faces of the cube, for example, may be laid out as indicated in Fig. 223. Laps are added so that the pattern may be cut out, folded and pasted to form a hol- low cube. In a similar way, patterns for the square, triangular and hexag- onal prisms may be developed. Exercise I. Make a pattern for a box 4" long, 2i" wide and i^" deep. Exercise II. Make a cover ^" deep, to fit the box made in Exercise I. If stiff paper is the material used, the cover should be made the width of a pencil line larger than the box. If cardboard is used, the cover should be made the thickness of the cardboard larger on each side. Before folding thick paper or cardboard the edges should be scored. Exercise III. Develop the surface of a cylinder 2" in diameter and _ 4" long. Demonstration : the ends of the cylin- der are circles (C and C, Fig. 224). The curved surface of the cylinder, i f unrolled, would form a rectangle as wide as the cylinder is long and as long as the distance around the cylinder. To find this distance, divide the circle into any number of equal parts, as 24 (Problem XII). Meas- ure 5^5 with the dividers. CONSTRUCTIVE DRAWING 161 and step off this distance twenty-four times on a horizontal line. The entire distance thus set off will represent the circumference of the cylinder. To make a hollow cylinder, leave a lap at one end of this rectangle and on the edges that are to be pasted to the circular ends, as in B, Fig. 224. Score 1-2 and 3-4, but not 2-4. To __ make the paper construction more perfect, two | ' ''■''- circular pieces should be pasted at each end, one inside and one outside. The inside circle will keep the cylinder round, and the outside one will cover Exercise IV. Make a pattern for a tin cup, 3" in high. Draw a well-shaped handle and space it off with the the strip of paper as long as the handle (Fig. 225). Exercise V. Develop the surface of a cone. Divide cone into a number of equal parts, as in the cylinder. I ever, these parts are not set off on a horizontal line, but radius of which is the slant height of the cone. Fig. 226. Note. In de- veloping surfaces it is best to draw first the views of the object. Exercise VI. Develop the surface of the frustum of a cone (Fig. 227). Produce the sides until they meet at the apex of the cone at A, and proceed as in the case of the cone. 3 Fig. 225 the laps. diameter and 2" dividers, making the base of the n the cone, how- upon an arc, the 162 ART EDUCATION— HIGH SCHOOL Exercise VII. Make a pattern for the lamp-shade shown in Fig. 228. Exercise VIII. Develop the surface of a square pyramid. Draw the top view with the sides of the base at an angle of 45° with the vertical plane (Fig. 229). In the front view the line A' C is not its true length, but the line Fig. 228 A' B', which is parallel with V, is. We can, therefore, take the line A' B' or A' D' for a radius and draw an arc of a circle (Fig. 230). Set off the sides of the base on this arc, and connect these points with straight lines. On any one of these lines draw a square equal to the base of the pyramid. To make the pattern of a frustum of a pyramid (Fig. 231), produce the sides to form a pyramid and proceed as in the case of the pyramid. If the frustum is inverted it may be developed in the same way. Exercise IX. Make a pattern for a square pan, shown in Fig. 232. Method shown in Fig. 233. Exercise X. Make a pattern for a pan 3" long and 2" wide at the A / \ / \ / \ CONSTRUCTIVE DRA WING bottom The sides are i" wide, and slant outward at an angle of 120° with the bottom. Exercise XL Draw the top and front views and the developed surface of a vertical square prism, cut by a plane at 45° with its axis (Fig. 234). Two of these sections put together will make an elbow in a square pipe (Fig. 235 rt and b). Exercise XII. Draw the top and front views and the developed surface of an equilateral triangular prism, cut by a plane at 45° with its axis. Exercise XIII. Draw the top and front vicAvs and the developed surface of a hexag- onal prism cut by a plane at 45° with its axis. \ I 164 ART EDUCATION— HIGH SCHOOL Exercise XI V. Draw the top and front views and the developed surface of a square prism standing with its vertical faces at 45° with V. The cut- ting-plane enters the prism at an angle of 45°. Exercise X V. Draw the top and front views and the developed surface of a cylinder cut by a plane at 45° with its axis (Fig. 236). Two of these together make an elbow of a stove-pipe (Fig. 237). Exercise XVI. Draw the same views, with developments, of a cylinder cut by a plane at 60° with its axis. Make a jointed pipe, as shown in Fig. 238. Exercise X VII . Make a pattern for the can, with cover, shown in Fig. 239- Exercise X J VII. Draw the views and the developed CONSTRUCTIVE DRAWING 165 surface of a square pyramid standing vertically, the sides of the base mak- ing angles of 45° with V. The pyramid is cut by a plane oblique to its axis. Show the true shape of the section (Fig. 240). Demonstration : Letter the points where the cutting-plane cuts the edges of the pyramid in the front view, F, G, H and I. To show where the plane cuts the edges in the top view, project lines upward from F and H, obtaining points F' and H' in the top view. To find points G' and I' in the top view, draw a line through G parallel with the base of the pyramid, to cut lines A'B' and A'D' in points J and K. It is evident that the width of the pyramid at this point is equal to JK ; therefore, 166 ART EDUCATION— HIGH SCHOOL make G'l' in the top view equal to JK. To find the true shape of the section, draw lines from F, G, H and I, perpendicular to the plane FH. Draw F'H' parallel with FH. Make ,-' G"I" equal to JK, and F"G"H"I" will be the true shape of the section. T o develop the surface of the truncated pyra- FiG. 242 Fig. 243 -j /Tr- . \ mid, (Fig. 241.) With radius A'B' or A'D', which is the true length of the edge A'B', describe an arc of a circle. On this arc set off the sides of the base of the pyramid, in points B"', C'", D'", E'" and B"". Make A'"F"' and A"'F"" equal to A'F, and A'" H'" equal to A'H. As the line A'G and the line behind it, A'l, are oblique to both V and H, they are not shown in their true length. This may be found as in Fig. 176, page 148, but the line A'J is the true length of the line A'G' and A'l; therefore make A"'G'" and A'"!'" equal to A'J. Exercise XIX. Draw two views and the developed surface of a square pyramid standing with one of its triangular faces directly in front of the observer. Cut the pyramid by a plane making an angle of 30° with its base (Fig. 242). Note : It must be remembered that the lines AB, AC, etc., are not shown in their true length. To obtain the true length of line A'B' and A'C refer to demonstration of Fig. 176. page 148. Exercise XX. Draw two views of a cone cut by an oblique plane (Fig. 243). Show the true shape of the section. In the top view, the distance CONS TR UC TI VE DRA WING 167 HT is equal to the distance MN in the front view. The reason for this may be understood by referring to the demonstration illustrated in Fig. 240. To find the section, the distance H"I" is transferred from HT in the top view, J"K" is transferred from J'K' in the top view, and the other widths in like manner, because these distances appear in their true length in the top view. Only the two outside lines A'B' and A'D' are shown in their true length. Develop the surface of the lower part of the cone. Exercise XXI. Draw the top, front and side views of a hexagonal pyramid, cut by a plane at 60° with its base. Machine Details The various mechanical devices for the production of motion, such as the lever, crank, eccentric, cam, pulley and gear, enter very largely into machinery, and therefore into the making of drawings showing the con- struction and details of machinery. In such work the general language of working drawings is employed, and some of the more common details of machinery are given here in order to show the various conventions used and the usual way of representing such objects. Cranks. The crank is a lever used ' ' ' mostly to obtain rotary motion, or to convert straight motion into rotary motion, as in the case of the steam engine ; or to convert rotary motion into straight motion, as in the case of the jig-saw. The length of a crank is the dis- tance between the cen- ter of the shaft and the center of the pin (Fig. 244)- The throw ^^^.^^ ^^^^^ of a crank is twice the Fia. 244 168 ART EDUCATION-— HIGH SCHOOL Fig. 246 length of the crank (Fig. 245). Figs. 244, 246, 247 and 248 show some of the common forms of cranks. For practice in drawing, select similar parts, and make working drawings directly from them. Eccentrics. The eccentric is another form of crank, and is used, principally, to slide the valve in a steam-engine. The complete eccentric has two parts, the eccentric (Fig. 249) and the strap (Fig. 250). The student may draw two views of the eccen- tric and strap when connected. Screws. The screw, which is based on the principle of the inclined plane applied to a cylin- der, is used for raising weights, and for fastening parts together. The motion is uniform, and in a plane parallel with the axis of the cylinder. The threads on a screw are usually V shaped or square (Figs. 251 and 252). In the V thread, the pitch is the space between threads, and in the square thread the pitch includes a thread and a space. In either case, the pitch represents the dis- tance the screw would move dur- ing one revolution. The most common forms of bolts, screws and nuts are shown on page 171. CONSTRUCTIVE DRAWING 169 Figure 253 shows the method of drawhig a V-thread screw. Let the diameter be 5" and the pitch i". Draw the front view of the cylinder, as ABCD. On AB describe a semicircle, A3B. Set off the pitch AE and divide it into any number of equal j^arts, as twelve. Through these points draw lines perpendicular to the axis of the cylinder. Divide the semicircle A3B into six equal parts. Project lines from i, 2, 3, 4 and 5 parallel to the axis of the cylinder. The intersection of these lines with the lines that divide the pitch will give the points i', 2', 3', 4' and 5', through which the required curve of the thread may be drawn. Sketch this curve with the free hand. Fig. 249 Eccentric Fiod With the dividers set equal to the pitch, locate points i", 2", 3", 4" and 5" above i', 2', 3', etc. In a similar way, set the dividers equal to two pitches, and locate points above i", 2", 3", etc. Repeat this operation, always measuring from i', 2', 3', etc. The curve obtained by this process is called a helix. With the 60" triangle and the T square draw the lines EG and AG, obtaining point G, and EH and KH, obtaining point H. These points locate the root of the thread. Through G and H draw lines parallel to the axis of the cylinder, cutting the line AB in points I and J. Draw another semicircle on IJ, and find the points for the inner curve. When the curves have been carefully drawn with the free hand, use the Erench curve to finish. Eigure 254 shows the method of drawing the square-thread screw. The width and depth of the groove is equal to the thread or half the pitch. 170 ART EDUCATION— HIGH SCHOOL Fig. 251 ^'^ \ CONSTRUCTIVE DRAWING 171 ^olts, Scr'euxs and Nuts Machine JSolt Saziara or Aexczyo-naL-Aeati /■ \^ • '-v^ 'N Thfi £oJ.t Stud £oZt SAaft Carriage Solt HotindL-hsad. CotxnfersrnA -Cay Sct^ki '~'' I'Laf-ZLca-cC ^ ■ M •Set Serena 172 ART EDUCATION— HIGH SCHOOL In practice, the curves of screw threads are not worked out, but are represented by the convention of straight lines, shown in Figs. 251 and 252. In the case of small screws and bolts the convention is as shown in Fig. 255. Note : For tables giving the number of threads to the inch, sizes of bolt-heads and nuts in proportion to the diameter of the bolt, and for other information of this kind the student should consult some standard work on Mechanics. To draw the thread on a bolt. Let AB (Fig. 256) be the diameter of a i" bolt. From a table of standard threads, it will be seen that there should be eight threads to an inch. Lay off i" on the line AD and divide it into eight equal parts, each part represent- ing the pitch of the screw. Through points i, 2, 3, etc., draw light parallel lines at an inclination equal to one half the pitch, as shown in Fig. 256. From A and B, lay off the points E and F, equal to the pitch. Through points E and F, draw lines parallel to AD and BC. This makes the roots of the threads. Draw the heavy lines halfway between the light parallels. In drawing screw threads, the lines must slant up- ward to the right for a right-hand screw, and downward to the right for a left-hand screw. In practice, draughtsmen do not space off to get the exact number of threads to the inch, but it is well for the student to do this until he is accus- tomed to the right spacing. The size of bolt-heads and nuts is in proportion to the size of the bolt. The proportion varies in different bolts, and also in different shops, but those proportions most commonly used are given as follows : Let D equal the diameter of the bolt. The short diameter of the nut and bolt is equal to \\ D plus \ of an inch (i^ D + |"). The thickness of the nut is equal to D. The thickness of the head (square or hexagonal) is equal to | of D plus is of an inch (i D + ^V")- CONSTRUCTIVE DRAWING 173 To draw the square head or nut. Draw the top view A and the front view B (Fig. 257). With radius equal to twice D, draw the curve 1-2-3. Draw the top view C. To find the points necessary in completing the drawing, project the points over from the front view, B, and down from tlie top view, C. This process was explained under Projections. To draw a hexagonal bolt-head and nut, turned so as to show three faces of the head and nut, the thickness of the bolt being given. 174 ART EDUCATION— HIGH SCHOOL (Fig. 258.) Draw the circle A, with diameter equal to the diam- eter of the bolt. With the same center draw a circle whose diameter is \\ times D -j- i". Through A, project to the right, the axis line of the bolt. About the second circle, circumscribe a 1 3xag'on, making one of its sides, as EC, perpendicular to the axis of the bolt. Draw the front view of the bolt, projecting the neces- sary lines for the head and nut from the end view. Make the thickness of the head ec|ual to %D plus yV"> ^i''d the thickness of the nut equal to D. Estab- lish E by laying off D from H, on the axis line. With E as center and a radius equal to D, describe the arc 1-2. Draw a line through 1-2, extending it in both directions to find points 3 and 4. Bisect the sides of the hexagon in points 5 and 6, and project from these points lines CONSTRUCTIVE DRAWING 175 L - \- - 'Arm Bore Hub ' -ftim Cyovun >Stra i^h t intersecting tlie line 3-4 in 7 and 8. Find the center for the curves 1-9-3 and 2-10-4 by Problem XXII, Ex. I. Complete the curves, and draw the line 9-10 tangent to the curves. Cams. It will be seen that the motions produced by the crank, eccentric and screw, are regular. The cam is a device by which either regular or irregular motion may be obtained. ' The cam is based on the principle of the inclined plane applied to a cylinder or disc. If the inclined plane A (Fig. 259) is applied to the periphery of j*~ ^ "H the cylinder or circular disc B, and the whole made to revolve in the direction of the arrow-head, it will raise the bar C at a uniform motion during one revolu- tion of the cylinder or cam. The bar would then drop back suddenly to the start- ing point, repeating this motion at each revolution. If the inclined plane had been irregular, as shown in Fig. 260, the motion would be irregular. In this way almost any motion can be produced. In the cam shown in Fig. 259, the motion is in a plane at right angles to the shaft. When the motion is to be parallel with the shaft, it is applied to the face of the disc, as in Fig. 260, or applied in the form of a groove, as shown in Fig. 261. This is the form of cam used in the sewing-machine. 176 ART EDUCATION— HIGH SCHOOL The Pulley. The pulley is used for the transmission of power by means of a belt or cable (Fig. 262). If the pulleys are of the same size both will revolve at the same rate of speed. If one is twice as large as the other, the smaller will make two revolutions in the same time that the larger makes one. The speed is in proportion to the diameter of the pulley. Pul- leys are usually made of iron or wood. They are sometimes made in two parts, and are then called split pulleys. The parts of a pulley, with the names, are shown in Fig. 263. Fig. 264 represents a five-arm pulley, showing a half elevation and a half section. The diameter of the hub is usually twice the diameter of the bore. The faces of pulleys are made either "crown" or straight (Fig. 265). Gears. Gears are wheels having teeth or cogs which mesh into each other. They are sometimes called cog-wheels (Fig. 266). Like pulleys, gears are used for the trans- mission of power and to increase or decrease speed. Duplicating Drawings It is always desirable and usually necessary to have several copies of a drawing. It is not necessary to redraw each one, but a tracing may be made on transparent paper or cloth, and from it blue-prints made in any quantity required. Tracing. To make a tracing, place the drawing to be copied upon the board, and over it place the tracing cloth or paper, tacking both firmly to the board. Many grades of tracing paper and cloth are in the market, but for durability, cloth should be used, the weight of it depending upon the use to which the prints are put. Drawings to be traced are usually made in pencil and not inked on the original. The inking is done directly upon the tracing cloth. Care must be taken to have the drawing accurate and complete before tracing it. Erasures and changes upon the tracing always mar the surface. Either side of the cloth may be used. If the ink does not flow well, rub powdered chalk over the surface of the cloth. CONSTRUCTIVE DRA WING 177 In tracing, follow the usual process of inking-in the drawing. Blue-Printing. Blue-printing is a photographic process. The tracing is placed face upward, over a piece of sensitized paper, known as blue-print paper, and exposed to the light for a short time, according to the sensitive- ness of the paper and the strength of the light. From one to five minutes is sufficient in strong sunlight, though on a gray day a much longer time is required, as experiment will determine. The sensitized paper is then removed and washed for several minutes in running water. The chemical coating of the paper is affected by the light, and after washing it changes in color from the original green gray to a strong blue. The lines covered by the black lines of the drawing become white, as the coating not exposed to the light readily washes off, leaving the white paper. Fig. 267 shows a blue-print frame. Fig. 268, on the next page, is a reproduction of a blue- print from a drawing. The blue ground of the print is represented in Fig. 268 by a dark gray tone, although the white lines in the print are also white in the reproduction. 178 ART EDUCATION— HIGH SCHOOL CHAPTER V ARCHITECTURAL DRAWING The Need of Buildings. Painting, sculpture, and architecture are usually spoken of as the fine arts, and of these three, architecture is easily the most essential, because it is concerned with the construction of the many different kinds of buildings necessary to serve the needs developed by the civilized human race. In the city, the homes of the people are built to suit their various conditions of life, and we find the tenement building, the apartment house, the detached dwelling and the city mansion. There are also buildings for public utility, such as the school-houses, the public libraries, the churches, the railway stations, the hotels and the theatres. In the city, also, are buildings demanded by manufacturing and business, such as factories and warehouses, office buildings and banks. Buildings must be constructed to meet an almost endless variety of needs, and in planning a structure the architect must know for what purpose it is intended and where it is to be located, so that he may consider the comfort and convenience of those who are to use it, as well as its external beauty and its environment. Conditions of Construction. As almost every civilized 'human being occupies some sort of a house, let us consider a few of the questions which the architect must take into account before he can draw suitable plans for a dwelling. He must know the number of rooms required by the owner, and the size and shape of the lot upon which the house is to be built. If the home is to be in the city, where land is valuable, the building will probably be planned so as to utilize, if not to cover, the entire lot. If in the country, where the land is less valuable, the location of the house may be governed by the local topography of the land, and the questions of drainage, water supply, ease of access, and the proper setting of the house become important. The question of building material must also be ]80 ART EDUCATIOX— HIGH SCHOOL met by the architect ; he must know whether the dwelHng is to be con- structed of wood, brick, stone, or cement ; he must understand the relative quaUty and strength of these materials, and his knowledge of these things must enter into and influence his plans. Another problem that confronts him is the matter of light. The majority of city dwellings must be constructed with the narrowest dimen- sion toward the street, making it necessary to construct wells and areas in large buildings for the admission of light and air to inner rooms. In the country, the dwelling should be so planned as to admit the health-giving sunlio-ht to those rooms which are to be most occupied during the day the living-room, the dining-room, and the kitchen. This thoughtful division of space into the required number of rooms becomes the basis of the first drawing or plan for the proposed house. As the architect pro- ceeds with his work, it is necessary for him to express in his drawings all the information needed by the builders in constructing the house. Conventions. He does this by means of conventions, which, as with working drawings of other kinds, have been accepted as a sign language conveying briefly and accurately the information necessary for the builders. The study of a simple problem in house-building is the surest way of arriving at an understanding of an architectural design in its most ele- mentary form, and of gaining a knowledge of the conventions used in this kind of work. /7-0- Problem I — A Miniature House Plan and Elevation. Let us assume that we wish to plan a house of one room, to be built of wood, with stone foundation, shingled roof, and with a brick chimney in the center. Let the house be 9'-6" x 17-0", in outside measurements. If we add the ell, as in Fig. I, the house will be more attractive and the problem more interesting. There I should be at least three views in our i ^, I working drawings of the house; one to show the size and shape of the floor space, called a plan, and two views of the 7-0 ARCHITECTURE 181 outside, called elevations. All drawings of plans and elevations are drawn to a scale. In this case we will take a scale of V to the foot (written J"=i'), thus making our drawings in each view 4V of the actual size of the house. Make a free-hand technical sketch of these views, placing the plan above the front elevation, and the end deviation at the side of the front. The plan is most important, for it controls all the other views. Although it is called a plan, it is really a sectional view, as by common consent and long usage it is taken to mean that which would be seen if the house were cut by a horizontal plane at the level of the eye, and the upper part removed. Such a cut would reveal the length and breadth of all parts of the house when viewed from above, and it would be in a drawing of this sectional view or plan that we would look for thickness of walls and parti- tions, widths of windows and ,,,p,„,,,, doors, chimney dimensions, etc. atod. ^j space j 'u " ^n?. The outside walls of frame houses k:^T\^^>( the arrange- ment of your rooms. Types of Roof. The selection of a roof for the house is next in importance. There are several well-defined types of A R CHITE C TURE 19J. roofs in common use, of which the simplest is the lean-to, or shed roof, which slants one way only (Fig. i;). The pitch roof is the style used in Problem I, in which the ridge is at or near the middle, with the roof slanting two ways (Fig. i8). A roof that slants four ways, like the sides of a pyramid, is called a hip roof (Fig. 19), while one that has double slants in two ways from the ridge is called a gambrel roof (Fig. 20). It is like a compound pitch roof. The mansard roof slants twice in four direc- tions, like a compound hip roof (Fig. 21). Various combinations of these types occur in the construction of buildings. In churches, towers and other buildings of a special nature we often find the conical roof and the dome. Make several sketches showing different styles of roof, adapted to the plan selected for your house, as in Fig- ures 22, 23 and 24. Select the style you desire to use in this problem. Divisions of Space. The sizes of the rooms will be governed largely by their specific uses. Let us take the follow- ing figures as approximate, and modify them to suit the shapes and arrangement of the rooms already decided upon : Kitchen, 130 square feet, with pantry closet 40 square feet; living-room, 150 square feet, with china closet ; bedroom, 1 10 square feet, with clothes closet; bath- room, 40 square feet ; hall not less than 4 feet wide "in the clear," so that people may pass each other easily. 192 ART EDUCATION— HIGH SCHOOL Before locating the plan of our house definitely, the points of the com- pass should be considered. If possi- ble, plan to have the morning sun in the kitchen, and the living-room • ar- ranged with windows towards the west. We are now ready to decide on the scale to which our plans and ele- vations are to be drawn. Each view will probably need to be drawn on a separate piece of paper, but the rela- tion between them will be just as vital as though they were all on one sheet, as in Problem I. Begin as before, with the plan. We have previously settled on the approximate size of each room, so that, working from our free-hand sketch of the ar- rangement of the rooms, we can esti- mate the size of the floor plan. This' ' } ^■l_A=JS!M_^^^^" estimate, although subject to change -•^r^'"^ I '^S^g^^^^^^- as we work out the room measure- ments carefully, will enable us to place our plan effectively upon the paper. After drawing the outline of the plan to scale, draw the outside walls 7" thick, as in Problem I. Then divide the space by partitions 6" thick, composed of 2"x4" studs, plastered on both sides. First, measure a room, then a wall, then a room again. Make -the necessary changes,' if any, ^ in adapting your estimates to the accurately drawn plan. After the parti- tions are placed, cut openings through them and through the outside walls, for doors and windows. Make outside doors 3'-o" wide, and inside doors D Fig. 25 ARCHITECTURE 193 2 '-6" wide. The placing of the windows is a matter of importance both from the inside and outside points of view. As a rule, they should be 2-5" wide. Next locate the chimney, planning its position so that both kitchen and living-room can connect with it. (No heat nesd be provided for the bedroom.) Of the three ways of locating a chimney, shown in Figures 25, 26. and 27, Fig. 26 shows the fewest corners in the room. This is important when the questions of placing base-boards, cutting carpets and cleaning corners are considered. Place the chimney where you think the space can be most easily spared and will interfere the least with the straight lines of the walls. Give it an 8" x 8" flue, with 4" brick walls. The chim- ney should be covered or shielded by walls built around it but not touching it, the protecting wall being kept i " from the chimney, thus allowing a free circulation .of air. This is a safeguard against fire, and will prevent cracks in the plastering. No timbers should be built into the chimney. This construction of the chimney is shown in the plan by drawing the walls around the chimney i" thinner than the other plastered walls, as here, plastering is placed only on one side. The Kitchen. We are now ready to particularize in our plans for the individual rooms. As the kitchen is the work-room of the house, it should be fitted with appliances that will enable the housekeeper to do her work conveniently. The placing of sink, range, tubs, plumbing, etc. must all be done with the idea of convenience in mind. The kitchen plumbing should be placed near the light, and yet it should be located' along an inside wall, so that the danger of frozen pipes will be lessened. The sink should be placed so that it will not be exposed to view when the front door opens to receive a visitor. A long telescopic view through the house should be avoided, either by the plan of the hall or by the method of hanging doors. Opening from the kitchen should be a good-sized €loset or pantry, fitted with shelves, drawers and lockers, or cupboards, in which dishes and cooking utensils, provisions and food of various kinds may be kept. A place should also be planned for a refrigerator, as ice is a necessity in every family. The refrigerator should be placed near the back entrance, so that it may be conveniently filled (see Fig. 11). A small entry is added, and the ice-box placed in that. The location of the laundry tubs will be 194 ART ED UCA TION— BIG H SCHO OL determined by the plumbing. In Fig. ii, notice the grouping of range, hot-water tank, sink, drain-board and tubs. The average size of a kitchen sink is 20" x 36"; of a range, 2-6" x 3-0''; of stationary tubs, 2-0'' square over all, with i " walls. Place gas outlets where they will shed light to the greatest advantage, at the same time considering convenience of location and direction of cast shadows. The Living Room. In planning furniture spaces for the living- room, remember that in oiu" problem the dining-table must be accommo- dated here. An average size of 4-0" square when closed may be taken for the table, allowing for an extension of 4-0" in addition. Sufficient space should be allowed for chairs about the table. Probably the center of the room will be the best space for the table, and the gas may come from fixtures suspended from the ceiling above (see Fig. 1 1). Between kitchen and living-room there may be a double-swing door, while between living-room and hall the door should be hung so as to disclose to the entering guest the attractive room within. In a private room, such as a bedroom, the door should be hung so that, when partly open, it may serve' as a screen to the greater part of the room. If you desire to place a piano in the living-room, plan for a space against an inside wall, measuring 5-0" X 2-0", where light may be obtained. Locate other pieces of furni- ture as the space and shape of your living-room will permit. Express the proportions and general shapes of the furniture by dotted lines, and draw all such blocked-in shapes to scale.^ To do this, you must know the average sizes of the pieces of furniture you wish to place. The closet to the living-room may be a shallow one, fitted with shelves, to serve as a china closet. The door should open so as to swing back against a dead wall. The Bedroom. Plan the fixtures and furniture of the bedroom in the same way. A full-sized bed is, on the average, 4-6" x 6-6", and requires about 8'-o" of space in which it may be turned. Be careful that draughts between windows do not fall across the head of the bed. Locate the gas jet conveniently in relation to the bureau or dresser. The closet to the bedroom should be fitted with a shelf, and the door should swing in such a way as to admit the most light when open. The Bathroom. Average sizes for bathroom fixtures are : bathtub, 2'-o''x5'-o" inside measurements, with 3" rim; bowl, 12" diameter, with ARCHITECTURE 195 3" of marble slab outside of it; seat, 18" x 18", with 6" behind it. Plan the location of these fixtures carefully, as well as the placing of the gas-jet and the swing of the door. Outside doorways show a slight projecting sill (Fig. 11), and 3'-o" will be found a good height from the ground level to the house floor. Profile of height's. Window Piaz.2a 7o5t %