WHITES DRAWING REVISED I VISoN . BCAKnAAN ® CQ 'NEW YORK CHICAGO 155/, m IVISON, BIIAKEAAN A OX BOOK No. 1 FOR FIRST HALF OF FIRST SCHOOL YEAR FOR TEACHERS WHITE’S Industrial Drawing REYiSED L -L IVISON, BLAKEMAN Sc COMPANY NEW-YORK AND CHICAGO NOTE. THE USE OE CL A Y; — The most convenient and satisfactory method of teachmg form to very young pupils is by the use of clay . Little children can themselves readily make from it almost any form they study, and it easily illustrates nearly every step of the early work of the course; it is therefore recommended in this course, and directions for moulding are given. Ln places where clay is not readily obtainable, or for any reason its introduction seems impracticable, any substitute may be used in its place. The sphere and spherical solids are readily illustrated by comi7ion fruits, and these, in the absence of clay, should be used for the purpose. The teacher may cut from apples, potatoes, or tur- nips the cube, the cylinder, the pyramid, cone, or, m fact, almost any illustrative solid which appears in these lessons, and such vegetable forms are hardly less valuable than those made of clay. Bar-soap may also be used in the same manner as vegetables in teaching form — soap having the advantage of being comparatively durable. Good results can be secured with paper, card-board, or wood forms, if judiciously used : the indispensable essential being to impart clear ideas and accurate knowledge, whatever the method employed. Copyright, 1887, by I\ u, Blakeman & Co. New-York and Chicago. i; WHITE’S INDUSTRIAL DRAWING— REVISED. BOOK NUMBER ONE. ® LESSONS ON FORM. WHY DRAWING SHOULD BE TAUGHT. All knowledge depends upon perception, and perception upon three senses — sight, touch, hearing. Sight and touch are depen- dent upon form. The study of form, then, is one of the most impor- tant factors in early education. Drawing, in all its departments, deals with form, and it is impossible to teach drawing as it should be taught without a constant reference to the objects and forms studied. •) In the public schools, drawing should be taught for the valu- able training which it gives to the eye and hand, and for its educational value, — not for the amusement of the pupils, or for the production of “ pretty things ” in the forms of designs and pictures. The General Plan of the Work is as follows: I, The study of forms as wholes. II. The analysis of forms and the study of their details. III. The producing of new forms, or new combinations of forms. The details of for7n are taken up in the following order : Points, straight lines, angles, triangles, squares, oblongs, curved lines, circles, ellipses, ovals, compound and reversed j curves. Hexagons, octagons, pentagons, spirals. In this little book, which is intended for the use of teachers in the lowest grades, the geometric forms, sphere, cube, and cylinder, and their applications, are the only forms taken up; and of the details of form, points and their positions, and lines. The Objects of these Lessons are: To lead pupils to see, to think, to express what they have perceived. Very little should be told to the pupils. Ask definite ques- tions, which shall lead them to think for themselves. Always present the form to be studied to the pupils, and study it, not study about it. In order to obtain the best results, each pupil should be sup- plied with the following articles : Materials. One sphere, i inch in diameter. One cube, i inch on a side. One cylinder, i inch in diameter and 2 inches long. One dozen sticks, i inch long, of each of the three primary colors — yellow, red, and blue. One dozen sticks, i inch long, of each of the three secondary colors — orange, green, and purple. A slate and pencil. A mass of clay equal in size to a cube 3 inches square. Care of Materials. When not in use, the materials, except the slates, should be kept by the teacher of the class; all the clay in a mass, and the other materials in small boxes. It is important to have all the materials properly marked, and so arranged that they may be given out to the class without con- suming too much time. Many ways of doing these things expeditiously are already familiar to most teachers. The practice of passing each article separately to the owner should not be permitted, as it takes too much time and creates confusion. A very good way is to have the materials in small boxes, with each pupil’s name on his box; to place the boxes on the end of each line of desks on one side of the room — the right side, for instance; each pile should contain the boxes belonging to the pupils in that line; as the teacher counts one, the pupil on the right-hand at the end of each line should lift the boxes, dropping the lower one, which should be his own, and place the others in front of his next neighbor; when the teacher counts the second pupil in each line should lift the boxes, dropping his own from the bottom, and pass them to the third pupil, who should proceed in the same way as the teacher counts three, and so on to the end of the line. After the lesson, when the boxes are to be collected, the same plan should be followed, — thus : beginning now on the left-hand, and counting one for the first pupil in each line to put his box on the box of his next neighbor, then two for the second pupil to put the two boxes on the box of the third pupil, etc. When the boxes are all collected on the right side of the room again, they may be collected by one pupil, and brought to the teacher, who places them in the closet. If kept in this way in the closet, the piles may be placed on the desks and counted back for the next lesson without any trouble of rearrangement. The slate pencils should be long, and well pointed ; they may be passed to the pupils in lines as described for the boxes. The pencils belonging to each line or row of pupils may be kept together by an elastic band ; they should be looked over care- fully after each lesson, and sharpened if necessary. One or two members of the class should be appointed to take care of the pencils, under the direction of the teacher; or, if the scholars are very young, the teacher should take charge of them. The clay should be kept in an earthen jar if possible; if not, in moist cloths, and covered with a piece of rubber-cloth or gossamer. When ready for use, the clay has about the consistency of new putty, but is not soft enough to be sticky. If the clay is too hard to use, let it stand in water for an hour or more, and then expose it to the air for about the same length of time. If the clay is too moist, allow it to dry until it is in a proper condition to use. When the clay is to be used by the class, take a mass of it from the jar, of such a size that each pupil may have a piece about as large as his cube. Form the clay into a cubical mass, and cut it into small cubes, as shown in Figure i. Cut horizontally first, then make the vertical cuts, using a strong, fine string or a piece of wire. Distribute the clay, =11111 —1 ^uimuffliiDiiiiiuiit: giving one piece to each pupil. •) -JULi When the lesson is over, collect all the forms modeled, select Fig. 1. those to be preserved, and swedge the others into a mass, ready for use in the next lesson. If the clay when collected is quite moist, it may be swedged into shape very readily by throwing it upon a hard surface a number of times; but if the clay has become somewhat dry, place it in a stout cloth, and let it stand in water a few moments, then twisting the cloth tightly around the clay, mass it in the cloth by throw- ing upon a hard surface as before. With a little thoughtful care, the clay may be easily kept in a good condition, and the inconveniences of “liquid clay” and •) “ lumpy clay ” be avoided. LESSONS ON THE SPHERE. The sphere is taken first, because it is a form with which all children are familiar, and also because it is the simplest of the geometric forms to mould. The steps in giving a lesson and the order of taking them should be the same in each lesson on form. They are here given. 1. Introduction. — Awaken the interest of the pupils. Have the attention of every one, — not by commanding it, but by in- troducing the subject in such a way that the attention will be given voluntarily. Make the introduction so interesting that even the dullest will be aroused. This may be done by mak- ing use of the pupil’s previous knowledge, his curiosity, and his imagination. In the first lesson on the sphere the distribution of the forms will be sufficient to awaken interest — especially if the pupils are told not to touch them, but to look at them, and see what they can find out about them, for questions will soon be asked about what they can see. 2. Study of the Form. — Ask the pupils what the form is made of, how it looks, etc. Take the form in the hand. How does it feel ? What will it do ? and similar questions. 3. Objects similar in Form. — After the form has been studied as above, ask pupils to find objects in the room like the form ; then to think of objects which they have seen like it. 4. Teaching the Name.— When the pupils are thoroughly familiar with the form, teach them its name, and give them practice in its use. The term Sphere is hard to teach, because nine- tenths of the pupils will call it “ spear.” W rite on the board, S-fear. Have them pronounce S-, then “ fear ”; then put the two together, first slowly, as S - - fear — then S - fear and S fear, or Sphere. Ask questions like. What have you in your hand? (An- swer, a sphere.) What is an orange shaped like ? or. What is a ball shaped like? or, What is a marble shaped like ? 5. Expression. — To be taken up in third lesson, by clay, and later by words and drawing. Fix these five steps thoroughly in mind, and follow them in giving the lesson, and there will be fewer dull boys in the class than usual during the time for drawing. Section I. LESSONS FOR ONE WEEK. Four Lessons of Fifteen or Twenty Mitiutes each. Lesson 1. The Sphere — Provide objects having the form of the sphere, and place in different parts of the room. Distribute spheres to the pupils. If models are not at hand and cannot be obtained, marbles or balls will do. Proceed with the lesson as already indicated. Lesson 2. Review previous lesson. Make the lesson interesting by thinking of new forms similar to the sphere; by thinking of all the things good to eat which are like spheres ; or of all the largest spheres the pupils have ever seen ; or the smallest. Lesson 3. Moulding. — (For hints on management of clay, see page 5.) After the clay is distributed, review quickly the form to be moulded. Then, taking the clay in the left hand, push in the corners with the thumb of the right hand. Now, with the hands open flat, roll the clay between the palms, gently and quite rapidly, round and round, until the sphere is formed. Test the spheres moulded, by rolling, by standing, by comparing with the models. Collect the forms moulded,' select those which are to be pre- served, and mass the others. Clean the pupils’ hands if necessary by using a large sponge or moistened cloth. Mark the spheres while moist with the initials of the pupils who made them, using a pin or sharp stick. Make the letters small and fine. Lesson 4. Review the moulding of the sphere, striving to obtain better spheres than before; then model some object like a sphere. Select some simple object, an apple, orange, cherry, etc., and have the sphere modified so as to be as near like the form as possible. Model the form with the fingers. Bits of wood, pegs, or apple stems saved from the children’s lunches may be used to form the stems to the apples, or toothpicks for cherry stems, etc., etc. The teacher’s ingenuity will help her in these lessons, and the little people will be found right willing to assist her in obtaining material either for models or for accessories in these form lessons. Figure 2 illustrates a few of the many forms which may be modeled. Section II. LESSONS ON .THE CUBE. The cube is studied next to the sphere, because it is the oppo- site of the sphere, and the details of each are made more promi- f) nent by contrast. Work for One Week, Lesson 1. 1. Introduction. — Provide forms based on the cube, and place in different parts of the room. Distribute cubes to pupils. In- terest the pupils in the new form, and review sphere rapidly. 2. Study of the Porm. — Ask questions similar to these: Of what is this model made ? How does it look ? How does it feel when held in the hand ? What will the block do ? Will it roll? Can it slide? Can it be made to slide without touching • V it ? (Yes : on a book or slate held obliquely.) ' 3. Similar Objects. — Find objects similar in the room. Think of similar objects. There are not so many simple forms based on the cube as upon the sphere, but the pupils will think of a number quite readily. 4. Teaching the ISTame. — Write the word cube on the board, and tell the pupils that a form like the one which they have been studying is called a cube, not a “ cue,” as many will say. Be careful to have the pupils pronounce the word correctly. Ask questions in such a way as to require the use of the term in the answer. Lesson S. Review of the cube, similar to the way in which sphere was reviewed in the second lesson. Bring out cubes by using more than one cube at a time. When the pupil mentions objects based on the cube, make pictures of the forms on the board. If you cannot draw well, don’t be afraid to try. Any sketch which hints at the form, even if it has but the remotest resem- blance to it, will be found enough to satisfy the child. Children’s imaginations are powerful, and a hint in the right direction is enough to call to their minds a vivid picture of the reality. Sketches upon the blackboard by the teacher will double the interest in a lesson. Compare with the sphere. Lesson 3. Moulding. — Distribute clay and models as for sphere. Review cube. The cube is best moulded by first forming a sphere rapidly, and then, holding it between the thumb and fingers, striking it gently upon the slate three or four times. Have the pupils do this in concert. Turning it, strike the opposite side in a similar manner, and so on until the cube is formed. The comers and edges may be sharpened if necessary by drawing the clay out a little between the thumb and forefinger. Test the form moulded by comparing with the model. Lesson 4. Review the moulding of the cube, as it is more difficult to obtain good results with the cube than with the sphere. An application of the cube should not be attempted until the third or fourth lesson. 8 Section III. LESSONS ON THE CUBE. — Cofi/mued. Work for One Week. Lesson 1. Review cube again, and mould. Strive for a correct expres- sion of the form by clay. This should be a lesson on telling the exact truth. The model has six sides alike, sharp edges and corners, and the pupil is to make one like it. Then, if the edges of this cube are not sharp and the sides alike, it is not a true story about the cube. Let each pupil strive to make the best cube. Lesson 2. Select some simple application of the cube (see Figure 3), and have the pupils mould a cube; then the application ; mould in concert as in previous lessons. Lesson 3. Distribute the clay, and after reviewing the cube and mould- ing it, let each pupil select some form based upon the cube, and mould it, without any help from the teacher. If the clay should become dry before the object is moulded, it may be sprinkled with water to moisten it. Lesson 4. Review.— Give each pupil a sphere and a cube. Have the two compared. Ask some pupil to tell all he can about one or the other. Place the sphere on the cube. Ask if any objects have been seen like these two forms combined. Strive for a correct expression of the forms by words. Section IV. LESSONS ON THE CYLINDER. The cylinder combines the qualities of both the sphere and the cube, and for that reason is taken next. It is the most difficult of the forms to mould. Work for One Week. Lesson 1. 1. Introduction. — Provide objects based on the cylinder, and cylinders of various proportions : As a lead pencil, a sage box, a pill box, and a lozenge. Review the sphere and cube. 2. Study the Form.— Ask questions to bring out the follow- ing : A cylinder is round, with flat ends ; it will roll and stand like a sphere, and slide and stand like a cube. 3. Similar Objects.— Pupils find objects based on the form in the room. Bright eyes will find many. Be careful to keep the bright boy from naming a dozen of the most evident, before the dull boy finds one. Teaching the Name This term cylinder sometimes proves to be difficult. “ Cynilder,” “ cyndiler,” and “clynder” are common. To overcome this difficulty, write the word on the board. Cyl-in-der, and have each syllable pronounced separately. Give practice in the use of the term, as was before given for sphere and cube. Lesson 2 . Review the Cylinder. — In this lesson bring out the term cylinders. Find objects formed of two cylinders united, as a mallet, the elbow of the stove-pipe, a bottle, etc. Find largest cylinder and smallest cylinder, making sketches on the board to illustrate. Lesson 3. Moulding. — Cut the clay into masses a little larger than usual. Distribute the clay and the cylinders. Review rapidly. Mould a sphere, then change to a cylinder by rolling carefully on the slate with the palm of the hand. The flat ends are obtained by striking the clay upon the slate squarely and firmly, as the sides of the cube were formed. Figure 4 illustrates the popular forms of cylinders during the first two or three lessons. A form like Figure 4,12, shows that the clay was rolled too hard ; like c, not hard enough ; b is the usual form,and shows that the clay was rolled too much before it was struck upon the slate to form the ends. A little care, however, will soon correct these faults, and good results will be obtained. a b c rig. 4. Lesson 4. Review moulding, each one trying to make the best cylinder. Section V. LESSONS ON THE CYLimER.— Continued. Work for One Week. Lesson 1. Review Moulding of the Cylinder, urging the little work- ers to do even better than in the last good lesson. Take a piece of clay and work with them, comparing your work with theirs. If any of them can “ do better ’n teacher,” they will be delighted, and think all the more of their teacher besides. Lesson 2 . Mould Applications of the Cylinder Figure 5 illustrates a few of the many objects based upon the cylinder. Fig. 5. Lesson 3. Review Sphere, Cube, and Cylinder, and mould Applica- tions of any or all of the Forms, each pupil selecting a form to mould. (See Figure 5.) 10 Let a few make a string of beads — each pupil making one bead. Or a few others a croquet set, or a string of grapes, or a basket of different kinds of fruit. Lesson 4. COLOR. Materials : Circles of Colored Paper, Colored Chalk, or Balls of Colored Worsted, and the Colored Sticks for the Pupils. — In the color lessons, which will be found through the course, be careful to teach a few things thoroughly at each lesson. The usual mistake is to try to teach too much. In this first lesson find out what the pupils know. Try white or black; if these are already known, take red. Place some red marks on the black- board, and objects having the color in different parts of the room. Hold the circle of red paper before the pupils, and ask them to notice its color. Tell them that they must look at it care- fully, for you are going to see if they can remember its color. Put the circle out of sight, and hold up some other object of the same color. Question the children about it. Try it again — this time showing them two or three other colors before again showing red. Ask them to find anything in the room the same color as the first circle they saw. Perhaps they will see the red mark on the blackboard, the geranium blooming near the window, Jenny’s dress, Harold’s necktie, or the ribbon on Marion’s hair. When objects have this color they are red; never mind what shade of red at present, simply the comprehensive term red is to be given. Strive now to associate the color and its name, by asking ques- tions which will lead the pupils to make use of the term red in expressing thoughts about certain things. Section VI. LESSONS ON THE HEMISPHERE. The three simple geometric forms, sphere, cube, and cylinder, have now been studied. The analysis of the forms comes next in order. O First, the sphere is cut in two, thus forming hemispheres. Work for One Week. Lesson 1. 1. Introduction. — Provide objects similar to the hemisphere, and place in different parts of the room. With a large sphere of clay, an apple, or if possible a wooden sphere cut in two, teach hemisphere. 2. Study of the Form. — By questions lead the pupils to dis- G cover the shape of the form : that one side is flat and the other rounding ; that it will roll on its edge, will stand and slide on its flat side, and stand and rock on its rounding side ; that two of them make a sphere. 3. Objects Similar. — First find similar forms in the room, then think of objects similar; then of objects which might be cut so as to make the form. 4. Teaching the Ifame. — Give the name Hemisphere. Tell them that hemi means half, and that hemisphere is really half- sphere. Give practice in use of term. Lesson 2 . Moulding. — Distribute clay and spheres. Review sphere and mould. Review hemi- sphere. Distribute thin, stiff cards, about 1^x2^ ins. in size, and show the pupils how to cut the spheres into two hemispheres. Place the sphere in the hollow of the left hand. Then holding the card in the right, as shown in Figure 6, cut the sphere through the center. Lesson 8. Review.— Mould the sphere and cut to form the hemispheres as in Lesson 2. Strive for accurate work, in both moulding and cutting. Lesson 4. MOULDING APPLICATION OF THE HEMISPHERE. First mould sphere and cut. Distribute two tooth-picks to each pupil. Give directions for making a ladle. Place a hemisphere in the hollow of the left hand with the flat side uppermost. Make a little hollow in the flat side by gently pressing the finger upon it once or twice. Insert the tooth-pick for the handle. The pupils may now make any other application of hemi- sphere they may think of. Perhaps a sunshade, a toadstool, a 11 little skillet, or a bird’s nest, or nut-shell, half a peach or half an apple. This last may be made quite natural in appearance by inserting a real apple-stem and real seeds. LESSONS ON DETAILS OF FORM. Thus far forms have been studied as wholes. These forms are now analyzed and their details studied. Forms are analyzed and their details studied in the following order ; surfaces, faces, edges, corners. for One Week. Order of lesson in Analysis : 1 . Review of form to be analyzed. 2. Call attention to the different parts, and especially to that detail to be studied during the present lesson. Observe by eye and hand. Ask questions concerning it, so as to bring out its characteristics. 3. Study from other forms and objects. 4. Give name or term. 5. Give practice in use of the new word. 13 Lesson 1. A SURFACE. 1. Review sphere, cube, and cylinder. 2. Placing the hand on the sphere, ask. What am I touching? What part of the sphere am I touching? (The outside.) Touch the outside of the cube, the cylinder, etc. How does the outside of these forms feel ? What can you do to the outside with your hand ? (Rub it, touch it, or move the hand over it.) 3. Find anything else over which the hand may be moved. (The desk, slate, chair, blackboard, wall, book, etc., etc.) 4. Anything upon which the hand may be moved is called a surface. Teach the term, being careful to obtain a correct pro- nunciation. 5. Ask questions in the answering of which the pupils must make use of the new word. For instance : When I move my hand on the blackboard, what do I touch ? On the book ? etc. A sphere has one surface ; a hemisphere two ; a cylinder three ; a half cylinder four; a square pyramid five, etc. Lesson 2. 1. Review surface. 2. Using various forms, as the sphere, a book, an apple, and a box. Bring out the fact that the fingers move along one sur- face, or back and forth upon it, while on another they move around. For instance: The fingers move along on the surface of a slate, but around on that of an apple. 3. Find these two kinds of surfaces in the room. 4. A surface upon which the fingers move along, a flat sur- face, is a plane surface ; a surface upon which the fingers move around, a surface which bends, is a curved surface. 5. Question the pupils as to various surfaces so as to require the use of the terms often. Find largest or the smallest plane surface and curved surface in the room. Lesson 3. MOULDING OF SURFACES. Distribute two pieces of clay and one card to each pupil, using one piece of clay. Mould a sphere. Study its surface. With the card, cut the sphere. How many surfaces has the hemisphere ? What kind are they ? etc. With the other piece of clay mould a cylinder. Study it as to its surfaces. Cut lengthwise. Study each half. Using the clay in one hemi- sphere, the card and the clay in Fig.'Y. one half cylinder, construct the “ little bridge ” shown in Figure 7. How many curved surfaces has it ? Other similar exercises may be given. Lesson 4. Color. — Review black, white, and red; then study yellow as red was studied. (See Section V., Lesson 4.) Section VIII. LESSONS ON THE DETAILS OF FORM. Face. — After much careful thought and study, it has been thought advisable to teach as simply “the plane surface of a solid.” Any other definition is perplexing to young children. Work for One Week. ^ Lesson 1. 1. Review plane and curved surface. 2. Notice that when a sphere is held in the hand in one posi- tion, it is impossible to see where the surface stops, or to see the whole of the surface at once ; the same with the curved sur- face of a cylinder. When a cube is held in the hand, the whole of one side may be seen, and the surface is smooth and flat. 3. Find other plane surfaces, of which the whole may be seen at once. 4. The plane surface of any form when completely visible is called a face. 5. Find faces, and use the new word in both questions and %) answers. A sphere has no face; a cylinder has two faces and a curved surface, a cube has six faces, etc. Lesson 2. As the new term face may be found somewhat difficult for the pupils to remember, in this lesson review the subject carefully, cutting a slice from an apple to form a face, or dropping a sphere of clay upon a flat surface to form a face. Make sketches on the board of the various faces found by the pupils, — long faces, wide faces, round faces, etc. 13 Lesson 3. Distribute the clay. Review face. Ask the pupils to mould any object they can think of which has a face. Make the repre- sentation of the objects as natural as possible. Lesson 4. Color. — Review red and yellow, and take blue, teaching it in the same manner in which red and yellow have been taught. (See Section V., Lesson 4.) Section IX. LESSONS ON DETAILS OF FORM. Edge. Work for One Week. Lesson 1. 1. Review plane and curved surface and face. 2. Place a cylinder upon a book, and inclining the book a little, let the cylinder roll off the book and drop into the hand. Ask, What made the cylinder drop ? (Probable answer— “ It rolled off”) Place a cube upon the book and push it off; then let it slide off, asking each time. What caused it to drop off? When the cylinder is rolled, why does it not keep right on rolling and not drop ? Ask such and similar questions, to bring out the fact that the surface stops, thus causing the objects to fall. 3. Find other places in the room where surfaces stop. 4. Where a surface stops, an edge is formed. 5. Give practice in the use of the new word, and notice that every edge is formed by the stopping of one surface and in most cases by the beginning of another. 14 Lesson 2 . Review lesson one, and by questions and illustrations bring out the difference between straight and curved edges. Notice that two plane surfaces coming together form a straight edge ; that a plane and a curved surface coming together form a curved edge; two curved surfaces, a curved edge, etc. Lesson 3. Review, finding long and short, straight and curved edges, edges with long curves, short curves, etc. Lesson 4. Color. — Review the three colors studied, red, yellow, and blue, and have the pupils use their colored sticks, arranging all the red in a row, all the yellow, all the blue. Make a row, using first a red, then a yellow, then a blue stick, then a red, and so on. Give other exercises similar. Section X. LESSONS ON ANALYSIS OF FORM. Corner and Its Picture, a Point. for One Week. Lesson 1. I. Review edges. 2 Using a book or box cover to illustrate, question pupils as to its edges. Have them move their fingers along two adjacent edges until they meet. Notice where the edges run into each other or meet. 3. Find edges in the room which meet. Find edges which run into surfaces and stop ; and by questions lead pupils to dis- cover that a comer is formed where two or more edges meet. 4. Teach the new term corner. 5. Use the word in questions and answers. ^ Lesson 2 . Review corner and teach the drawing of the corner. Select some corner in the room and tell the pupils that you will make a picture of it upon the board. Place upon the board as its picture simply a pomt or dot. If any lines are drawn you have more than a picture of the cor- ner, for portions of the sides have been drawn. Ask some pupil to make a picture of a corner upon the black- board — not a picture of any comer, but of some particular cor- ner. Ask others to make similar pictures of comers. In the first work of the little people, six kinds of dots, illus- trated in Figure 8, will proba- r — ' 1 bly be found. Say little about | O + i ’ 1 it, however, during this lesson; Fig. 8. simply keep the little mind occupied with one fact, — that a point is the picture of a corner. Lesson 3. Review, making points, pictures of corners. Make a number of such pictures on the board. Ask the pupils to make one on their slates. Pass through the aisles and notice the various kinds of dots. Ask how many points are upon the blackboard. How many kinds of points? (Only one kind.) Tell them that you have found two or three kinds, and draw the different kinds on the board. Show them why some are wrong and others right. Teach them how to make the best points — small, like the last in Figure 8. Lesson 4. Color. — Review the three colors, red, yellow, and blue, making sketches of simple objects upon the board and allowing the pu- pils to color them with the three colors. Give the term Primary. These colors are called primary be- cause no other colors can be mixed so as to make any one of them. Illustrate Vvhat is meant by mixing colors, in the follow- ing manner: With a yellow crayon make a number of heavy marks close together upon the blackboard ; close to these make a number of blue marks; with the finger blend them together by 0) rubbing gently. A green will be the result. So, green is made of two colors — blue and yellow. Red or yellow or blue can- not be made in any such way, so they are first or primary colors. Ask questions about different objects, having one or more of these three colors upon them, in such a manner that the term Primary Color maybe used, and the children become familiar with it. Continue until the three primary colors are known at sight and the meaning of primary, with reference to color, under- stood, as the meaning of primary is understood when it refers to schools. 16 Section XI. LESSONS ON POSITION OF POINTS. Work for One Week. First teach simply the positions without having pupils make points. Lesson 1. Slates upon the desk, with long edges parallel to long edges of the desk. All sit up straight. Hold up the right hand. (The teacher being careful to hold up her left, because what is right to her appears to be left to the little eyes in front.) Now, can every- body do like this? (Figure 9, pointing straight up with the forefinger.) Now, all together, put the finger down on the middle of the slate. See that every finger is in the right place. All hands up again ; now, all together, finger on the middle of the slate. Practice this until perfect unison is obtained. Now, move the finger from the middle or center to the top of slate. Then center, top, bottom, top, bottom, center, bottom, center, top, etc. ; first slowly, then more rapidly. Try it upon the top of the desk or upon a book — for variety. Lesson 2. Review center, top, and bottom, and add left side and right side, having pupils work in perfect unison. It may be necessary to call the pupils’ attention to the fact that the left is toward the v^indow and the right toward the blackboard or some such local objects, to fix in their minds which is left and which right. 16 Lessou 3. Review the five positions, skipping about, going first slowly, then more rapidly. In this lesson turn the slate with the short edge toward the top, so that the pupils will know that its posi- tion upon the desk makes no difference; that top means farthest away, and bottom nearest ; and that left and right are positions relative to themselves, and not to the slate or book. Lesson 4. Review the same, being careful to have the fingers find the middle of the top, 7niddle of the left side, etc. Review often. Section XII. LESSONS ON POSITION OF YOmU^.— Continued. At this stage of the work the use of “ men ” will be found of great assistance in teaching positions, etc. By “men” are meant pieces of wood about the size or shape of “ roll lozenges,” or buttons, or kernels of Indian corn. Each pupil should have twelve “men.” These will be found not only useful, but in- tensely interesting to the children; for they are now flies, now frogs, or trees, or boys, or soldiers, as the teacher suggests. Work for One Week. Lesson 1. Review center, middle Of top, middle of bottom, middle of left I side, middle of right side, using “ men.” Make the lessons inter- esting. For instance : We will play that the slate is our field and the frame the fence around it, and in the field we are going to set out some trees. We must have them in just the right place every time. Each tree must be set out right the first time, be- cause we can’t set out the same tree twice, very well. Now, see who will have the best-looking field. First tree in center of field, next middle of left side close to the fence, middle of right, etc. The teacher will readily think of many similar ways of making the lessons enjoyable. We remember longest what we learn with pleasure. Lesson 2. Review rapidly the five positions already studied, and add upper right corner and lower right comer. Holding a slate be- fore the pupils, place your forefinger on the right side of the form; ask — Where is my finger now? (Ans. — “Right side.”) Now moving it up to the top of the right side, ask — Where now? (Probable answer — “At the corner.”) Which corner ? (Probable answer — “ Right corner.”) Moving the finger to the lower right corner, ask. But isn’t this a right comer too? (“Yes.”) Moving the finger to the top again, ask — Then if both are right corners, which right corner shall we call this? (Ans. — “ Top right comer, or upper right comer.”) Right ; and this ? moving the finger to lower right corner. (Bottom right corner, or “ downer ” right corner, or lower right corner.) Ask pupils to point to the different positions in concert, skipping about from one position to another, so as to require the greatest amount of thought. Lesson 3. Review last lesson and in a similar manner teach upper left and lower left corners. Use the “ men.” Lesson 4. ^ Review all the positions, first having the pupils point to them in unison, then placing “ men ” according to directions, — sometimes using the nine “men” for the nine positions, then dictating two or three of the positions only, so that there is a chance for a misplacement of the “men”; or, set out all the nine trees and have two or three of them die, and so that they must be dug up. Section XIII. LESSONS ON BISECTING. 1^) Bisecting is cutting in two equal parts. Teach by cutting strips of paper, by breaking splints, by using pupils, etc., etc. Work for One Week. Lesson 1. Ask Johnny, who sits in the first front seat, to stand in front of his desk, and Jimmy, who sits in the last front seat, to stand in front of his. Ask if there is a boy in the room who thinks he can stand just in the middle between Johnny and Jimmy. So out 17 comes Sam, and stands proudly up in the middle. Is he just in the middle ? Let’s see. Have a long string and ask some smart fellow to help measure. Measure from the top of Jimmy’s head to the top of Sam’s, and then from the top of Sam’s to the top of Johnny’s. Do they measure just alike ? Try the girls the same way. Now we will play that the slate is the floor. Select one piece of com or one “ man ” for Johnny,— he came first,— and put him at the left side; now one for Jimmy, at the right side. Now be careful to put Sam half-way between so that they will measure just right. This is bisecting. When we divide a distance into two parts just alike, we bisect it — not “bi-set.” Teach the word coi rectly. Lesson S. Review. This time, perhaps, sketching on the board, two birds on the telegraph wire and another to bisect the distance between them, or two boys on a fence, and a third to bisect, having the children follow upon their slates, using the “ men ” to represent the birds or the boys or the trees or whatever the lesson is about. Lesson 3. Review. This time, after the “ men ” have been placed in position, lift each up a little and place a point on the slate just under it, then remove the “ man ” entirely. The point must be made but once — no erasing. 18 Take special care to have the points very small. Figure lo shows position of hand and pencil while making a point. Figure II shows a little point “ with a fence around it” or a little ring around it to Fig. 10. make its position on the slate more evident. Make the points small and the little rings round. Section XIV. Lessons for Otie Week. Lesson 1. Review sphere, cube, and cylinder, and mould applications of the forms. Allow each pupil to select his own form to mould and his own application. Lesson 2. Color. — Review the primaries and teach orange. The best way to teach orange is to make the color before them. Take a lump of gamboge, ivhich may be obtained at any apothecary’s for a cent or two, and dissolve it in water; it will form a beauti- fully yellow color. Have this in two clear glasses upon the desk ; pour into one some red ink, stirring it -with a stick; add a little red at a time until a brilliant orange is formed. Compare this color with the yellow in the other glass and with the red in the bottle. Find colors in the room similar to the color just made, and give the name orange — a secondary color — so called be- cause it is made from two first or primary colors. Lesson 3. Review surface, edge, and corner, points and bisecting, — plac- ing points on slates, and bisecting distances between points. Mark the slates — a star for perfect, i for good, 2 for fair, and 3 for wrong. Lesson 4. Color. — Review the three primaries and orange. Teach green and purple as orange was taught ; i. e., by producing the colors before the pupils. For the primary blue use Prussian blue, or if that cannot be had use bluing, sometimes used in rinsing water. Blue and yellow make green, and blue and red make purple or violet. Use colored paper and colored crayons in trying the various colors, to see if the pupils can associate the names with the proper colors. Review often. Section XV. LESSONS ON THE JUDGMENT OF DISTANCES. The power to judge distances accurately is exceedingly valua- ble to any person. In the drawing-books of this series no guide- points are given, so that the ability to judge short distances A accurately is absolutely necessary. One inch is taken for ^ the standard at first. Work for One Week. Lesson 1. Teaching “Inch.” Distribute the cubes. Fit a cube into a comer of the slate as shown in Figure 12. Take a pencil and place a point at the comer “out in the slate”; i. e., one inch from the frame at the top and side, — usually called one inch from 12. comer. Make a similar point at each comer of the slate. Review. Lesson 2. Place the cube on the upper left-hand corner of the desk and don’t touch it again until permission to do so is given. Look at 19 the cube carefully and try to fix in mind just how far it is from one of its corners to another. Place a point one inch from the corner of the slate as in last lesson, but “ guess at it ” — do it by judgment; don’t measure. Review. Lesson 3.. Same again. The teacher working with the pupils and en- couraging them. Strive to place the points accurately the first time. Allow no erasing whatever. Put the little rings around the points. The teacher to rank the work after the lesson. Lesson 4. Color. — Review of the primary and secondary colors, using the sticks. Figure 13 illustrates one method of using the sticks. Place, for instance, the yel- low stick upon the desk and near it the blue. The pri- maries yellow and blue united form green. Then a green stick is laid across them. Same with other col- Fig. 13. Fig. 14. ors. Figure 14 illustrates a similar arrangement, using colored paper triangles instead of sticks — the two slanting primaries forming the lower secondary. The teacher will think of a number of similar exercises. Section XVI. LESSONS ON LINES. Lines are pictures of edges. As edges go from one corner to another, so lines go from one point to another. Work for Ofie Week. Lesson 1. Review edge, corner, and point, and teach line, the picture of an edge. Select some object — a book, perhaps; ask a pupil to come to the board and make a picture of one corner ; call an- other to make a picture of another comer. Question tne pupils about the edge between these two corners, its direction, etc. Ask them the easiest way to make a picture of the edge, now that they have the two corners drawn. Ask some one to come to the board and draw the line connecting the points. Others draw similar lines. Lesson 2. Review last lesson on the slates, using the cubes; place points one inch apart, — pictures of two comers of the cube, then draw a line connecting the two points ; draw other edges of the cube in a similar manner; no erasing or ruling allowed. Lesson 3. Review of drawing lines.— Figure 15 illustrates the quality of line for which to strive. The points in the first are too large. In the second the pupil did what was * — * required of him, viz., to make the points very small, — to start at the left side and rig. 15. draw without stopping to the right— freehand and no erasing. This perhaps is the best line he can draw at present, but never mind; he made it right, and the quality v/ill improve with practice. His mind thought right, and his hand will soon do right. Lesson 4. DICTATION LESSON. Place a point in center of slate. Place a point one inch from the top of the slate. Draw a line from one point to the other. Place a point one inch from the bottom of the slate. Draw a line from the middle point to the bottom. Place a point one inch from the left side of the slate. Place a point one inch from the right side of the slate. Draw a line from the left point to the right. Result— a cross. Give such simple exercises as the above, simply giving all directions with no help by sketches on the board; thus train- ing the pupils to think and act for themselves. Assure them that if they listen to what their teacher says and do the best they can, they will do just right. If these lessons do not occupy all the time allowed for drawing during the first half-year, give simple exercises on the subjects already studied, and review color carefully. Keep the children interested in their work, make it pleasant for them. Don’t discourage first attempts, be they never so poor. In short, to teach children be a child yourself. Exercise L TO TRMS PTIPHS TO JUDGE DISTANCES.— 1 inch. Directions to the Teacher, i. Teach pupils to know these positions on the slate or desk : center, top, bottom, left side, right side ; upper left corner, upper right corner, lower left corner, lower right comer. 2 . With blocks or pieces of pasteboard one inch square, teach inch. Fit a square into a corner of the slate and place a point at the corner of the square out in the slate,— one inch from each side of the slate, usually, called one inch from the corner. Same for other corners. Place point in center of slate, one inch above center Ijelow, to left, to right, etc. Repeat often until the points can be placed without the squares for measures. Make points very small, and put a ring around each to make the position more evident. Place points by judgment in space below, as shown in illustration. Exercise V. VEKTICAL LINES. A vertical line is an upright straight Teach from objects, and draw on slates. h Exercise VI. Place points one inch from the comers of the space below. Bisect distance between upper points. Bisect each half of the distance. Bisect each of the spaces thus formed. Bisect the resulting spaces. Same between lower points. Practice movement, and draw vertical lines in unison, light, free lines. c ( Exercise VII. Study the faces of a cube. Notice the edge bounding each face. By what would you represent these edges in drawing ? Divide the space below into two equal parts by a vertical. In each space make a picture of one face of a cube. Make a large picture of the face. Think before placing a point. Think before drawing a line. Kxerciae Vni. APPLICAHOIT OF YEBXICAI. AITD HOEIZONTAL LINES.— A Chair. Directions to the -Teacher. Place points one inch from each corner of space at right. Draw long vertical line and bisect it. Bisect distance between points at the right. Draw right vertical line and ■ bisect it. Complete as shown in illustration. Exercise IX. DICTATION. Place points one inch from each corner of space below. Bisect distance between points at top, and then bisect each half at the top. Erase the outside points and the center point. Connect the two I remaining points by a horizontal line. Connect the points at the bottom by a horizontal line. Bisect this line, then bisect each half of it. Draw vertical lines from ends of upper horizontal to points on lower horizontal line. Result, a hat. Ixeroise X. OBLIQUE LINES. Directions to the Teacher, i. Teach from objects. Use edges in room, string, pointer, etc. Contrast with An oblique line slants or leans over. horizontal and vertical. 2. Place points one inch from each corner of space below. Bisect distance between them. Draw my line not horizontal or vertical is oblique. oblique lines connecting the points in as many ways as possible. Insist upon free work. Exercise XI. APPLICATIONS OF OBLIftlJE LINES, Directions to the Teacher. Cut an arrow-head as shown in illustration, from paper, size four inches wide by six inches long. 2. Have drawing made from it in left half of space above. Give pupils verbal directions, but no blackboard help. First point one inch from middle of top of space. Exercise XII. I. Cut a spear-head as shown in illustration, from paper, size four inches wide by six inches long. 2. Have drawing made from it in right half of space above, blackboard to illustrate if necessary. First point same as in last ; next points, one inch from lower corners of space. Use Exercise XTTt. APPUCATION OF THE THREE BUTOS OF LINES. i Directions to the Teacher. i. Draw a dog- kennel, as shown in illustration, on the blackboard, and i^^lain. 2 . Have it drawn in space at right. Place .points one inch from each corner. Bisect distance between points at top, then between points at sides. Draw the outer vertical lines and the lower horizontal Bisect distance between upper ends of vertical j 'ten bisect each half of the distance, and connect I these last points by a horizontal line. Draw vertical ) lines downward from its ends. Draw tlie oblique lines, j Exercise XIV. Give each pupil a number of two-inch j colored sticks or toothpick-s, and ask him to arrange them on page lo so as to represent some common object. For ‘ example, the chair on page 6 may be made by using fine j two-inch sticks. The hat, resulting from the dictation j on the same page, may be made by using three two-inch sticks and two one-inch. After the sticks are laid place a point at each end of each stick, remove the stick, and draw a line in itsplac-., thus transferrinjr >he picture to the page. 11 Exercise XV. fttJADKISECTING. Biaectiner a line and bisecting’ each half, or dividing into four equal pai-ts, la auadriaecting. Directions to the Teacher, i. Use blocks or pegs first, then lines on slates, and lastly in books. 2. First points one-half inch from comers ; others as shown in illustration. Quadrisect each line. Repeat the work in the second space given below. Strive to be more accurate than in the first. Note : Point B is found half way between the points in the lower comers of the space. Points 1,2,3 are found by quadrisecting the distance between points A and B. Find other points in same way. 9 Exercise XVII. APPLICATIONS OF PARALLEL LINES. Directions to the Teacher, i. Have these appli- cations drawn first on slates, then select two of them, and have them drawn in spaces at right. Points for positions of drawings, by half-inches and inches, as shown in illustrations. IszeFcisa XVIII. AFPUCAIIOHS OF PABMXEL UXES. Directions to the Teacher. Either cut a frame rom paper six inches square with sides one inch wide, nd have a drawing made from it in space at right, or di- ide the space, as shown in lower illustration, and make jwo drawings from a large book. Draw the front and back dges as shown. Points for corners one inch from sides ' space, and one>half inch from top, Bottom same. Sxercise XIX. PERPENDICULAR LINES, Lines forming- a square corner are perpendicular. Directions to the Teacher, i. Teach from objecUs. ^upils dra-w at board. Then have them dra-vv in the space at he right either the face of a cube standing upon one corner, ,s in the upper illustration, or the figure given above, the ■blique lines in a square. If the cube is selected, have it drawn as large as the pace will allow. If the lines in the .square, place first points one inch from omer. Before drawing this figure the pupils should study c carefully, and discover how to draw it accurately. (See Exercise XXII. REPETITION, When a number of forms or called a Repetition. Repetitions or obliquely. objects alike are placed in may be made horizontally, First. A GREEK BOEDER. Repetition of Parallel Lines. Second. A GREEK BORDER OF PARALLEL OBLIQUE LINES. Third. A GREEK FRET. A Border of Perpendicular Lines. Exercise XXIII. In the upper space on page 19. Make a drawing of the second ^ r given on this page. Place first points one-quarter of an inch from corners of space. By means of a rule place points one-half an inch apart in a straigh^ row between the upper left point and the upper right. Same between the lower two points. Draw free hand. i Exercise XXIV. In the lower oblong make three such rows of points, and draw the Fret free hand. DRAWING OF A GREEK BORDER COMPOSED OF OBLIQUE LINES, AND A GREEK FRET. Exercise I. EEVIEW.-HALF-INCH. Directions. Place points in space below, as shown in first illustration. First points one-half inch from corners ; then center point, etc. Exercise II. KEVIEW.-BISECTING. Exercises to be drawn bn slates, similar to second illustration. Put rings around points to make positions more evident. Exercise V. KEVIEW OF HORIZONTAL LINES. Strai^Lt, Level Lines are Hoi’izontal. Draw on slates lines as shown in first illus- tration. Part of the class draw on boards. Exercise VI. OBJECT, WITH HORIZONTAL LINES. Draw a box from the object in the space below, similar to second illustration. Points, one-half inch from corners. Draw horizontal lines from left to right. No erasing in any exercise in this book. +■ ii Exercise XI. EEVIEW OF PARALLEL LINES, PERPENDICULAR LINES, AND THE STUDY OF ANGLES. In Book 2 you studied about parallel edges and lines. Can you find any parallel lines on this page ? Any perpendicular lines ? Any lines near together, and yet neither parallel nor perpendicular ? Can you find two lines starting at a point and going in different directions? Can you find two lines starting at a point, and going in nearly the same direction ? Going in nearly opposite directions? The difference in direction of two straight lines inclining to a point is called an Angle. How many angles can you find on this page ? Lay angles, using sticks. Draw angles on board and slates, after finding angles in the room. Exercise XII. In the space below draw a number of angles, arranging them so that they will look well on the page. Remember, the size of an angle is not dependent on the length of its sides. o ( asRrr Directions to the Teacher. Teach from objects, the curved line. When studying edges two kinds of edges are found. What are they ? How is a straight edge represented ? How shall we represent a curved edge ? Review faces. Square face from a cube, and round face from a cylinder and hemisphere. Here is a picture of the round face of a cylinder. (Draw one on board.) Pupils select rings to represent faces of different sizes. Lay rings on paper and trace around them, then practice movement on slate, tracing around and around, as shown , i I, in the direction indicated by the figures. Exercise XIX. j Practice movement and drawing again on slate or manilla paper. A picture of a round face in a circle. Exercise XX. Trace around the circle, as indicated in the space at the right, beginning at point i, and passing round and round many times. Draw very lightly, that is, sketch. + SIMPLE CURVES. A circular curve is sometimes called APPLICATION OF ABCS COBVING UPWABD. Call pupil’s attention to the parallel arcs of the arches. Notice that all- the longer arcs are on the same level ; also all the shorter arcs. -> — I — ' — ^ — ' — 1 1 ! 1 1 T 1 1 1 , 1 A Exercise XXIV. BBIDGE. Make a drawing of a bridge with boys fishing, as shown in illustration. The guide- lines given above are to be used in determining the height of the arches, their width, etc. The longest horizontal lines may be sketched by use of a rule if too difficult to sketch freehand. Wlien all the lines are sketched, line in, as shown in illustration. If the boys are loo difficult for pupils to draw, they may be omitted. STTvrPT.T! CUKVES. — Arcs Curving Downward, and Application. These curves should be sketched from left to right with one movement of the whole arm. I . ^ ^ ^ 1 r-7-— H 1 1 ^ ^ ^ > 1 ^ 17 4 deawing peom objects. 7 Exercise XXVII. From a bowl or cup, similar to that shown in the illustration, make a large drawing in the space at the right. Have the pupils study the object carefully first, to determine the proportion. Notice the comparative width top and bottom. How does the width compare with the height ? Notice the angle, the slope of the sides as indi- cated in the illustration by the dotted lines. Sketch first, then line in. Exercise XXVIII. From a cup and saucer make a large drawing (full sise) on page 19. Study the objects first and determine the proportions; then sketch and line in with a bold gray line. Note. If this is too difficult, draw the wash- basin. This, like the saucer, may be represented by two straight lines and two curves. Note. In drawing a line, hold the pencil - 4 - SKETCHED LUOIS AND OTAWN LIKE, 5. t less than one inch from the point ; in sketching a line, two c H ^ — tH- Exerciso I. Place points for ohiique lines ne-half inch from corners of first space at the right. Com- plete, as shown in illustration. kEseiciso XI. Place points as in Exercise I, and complete, sketching the lines instead of drawing them. Exercise V. TRIANGLE. A piano fig'iire having' three aides and three angles. UiRKCTiONS TO THE TEACHER. Cut :i large number of triangles of different shapes and sizes from paper or cardboard ; draw others upon the board. From ' these teach triangle to the pupils. Lead them to discover for themselves the number and kind of sides, the number of angles, etc. Have them cut triangles of paper and draw them on board. Exercise VI. In the space below ask pupils to draw three triangles of such size as to fill the space well ; but no triangle to be exactly similar to any given in the illustrations. Exercise VII. EIGHT-ANGLED TEIANGLE. Triangles are divided into six classes, according to their characteristics. A right-angled triangle is a triangle having one right angle. Cut right-angled triangles from paper, of different sizes and proportions. Study from objects. On the left half of the space below draw from paper a right-angled triangle, similar to that shown in illustration. Draw large. Points, one-half inch from corners. Measure the size of your drawing, and cut a triangle like the drawing from colored paper, and paste it in the proper position upon the page. See illustration. APPLICATIOK OS’ RIGHT-ANGLED TRIANGLES. t: “ '\il IE ^11 , S“ ® ■'¥■ f ill- Ezercise VIII. In the .space at the riglit enlarge the drawing of the corner bracket shown in the illustration (the teacher having first made a bracket like this, and from it having explained the drawing). Exercise IX. Construct the bracket of paper (the heavy lines reprc.sent the lines to be cut). Make a crease through it on the vertical line. Fold edge a to b. The pupil may cither paste the two thick- nesses together, and thus put the bracket into j^ermanent shape, or he may paste the pattern in the space below, leaving that part above the horizontal and that to Ijic left of the vertical crease unpasted, so that the form may be easily folded into shape and laid out flat again. .11 w I. Oi Oi TEE ISOSCELES TE TANGLE. >r stand is c.alled its base. The vertical distance from tliis line to the highest poi IS equal-legged ; f.c. , having two legs or sides alilce. Exorcise X. Study isosceles trl.angle first from objects. When thoroughly understood, ask pupils to cut frotn colored paper an isos- celes triangle 314 inches by 4^.^ inches, and bring it for the next lesson. Exercise XI. Paste the triangle upon the left side of the page, and make a drawing of it upon the right. ini of the triangle is called MEMORY DRAWING AND DICTATION. the left-hand space belovv' make a memory drawing of Exercise XI. In the right-hand space make a drawing from a simple dictation given by the teacher. Exercise XIV. Exercise XV. ■i DRAWING FROM THE OBJECT. These illustrations represent suitable o^jjects from which to make drawings. Drawings of similar objects arc recommended for this page. _j ^ , . 1 , ^ ^ 1- , ; , Exercises XX and XXI. In making a drawing from an object, study the object care- fully before beginning to draw. Determine its whole height and its entire width. Compare these, thus obtaining the proportion of the object, and the amount of surface to be covered by the drawing. Indicate by light lines the width and height. Analyze the object and decide upon what line to draw first, what next, the How to Study ths Square. Directions to the Teacher. From cubes of various sizes, blocks, boxes, and pasteboard squares, teach the square. Lead he pupils to see that it is jounded by four equal straight tides, and that it has four right ingifig. Ask each pupil to cut i ^^Pre of paper four inches on ■Mude. Fold the square so that )ne side will cover the opposite ide. Fold for another crease at right angles to this. Notice vhere the creases cross each other, and how they divide the square. These creases form the diamehrs of the stjuare. Fold one corner )ver to the opposite corner. Fold again at right angles to this, £if., through the other corners. Notice how these creases divide he square. These foi ai the diagonals of the square. A square las two diameters and two diagonals. Question pupils closely as o the possibility of drawing other diameters and diagonals in a quare. Be sure that they all understand that the diagonal is not lecessarily an oblique line, but that it may be otherwise according 0 the position of the square. XXII. Place points one-half inch from corners of space at right. Con- ect points so as to form a square. Bisect each side of square, nd draw inner square, as shown in illustration. Draw the iameters of the larger square. cover. Exercise XXIV. SQTIABE WITS DIAMETERS AlfD DIAGONALS. Diameters always connect the niidtile of opposite sides'. Di agonals connect opposite corners, no matter in wliat [wsition ihi square may be. Enlarge the illustration in space 116101^ Corners one-h.alf inch from corners of space. Exercise XXV. FOiJJJ-POIKTED STAR IN A SQUARE. Ill spr.ce bclo-.v [iLice points oi;c-lir,lf inch from l!ic corners. Ske.teh lir.es, connecting tlio points so as to form a squ.ire. Sketch its cliamcters, aiul lii.ect each semi-diainotcr. Line in the figure, as siiown in illustration. E.xeroise XSVI. PIN-Y/HEEL. Cut a pin-'vheel, as shown in illustration, from paper; size, five inches siiraro. Make a drawing from it in space below. Corners one-half inch from corners of space. Pupils con.struct one from tlicir drawings. Lead the dotted corners over to the center, and in.'eri a pin in. position indicated by points. KEVIEW OF EIGHT-ANGLED TKIANGLE, AND APPLICATION. « i ! ECTIEW-WmATEEAL TEIAMLE AND APPLICATION. P.i O-AnWo., ■•. ..“"4 “ “"L . . ^ Of the base-line, set 0.1 its len-th upon the vertical Ime.complet BUAWIKG FBOM OBJECTS. Or to be used as the teacher thinks best. • Exercise IX. , Make a drawing from one or more objects on this page. The Ijlastrations are given to suggest I suitable objects, and to show the THE SaHAEE. Diameters and Diagonals. For definitions, see second page of cover. Diameters and diagonals will be best understood by folding pape^ squares to obtain them. square concentric with this. _ Can you fold a four and one-half inch paper square in such a way that, by making one cut. a central smaller square will be removed, leaving a square frame of paper, like that represented by your dr.awing ? Try it, THE SQUARE- APPLICATIONS. Dictation and square frame of paper. % Exercise XL DICTATION. Place points one -half inch from comers of space above. Sketch a square with these points as comers. Sketch its diagonals and bisect each semi-diagonal. Line in the outer quarters of each diagonal. Line in the top and bottom of the square. Draw a small square, using the points on the semi-diagonals as corners. Result — a spool. Exercise XII. Make a square frame of paper, as suggested on page 6, and paste SQUARE AND ITS DIAMETERS. AND APPLICATION. down. Result — a triangular basket. Draw the pattern in the space at the right. Begin with the center point. Pupils construct as shown in the illustration. Points shown in p^ern show positions of holes for the string to suspend the ®ket. Note : The basket may be ornamented in various ways. One effective way is to modify the corners. Each comer is, of course, a half square. These half squares may be cut like any of those shown on page 1 8. If the corners are thus modified, have the four corners alike. APPLICATIONS OF SQTJAEE ON ITS DIAGONALS. V For wall-pocket, cut an oblong from paper, size five by seven and one-half inches, and fold to obtain the light oblique lines shown in illustration. Cut as shown by heavy lines. i Exercise XVIII. In space at the right make a drawing from the pattern of oii'-. the wall-pocket. Begin in center. To construct the pocket, cut the pattern from paper, as indicated by the heavy lines (light lines indicate creases). Bring point a to and fold -^cr c over the short oblique edge near a, to form the 9 ii f c MEMORY-DRAWING AND DICTATION. Exercise XX. In left-hand space below, make a memory-drawing of some previous exercise. Exercise XXI. In right-hand sp.ace below, make a drawing from a dictation given by the teacher. APPLICATIOIf OP THE OBLOHG.- The Facca Brick. h— -r--— f-.— -H - Exercise XXIV. Have pupils study the shapes of the faces of a brick. Measure them. Find their proportions. In the lower left comer of the page are two points. Connect these by a vertical line. This line represents one short edge of an end face of a brick. Draw the other edges in proper proportion. Draw three faces, as shown in illustration. Have the drawings the proper size to correspond wi'h the drawing of the end face. % applications op the oblong. REEL. XHIT^ L/IZa Exercise XXV. To be constructed by tl Cut the reel from pasteboard two j and one-quarter inches by four and | one-q>: after inches, as shown in illus- | tration. Make a drawing from it in j first space at the right. Guide-lines j one-Vialf inch from the sides of the | obloug. j I Exercise XXVI. In the second space at the right make a drawing of a prettier shaped reel of your own design. Can you not improve upon tiie first reel drawn by adding curves here and there ? Be careful to add only such curves as will increase the beauty of the object with- out interfering with its use. le pupil. APPLICATIONS OF TRIANGLES IN BORDERS— Repetition. The units in both borders are examples of modified geometric forms. Both are Isoscele Triangles, one with the point removed, the other with its base notched BORDER OF ISOSCELES TRIANGLES.-To be Completed. This border may be constructed by cutting the units of colored paj^er and pasting on a card. PEACTICE PAGE. Review of Light and Dark Lines, Sketching and Drawing. Exercise I. These illustrations are given as sug- gestions of blackboard exercises for practice in free bold drawing. Six exercises are illustrated. Have the pupils sketch and draw upon the board from dictation, and in unisonj one or two of the.se exercises. Exercise II. In the space at the left draw the figure given below. Place points first, then sketch each line once. No erasing. KEVIEW. -Square on its Diameters, with Diagonals. Exercise III. Place point in center of space. Sketch horizontal diameter, extended to within one-half inch of each side. Complete as shown in illustration. In the space at the right enlarge the illustration given above it. Beginning with the central point as before. 1 1 1 > 1 1 1 1 EEVIEW. Square on its Diagonals, with Diameters. ,1 Exercise IV. What will be the size of a paper square whose conurs «) touch the ends of the diameters in your drawing at the left Cut a square of the proper size to meet these conditions, a paste over your drawing. Cut square to fit in the drawing! the same way. Paste it in position. , Sxereige V. To be constructed by the pupils from the drawing. Place points one-half^nch from corners of space at the right. Draw the outside square, using these for the corners. Draw the aside squa^. Points one-half inch from corners of larger square, i’risect its four sides, and draw lines to form the small squares, psmplete as shown in illustration. • Cut a six-inch sc|uare from paper I ^ ^ ^ . T- APPLICATION OF THE SQUAKE.— An Envelope. and modify it as shown by heavv lines^n illustration. Fold upper right and lower left corners over to center first, then fold others. Result, an envelope about four inches square. 4 PATTERN FOR A SatTARE ENVELOPE. Place points one-half inch from corners of space at the right. Sketch the square. Sketch its diameters and diagonals. Place points one-quarter inch from each end of each diameter. Complete as shown in illustration. Pupils to construct an envelope from their dravn'ngs. 1 THE EHOMBUS. A rhombus has four equal sides like a square, but not four right angles. Parts of the rhombus, similar to parts of the square, have similar names. r— ' — +“---' — r--- '-! -I --I-- r - -I 1 1 1 -I- \ , Exercise Xm. ONALS. Place point i i I i I EHOMBUS AHD ITS DIAG- in center of space above. j Exercise XIV. DICTATION. Place points one-half inch from each corner of space above. Quadrisect at top and bottom. Line in last three quarters at top, and first three quarters at bottom. Connect ends of lines so as to form a rhombua. APPLICATlOir OF KHOMBXTS IN DESIGN.— Symmetry. When a figure may be divided into two equal and similar parts by a line through it I — ^ — , — r—i—T—T—r 1 r- r ^ s said to be symmetrical. The line is called its axis of symmetry. ^ , 1 , _ 1 , Exercise XVI. Place points one-half inch from middle of each side of space. Sketch the diagonals. Sketch the rhombus. Sketch its diameters. Divide diago- « ls to obtain points for cen- 1 rhombus. Quadrisect its sides, and from these points , J' sketch lines parallel to diamc- !;■ ters, as indicated. Complete. Would this figure be any ; more pleasing if all the rhombs were the same size ? t'ut five equal rhombs from paper, and arrange them in the position indicated. If you think the eti'ect is more pleas- j ing, paste them on the page | to cover your drawing. THE OCTAGON. — Oa its Diameters. For definition, see secoi.d page of cover. Cut an octagon from paper, and fold for diameters and diagonals. I ■ I ' I ■ r-n 1 1 f ^ H- 1 h- 1 ^ r- Place points one-half inch from corners of space at the right. Sketch the square. Sketch its diagonals. From each corner of the squaie set off the length of a semi-diagonal upon each side of the square. Connect the points so as to form the octagon. Sketch the diameters of the octagon. Line in as shown in illustration. Add a concentric circle having a diameter equal to one-half the diameter of the octagon Can you fold a sheet of paper in such a way that by making one cut with the scissors an octagon will be formed? Try it. i IKE OCTAGOIT.— On its Diagonali. The octagon on its diameters was drawn in a square ; this octagon outside of two concentric squares. Ixercise SIX. j Place points one-half inch from the middle of each side of space i the right. Sketch the vertical and horizontal lines for the diago- als of the first square. Sketch the square on its diagonals. Bisect ich side. Sketch its diameters. Extend each semi-diameter beyond ^e sides of the square to the length of a semi-diagonal of the square, raw the octagon as shown iu illustration. Add a concentric octa- on having diagonal-s three-quarters of an inch shorter each end. ' Can you fold a sheet of paper in such a way that by making two iraight cuts with the scissors an octagonal frame will be made? REPETITION OVER A SURFACE. TTnits. Exercise XXIII. In the space at the left are given a number of modified geometric forms | suitable to be used as units. Which of these do you consider to be the bestil unit? Why? Which do you consider next best? In the left-hand space i below make a careful enlarged copy of one of the units. Exercise XXIV. In the right-hand space make a careful enlarged copy of another unit | given in the illustration. EEPETITION OVER A SURFACE. Orig-inal Units. c c Exercise XXV.— In the space above sketch two original units (modified squares) — one a unit to be repeated in a field like Fig. i. the other to be repeated in a field like Fig. 2. Sketch them as large as the space will allow. Exercise XXVI.— Which kind of a field do you prefer to use— Fig. i or Fig. 2? Using a ruler and drawing accurately, lay out the selected lines in the space given on page 19. If you have selected Fig. i, make your squares inch on a side. If Fig. 2, 2 % inches. At home, cut a unit like that which you have drawn, of such a size that it will fit into the spaces of your field on page 19. Exercise XXVII.— Trace the units in their proper positions. Exercise XXVIII. — Line in the design. i^u REVIEW.— The Octagon. Insist upon free drawing and unison work. Exercise V. CONCENTRIC OCTAGONS. In the space above, draw the figures in the order shown in small illustrations. First points one -half inch from comers of Exercise VI. DICTATION. Find center of space above. Through this point sketch the four diagonals for an octagon — ^units, diagonals. Sketch the octagon. Trisect each semi-diagonal. Use the inner thirds as diameters for a circle. Sketch the circle. Trisect each side of the octagon. Sketch lines from these points to the center. Line in circle. ' Line in outer Call to mind the forms of snow crystals. If possible, show two or three illustrations of them to the pupils. Analyze the figure to be drawn before beginning the drawing. Study the construction, as shown in small illustrations. Place points one-half inch from the middle of the left and right sides of the space at the right. Sketch the hexagon as in Exercise VIII. Complete as shown in illustration. „ 1 ! Note. — Some excellent illustrations of snow crystals may be found in “Cloud Crystals, a Snowflake Album ” f Appleton, N.Y.). THE HEXAGON IN NATURAL FORMS. Many of the forms in nature are based on geometric plans. Two illustrations of this are given on this page. One the leaf of a tulip tree, the other the flower of the anemone. (Conventional drawings of them.) If possible, obtain a leaf of the oxalis or wood sorrel, and a flower of the sassafras or the yellow star flower (hypoxis), and study those instead of the illustrations. Decide upon which you will draw. Sketch the construction lines. Exercise XV. -b,... rw rlrawinrr APPLICATION OF THE PENTAGON.-SILK-KEEL. — r ■f -T 1 To be enlarged in space below, as shown in illustration. Pupils make a pentagon from paper one and one-half Exercise XIX. >v V- ^ ^ inches on a side, and | Jise in obtaining position of ligure in space. Sketch as shown in illustration. Exercise XX. In the space at the right sketch a design for a pentagonal silk-reel. That given above is bounded by straight lines. Your original design may be much better in shape. ■ APPLICATION OF PENTAGON-DICTATION Place points for a pentagon of such a size as to properly fill the space the right. Sketch lines as follows : top point to lower left ; top to lower jht ; upper left point to upper right ; upper left point to lower right ; )per right point to lower left. Line in a five-pointed star, and erase the )rtions of the light lines not used in fonning the outline of the star. Upon page 8 were given natural forms based on the hexagon — here are given two of the almost unlimited number of forms based on the pentagon. One an ivy leaf, the other the flower of the convolvulus. Exercise XXII. Study leaf forms based on the pentagon, and in the left space on page 13 make a conventional drawing of one — i. e., draw the general shape — omitting all serrations and all veins but the midrib. (Currant, maple, wood- bine, etc., are good examples. ) Exercise XXIII. Study flower forms based on the pentagon. Make a con- ventional drawing of one in the right space on page 13. (The rose, apple, peach, and pear blossoms, blackberry, cherry, etc., are good examples.) APPLICATION OF PENTAGON. ^'1 . 'iiy DESIGN.- REPETITION AROUND A CENTER. Units of design in these exercises consist of geometric forms, modified. In modifying a unit, retain the general shape of the original form. 1 1 , 1 , ^ , 1 1 1 C 1 I I I ' I Exercise XXVI. Complete the design above. Study carefully the construction of the design. Continue lines of the units, and notice what figures they form. Sketch design first, then line in units and the inclosing form. Use the rule (and eraser, if necessary) and make such an accurate drawing that it will be almost impossible to detect which is the m and which the printed line. Exercise XXYIII. A SYMMETRICAL UNIT. Exercise XXIX. COMPLETE THE UNIT. -V f APPLICATIOirS OF CIE'DISS.—From Objects. Obtain objects to illustrate this lesson, if possible. Have drawings made from them. T Phe upper fi.giire Is the draw- ? of a wlilrligie cut from thin ood or metal; the lower, of a dket pm-ca.se, made of paste- ard and covered with cloth, th the initial of the pupU »ked upon one side, as shovm. ExeMJce V. In the first space above, make a drawing from a whirligig. Sketch the horizontal diameter of the circle first; bisect it; sketch the vertical diameter; sketch the circle; line in, and add the little circles for the holes for the string. Boys to construct one from their drawings. Use thin hard wood if possible ; pine will do, but hard wood better. Fsercise VI. In the second space above, make a drawing from a pocket pin-case (see illustration). Sketch as in last lessen ; line in the circle. Each pupil put his own initial on this drawing. To construct: cut two circles like the drawing from pasteboard, and cover each with cloth; place them back to back, and sew them together around the edge. If the initial is to be worked, it should be made on one piece of the covering before it is sewed upon its circle of pasteboardo ' ^ „ ELLH’SES AKD APPLICATIOITS. The four quarters of an ellipse must be alike. Remember this in drawing Exercise XIX. ' — I — 1 — I—. — I 1 1 r— I 1 1 r 1 1 1 . ---I ELLIPSES PLACED OBLiaUELY. Exercise XTg. i V. In the space above, draw three ellipses upon the diameters given as • guide-lines. Notice that the two diameters of an ellipse are always at right angles to each other, and always bisect each pther, no matter what the position of the ellipse may be. Practice drawing oblique ellipses without sketching their diameters. SngMOR-y.DEA’WnSTG AOT> DESIGW. ^ _ . Zeroise Tm. In left-hand soace below, make a memory-drawing of some figure previously dra^-in this book. Exemse Z^T. deriving its curves from those found in the historic ornament on page l6. Make the vasd siimlai to that in rxercisc XXV .1, _| — ^ p__T 1- ^ j — , 1 — — — i 1 I ; I -i In right-hand "Spac^b^lpw, draw a vase form, t r WHITE’S NUMBERS Book Number One embraces the work .of the first half of the first school year, and is intended for the use of teachers. In it the general analysis of the lessons is laid down, the materials to be employed are enmnerated and dpscrbed, and methods are given with some detail. A prominent feature of this book is the complete exposition of the proper use of clay and clay modeling in the teaching of form to young children. The work of each week is designated, and a sufficient number of illustrations given through- out the book to make clear the author’s meaning at every point. Book Number Two (second half of first school year). According to the |Jan of the series, this is the first book which is to be placed in the hands of the pupils. Beginning with training pupils to judge distances, it proceeds with straight lines and applications ; the division of lines and their relations ; and in- cludes the construction of a'^iumber of simple objects which the pupils'are supposed to make. Book Number Three first reviews the principles taught in the previous book, and teaches the angles and their applica- tions, both in objects and in symmetrical figures ; of triangles, with their applications, and the construction qf objects based . thereon, and concludes with the ^ymrnetrical repetition of trian- ■ gular forms, as seen in borders, etc. Book Number Four, 'after reviewing the principal ele- ments embraced in the previous book, continues with triangles _and their applications, and takes up the square, its parts, divis- ions, and applications, and introduces memory drawing, dictation, and drawing from the object. In this, as in the previous books, a number of examples are ^iven, which the pupils are required to construct from their own ara wings. DRAWING— REVISED. TO EIGHT. Book Number Five extends the work of Book Four, and takes up’ the drawing and construction of somewhat more diffi- cult objects; the oblong, and rix-pointed and eight-pointed sta'rs; while the application of each of these figures in objects and decoration is introduced. Book Number Six reviews the principles of Number Five by having the pupils draw and Cut out familiar objects based upon the square and the oblong. The rhombus, its application in object drawing and decoration, are given, -and the construction of the octagon and hexagon is shown, with practical applications; and as a special feature of this book, the principles of radial design are illustrated. Opportunity is given in this, as in other books, for memory drawing, dictation drawing from the, objects, and for examination. Book Number Seven , introduces a method of drawing the pentagon, its applications in familiar objects and in decorative design; and also here, for the first time, begins the systematic study of simple curves. The treatment of curves is original and practical, and the applications given^afe of the most valuable and instructive kind. Radial ornament is further illustrated, and elements are given from which the pupils* may select for original arrangements. Book Number Eight introduces the circle and its parts, with practi|Ce in drawing free-hand circles as employed in ornament and in the drawing of objects. The ellipse and the oval are taught; and in this book, for the first time, an instruc- tive study of some of the simpler principles of historic ornament is taken up. THE ALPHABET OF MANUAL TRAINING. WHITE’S INDUSTRIAL DRAWING REVISED THE SIMPLEST . THE MOST PRACTICAL ♦ THE MOST COMPLETE » THE MOST EASILY TAUGHT. ' Numhers 1 to 8, t COMPLETE IN EIGHTEEN BOOKS. i 3 6x9 inches^ 20 pages. Numbers 9 to 18, size 8x11 inches, 20 2 every for the first year of school life, The new edition of Whi ' numbered consecutively from No. 1 upward, to be followed in order in the series. , , „ „ industrial Drawing is believed to give more practical instruction with less waste of time than any system heretofore publ«hed. Form, the language of form, and the different modes of form-representation. logically taughl, while the aesthetic side of the subject of drawing receives proper a etiZ;rTrcon^^^ tLt’ the instruction given in Historic Ornament, and the work based thereon introduced in their appropriate places. While drawing from ■ - - • “ ■ j scale for the pur- classic design, and p».ko p.«,».r »»p. .n.„-p ...... The use of objects in teaching and the making of objects drawn are distinguishing features of the system. numbers nine to eighteen. The work introduced in the lower numbers is continued and extended, and the more technical subjects are .PJ..B P..n rrop, ... nr.,, .h. .hr..,P ». .p.*«.rKj. .. .. ... rir; .s rrr:,r.'r,„".r:“ J ... ........ .. * Special terms for introduction. 'IVISON, BLAKEMAN & COMPANY. PUBUSHERS, . NEW-YORK AND CHICAGO. 3 0112 077867361