UC-NRLF 
 
 
THE 
 
 TEACHING OF DRAWING 
 
 BY 
 
 I. H. MORRIS, Art Master 
 
 AUTHOR OF 
 'GEOMETRICAL DRAWING* AND 'PRACTICAL PLANE AND SOLID GEOMETRY 
 
 THIRD EDITION 
 
 LONDON 
 LONGMANS, GREEN, AND CO. 
 
 AND NEW YORK : 15 EAST 16 th STREET 
 1894 
 
 Ail rights reservzd 
 
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 PREFACE 
 
 The object of this manual is to provide a fairly complete 
 course of methodical teaching in drawing, as required in Ele- 
 mentary schools by the Department of Science and Art. It is 
 universally admitted by all who have either to supervise or to 
 examine the work done in schools, that there is abundant room 
 for improvement in the method of teaching this important 
 subject. 
 
 The methods, hints, and suggestions given, are the outcome 
 of an extensive practical experience in Elementary Schools, 
 Art Night Classes, and Schools of Art ; and although doubtless 
 familiar to some, the author ventures to hope that they will be 
 of material assistance to many who may not have had the 
 opportunity of receiving a special training in drawing. 
 
 The book contains about 700 illustrations, which have 
 been specially drawn for the purpose. The Freehand examples, 
 which are mostly shown in stages, may be divided into three 
 sections, viz., Conventional Ornament, Plant Forms, and 
 Common Objects. Many are original drawings, others are 
 based upon examples from the Illustrated Syllabus, Dyce's 
 Drawing Book, Examination Tests, Casts of Ornament, &c. 
 They are selected to illustrate definite principles which the 
 teacher may readily apply to other figures. Considerable space 
 is devoted to the teaching of Scale Drawing, Model Drawing, 
 
 295686 
 
i v The Teaching of Drazving 
 
 and Solid Geometry, as these parts of the subject require the 
 most skilful and intelligent teaching. 
 
 Especial attention is directed to the large number of speci- 
 men lessons. These are given chiefly with a view of affording 
 assistance to young teachers and those who may not have had 
 much practical acquaintance with the subject. 
 
 I. H. M. 
 
 Sheffield : August 1893. 
 
CONTENTS 
 
 CHAPTER I 
 
 INTRODUCTION 
 
 PAGE 
 I 
 
 CHAPTER II 
 
 INFANT SCHOOLS 
 
 Code requirements . 
 
 
 3 
 
 Apparatus . 
 
 
 . 
 
 4 
 
 Use of Crayons. 
 
 
 ., 
 
 5 
 
 Upright Lines , 
 
 
 . 
 
 6 
 
 Level Lines 
 
 
 , 
 
 7 
 
 Combinations of 
 
 Upright 
 
 
 and Level. Lines 
 
 . 
 
 8 
 
 Prets . 
 
 
 
 lO 
 
 Objects composed of Up- 
 right and Level Lines 
 
 Slanting Lines and Pat- 
 terns composed OF 
 Upright, Level, and 
 Slanting Lines . 
 
 Objects ..... 
 
 12 
 
 16 
 
 20 
 
 CHAPTER III 
 
 STANDARD 1 
 
 Syllabus and Apparatus . 
 Introductory Lesson 
 Method of using Pencil 
 
 and Ruler . 
 Lesson. Horizontal Lines 
 Vertical, Oblique, and 
 
 Parallel Lines . 
 Arrangement of the 
 
 Drawing .... 
 Angles .... 
 
 23 
 
 Lesson. The Square 
 
 33 
 
 24 
 
 Dictated Drawing. Dia- 
 
 
 
 meters and Diagonals 
 
 34 
 
 26 
 
 Lines intersecting at 
 
 
 27 
 
 Right Angles 
 Bisection and Trtsection 
 
 35 
 
 29 
 
 of the Eight Angle. 
 
 37 
 
 
 Examples .... 
 
 39 
 
 30 
 31 
 
 Memory Drawing 
 
 42 
 
VI 
 
 The Teaching of Drawing 
 
 CHAPTER IV 
 
 STANDARD II 
 
 PAGE 
 
 Syllabus and Apparatus 43 
 Ruler work. Parallels 45 
 Perpendiculars . . 46 
 
 Curves and Common Ob- 
 jects .... 48 
 
 CHAPTER V 
 
 OF 
 
 Syllabus . 
 Freehand Drawing 
 Curved Figures 
 
 ,, First Stage 
 
 ,, Second Stage 
 
 ,, Third Stage 
 
 ,, Lesson 
 Examples . 
 
 Freehand Drawing i 
 Right-lined Forms 
 
 STANDARD III 
 
 
 
 
 52 
 
 Drawing of Geometrical 
 
 F 
 
 Figures with Rulers 68 
 
 52 
 
 Lesson 
 
 69 
 
 53 
 
 Examples . 
 
 
 
 7i 
 
 53 
 
 Triangles . 
 
 
 
 76 
 
 . 55 
 
 Zigzags 
 
 
 
 78 
 
 . 58 
 
 The Hexagon 
 
 
 
 79 
 
 . 61 
 
 F 
 
 Lesson 
 
 The Octagon 
 
 
 
 81 
 
 82 
 
 . 66 
 
 The Pentagon 
 
 
 
 83 
 
 CHAPTER VI 
 
 FREEHAND DRAWING. STANDARDS IV-VII 
 
 Lesson 
 
 Examples. Standard IV 
 
 V 
 
 Method of drawing 
 
 Vases .... 
 
 86 
 89 
 99 
 
 99 
 
 Lesson . . , ^ . 104 
 
 Examples. Standard VI 116 
 
 VII 128 
 
 CHAPTER VII 
 
 SCALE DRAWING. 
 
 Syllabus and Apparatus 
 Introductory Lesson 
 Construction of Scales. 
 Lesson .... 
 Examples .... 
 Drawing to Scale on 
 Plain Paper 
 
 134 
 136 
 137 
 138 
 140 
 
 142 
 
 STANDARD 
 
 IV 
 
 
 
 Drawing 
 
 ON 
 
 Squared 
 
 
 Paper . 
 
 
 . 
 
 147 
 
 Enlarging 
 
 OR 
 
 Reducing 
 
 
 A GIVEN 
 
 Fig 
 
 ure. 
 
 151 
 
 Lesson 
 
 
 . , 
 
 151 
 
 Tests . 
 
 . 
 
 . 
 
 154 
 
Contents 
 
 vu 
 
 CHAPTER VIII 
 
 PLANE GEOMETRY. STANDARDS V AND VII 
 
 
 PAGE 
 
 
 PAGE 
 
 Syllabus and Apparatus. 
 
 
 Tests . 
 
 . 164 
 
 Standard V 
 
 156 
 
 Syllabus. 
 
 Standard VII 166 
 
 Lesson .... 
 
 158 
 
 Tests . 
 
 . 167 
 
 Examples .... 
 
 159 
 
 
 
 CHAPTER IX 
 
 SOLID GEOMETRY. STANDARDS VI AND VU 
 
 Syllabus and Apparatus. 
 
 
 PENDICULAR NOR 
 
 
 Standard VI 
 
 172 
 
 Parallel to the V.P. 
 
 185 
 
 How to make Models . 
 
 173 
 
 Plane Figures 
 
 187 
 
 Plan and Elevation 
 
 176 
 
 Sections .... 
 
 189 
 
 Solids Standing on a 
 
 
 Tests 
 
 194 
 
 Face .... 
 
 180 
 
 Syllabus. Standard VII 
 
 197 
 
 Lesson I . 
 
 180 
 
 Easy positions of the 
 
 
 Lesson II . 
 
 181 
 
 Circle, Cylinder, and 
 
 
 Lesson III ... 
 
 182 
 
 Cone .... 
 
 197 
 
 Solids Standing on an 
 
 
 The Circle 
 
 198 
 
 Edge .... 
 
 i*3 
 
 The Cylinder and Cone . 
 
 200 
 
 I. Edge Perpendicular to 
 
 
 Sections. The Sphere . 
 
 201 
 
 the V.P. . 
 
 183 
 
 ,, The Cylinder 
 
 202 
 
 II. Edge Parallel to the 
 
 
 ,, The Cone 
 
 203 
 
 V.P 
 
 183 
 
 Tests 
 
 205 
 
 III. Edge neither Per- 
 
 
 
 
 CHAPTER X 
 
 MODEL DRAWING. STANDARDS V AND VI 
 
 Syllabus. Standard V . 208 
 Introductory Lessons 209 211 
 Arrangement of the 
 
 Models . . .212 
 The Cube. First Lesson . 212 
 
 ,, Second Lesson 214 
 
 ,, Third Lesson. 215 
 
 Common Errors . .215 
 The Square Prism, Frame, 
 
 Box, Slate and Book 216 
 
 The Cylinder, Axis ver 
 tical. First Lesson 
 ,, Axis hori 
 
 zontal. Lesson 
 
 The Cone . 
 
 The Box, Open Book, Cy 
 linder and board, 
 Cone and Slate, Jar, 
 Jugs, Gallon Bottle, 
 Roller, Saucepan 
 
 218 
 
 220 
 223 
 
 224 
 
Vlll 
 
 The Teaching of Drawing 
 
 The Hexagonal Prism. 
 Axis vertical. Les- 
 
 PAGE 
 
 The Cylindrical Ring . 236 
 
 Vases .... - 237 
 
 sons .... 229 j Syllabus. Standard VI . 242 
 
 ,, Axis horizontal 231 Groups and Common Ob- 
 
 The Triangular Prism, jects .... 242 
 
 Pyramids . . . 234 ' 
 
 CHAPTER XI 
 
 LIGHT AND SHADE. STANDARD VII 
 
 Syllabus .... 248 
 
 Materials. . . . 248 
 
 First Lesson . . . 249 
 
 Second ,, The Cube . 251 
 
 The Cylinder . . . 254 
 
 The Vase .... 
 Shading from Casts 
 Method of Shading the 
 Cast .... 
 
 256 
 256 
 
 259 
 
 CHAPTER XII 
 
 THE ELEMENTARY DRAWING CERTIFICATE 
 
 Requirements for First 
 
 Class Certificate . 262 
 
 Requirements for Second 
 
 Class Certificate . 262 
 
 Elementary Stage Free- 
 hand .... 263 
 
 Elementary Stage Model 263 
 Elementary Stage of 
 
 Shading from Casts. 266 
 Elementary Stage of 
 Practical Plane and 
 Solid Geometry . 267 
 
THE 
 
 TEACHING OF DRAWING 
 
 CHAPTER I 
 
 INTRODUCTION 
 
 Now that Drawing is practically compulsory ' for boys in schools 
 for older scholars,' as a condition of earning the annual grants, 
 it is absolutely necessary that it should be taught intelligently, 
 systematically, and thoroughly. By intelligent teaching is 
 meant the training of the eye to see, the mind to think, and the 
 hand to carry out the representation of the forms seen, or the 
 conceptions formed in the mind. Drawing taken without 
 method is neither useful nor interesting to the pupil, whereas 
 when well taught it is the most pleasurable and fascinating sub- 
 ject taught in our schools, providing, as it does, a complete 
 change from the ordinary routine of school work, and calling 
 into exercise faculties which otherwise would not be properly 
 developed. 
 
 It is now a well-established fact, based upon actual experi- 
 ence, that with very few exceptions all children may be taught 
 to draw. They will not all arrive at the same pitch of efficiency- 
 some can only crawl while others walk or even run. The ad- 
 vantages of a training in drawing from an educational point of 
 view alone are quite sufficient to justify its position as a most 
 important branch of school work. The powers of the eye, the 
 hand, and the mind are all more fully developed ; habits of 
 
 i B 
 
2 ,,, , The TeacJiing of Drawing 
 
 neatness and' careful' observation are formed, ability to perceive 
 anda^rfet^aie.b^aO^ojf forni is cultivated, and the imaginative 
 and inventive' faculties are 'all' fostered and increased. In addi- 
 tion to these points, we may mention its great importance in 
 connection with industrial and commercial pursuits. It is the 
 one part of technical education that can be well and easily done 
 in ordinary schools. 
 
 To secure success the teacher must be enthusiastic in the 
 work, and continually adding to his or her own store of art 
 knowledge, or the work will become mechanical and uninterest- 
 ing. Collective teaching from the blackboard will do more 
 than anything else to stimulate the teacher's energy, and as 
 large copies are now chiefly used for testing the work done, and 
 the necessities of schools require large numbers to be taught 
 simultaneously, it has now become imperative that the same 
 methods so successfully used in teaching other subjects should 
 be applied to drawing. The old plan of giving out copies and 
 the teacher going round to each pupil individually, is rapidly 
 and deservedly becoming a thing of the past. The advantages 
 of blackboard teaching are so obvious that they scarcely need 
 repetition : the great saving in teaching all the class the same 
 thing at the same time, the ease with which errors can be 
 pointed out and difficulties illustrated, the demonstration of 
 proper methods of procedure, the stating of the reasons for 
 the various steps taken, and the fact that the pupil is encour- 
 aged to try and imitate what he sees the teacher doing, are 
 reasons quite sufficient to justify its adoption. The teacher is 
 also enabled to more effectively supervise the work done, and 
 can grade his lessons so that one naturally follows from the 
 principles last taught. 
 
 I would here point out that it is not at all necessary that 
 the teacher of drawing in an elementary school should be an 
 artist : extensive practical experience has clearly shown that 
 the ordinary teachers of the school, even when not possessed 
 of much artistic ability, can by preparation and careful atten- 
 tion to good methods produce excellent results in the element- 
 ary work. 
 
CHAPTER II 
 
 INFANT SCHOOLS 
 
 Drawing in infant schools is somewhat beyond the scope of 
 this book, which is written more with a view of dealing with the 
 teaching of drawing as required in schools for older scholars by 
 the Science and Art Department, and which the teachers must 
 necessarily thoroughly master to meet the requirements and 
 earn the grants. This money payment hampers and restricts 
 in many ways, by confining all to one hard and fast line. Many 
 would like to vary the course or introduce fresh matter, but 
 there is not time to do both, and to earn the payments it is 
 necessary to keep to the beaten track. 
 
 In infant schools this is not the case to so great an extent, 
 the teacher having a little more freedom of choice. The Code 
 now offers a grant of one shilling on the average attendance of 
 the boys if drawing be satisfactorily taught, and as drawing is 
 now obligatory for boys in schools for older scholars, it certainly 
 appears more rational that the infant boys should draw instead 
 of practising needlework. In circular 291 to H. M. Inspectors 
 the Education Department states, ' That drawing may be taught 
 to boys in infant schools on the lines of the Froebel system. Slates 
 ruled with crossed lines, making squares a quarter of an inch 
 wide, should be used, and on them the children should be made to 
 draw perpendicular, horizontal, and diagonal lines. 
 
 ' Interest may be given to the exercise by making figures or pat- 
 terns out of the combinations developed in this practice ; but the 
 mam object of the teaching should be the training of the hand to 
 execute with nicety and precision, and the eye to discern degrees of 
 variation in the straight lines from the perpendicular or hori- 
 
 b 2 
 
4 The Teaching of Drawing 
 
 zontal, and to compare and judge the relative lengths of the lines 
 and the angles made by their junction? 
 
 Article 98/; of the new Code prescribes simple geometrical 
 drawing as one of the employments which best satisfy the 
 third of the requirements necessary to obtain the highest 
 grant. 
 
 Drawing can be readily carried out without much additional 
 expense : the children simply require chequered slates ruled in 
 squares about a quarter of an inch wide, and the teacher a black- 
 board ruled with red lines forming squares two inches in width. 
 Red lines are preferable to white, as the chalk marks can be more 
 easily distinguished. Cards and copies are only necessary for 
 the use of the teacher, and those should be selected which 
 show patterns and representations of objects treated in the 
 flat that is, showing only length and breadth. Copies showing 
 thickness should not be taken, as infants are quite incapable 
 either of understanding or representing these successfully. 
 
 There are numerous Kindergarten books and cards 
 published from which the teacher may select the material for 
 the lessons, which may also be made a powerful aid in teaching 
 number and imparting general information. 
 
 In the following suggestive course, the patterns are largely 
 based upon the Department's circular, as there is plenty of 
 instructive and interesting matter embodied in the three posi- 
 tions of lines, upright, level, and slanting, and the great variety 
 of combinations that may be made from them. 
 
 Endless and wearisome repetition of lines in any particular 
 position should be avoided, as the child will probably draw the 
 second line quite as accurately as the twentieth. The lines 
 may also be varied in length and symmetrically arranged so 
 as to form a simple pattern from the beginning, thus adding 
 variety and interest to the lesson as well as training the eye in 
 habits of observation. The examples given are not intended 
 to be exhaustive, but merely indicative of the method of proce- 
 dure. A few suggestive questions and hints are here and there 
 given as a guide to young teachers. 
 
 The children should be taught to draw the lines from top 
 to bottom, and from left to right. In beginning a copy, the 
 
Infant Schools 5 
 
 teacher should mark the position of one of the left hand 
 corners by a small dot on the board ; this should be repeated 
 on the slates by the pupils. The number of squares required 
 for the line should be counted and a small dot made to 
 indicate the end of the line. The two dots should now be 
 joined. This method should be followed throughout, as the 
 pupils work more accurately and systematically by this means. 
 
 As the children advance to the drawing of simple patterns, 
 portions of the copy may be emphasised by shading, as shown 
 in figs. 49, 50, &c. This adds to the appearance of the draw- 
 ing, and is valuable as a means of directing attention to the 
 shapes of the spaces. As further progress is made, crayons or 
 coloured chalks may be used. For example, if the shaded 
 spaces in figs. 49, 50, &c, are suitably coloured, a great charm 
 is added to the work. In other copies, two colours might be 
 used, thus producing a very pleasing effect. 
 
6 The Teaching of Drawing 
 
 Upright Lines 
 
 Question on the kind of line. ' Straight.' ' Upright.' Illus- 
 trate what ' upright ' means by a piece of string with a weight 
 attached. Elicit plenty of examples, and take the walls as 
 a basis. Explain use of plumb line in building a wall. Why 
 
 
 
 
 
 
 
 
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 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 must the wall be upright ? Illustrate with a pile of books or 
 wooden bricks, showing that they will fall if not upright. 
 What are the walls made of? What is the man called who 
 builds with bricks, &c. ? How long is the first line ? How 
 many of the first make one of the third ? How many lines are 
 there ? How many are of the same length ? &c. 
 
Infant Schools 
 
 Level Lines 
 
 Proceed in a similar manner to that suggested in dealing 
 with upright lines. 
 
 Take the floor as the object of comparison. Elicit the 
 various parts of the room and furniture that are level. 
 
 
 
 
 
 
 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Show with a glass of water that the surface of the water is 
 always level, while the surfaces of solids will remain in whatever 
 position the object may be placed. 
 
 Recapitulate the facts concerning upright and level lines, 
 and give plenty of illustrations. 
 
The TeacJiing of Drawing 
 
 Combinations of Upright and Level Lines 
 
 How many upright lines in fig. 10 ? How many level ones ? 
 How many lines altogether ? What is the figure ? What do 
 we call the point where two sides meet ? How many corners 
 
 
 
 
 
 
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 are there? Are they all alike? Elicit plenty of illustrations 
 showing how common this corner is. Show that there are 
 corners of different sizes, and let the children test whether the 
 corners are right angles, by fitting in a book or a slate. Explain 
 why fig. 1 1 is not a square, and draw it in different positions. 
 
Infant Schools 
 
 
 
 12 
 
 
 
 
 
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10 
 
 The Teaching of Drawing 
 
 Fret patterns afford a great variety of pleasing exercises, 
 and give excellent practice in cultivating habits of observation 
 and accuracy. 
 
 Plenty of illustrations showing the use of this ornament in 
 
 
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 the decoration of borders of oilcloths, carpets, wall-papers, &c, 
 can be easily shown, thus adding interest to the lesson. 
 
 The numbers placed beside the lines show the order in 
 which they should be drawn. To make this perfectly clear, 
 fig. 19 is shown in its three, and fig. 20 in its five, separate 
 stages of development. Each of these steps marks a stage 
 
Infant Schools 
 
 II 
 
 
 
 
 
 
 
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12 
 
 The Teaching of Drawing 
 
 when the slates should be examined, and forms a complete 
 copy in itself, increasing in difficulty towards the last. The 
 
 
 
 
 
 
 
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 children also are being unconsciously trained in the proper 
 method of building up a pattern. 
 
 The various objects should all be explained and questioned 
 upon for a few minutes j for example in fig. 29, after ascertain- 
 
Infant Schools 
 
 13 
 
 ing what object is represented, these other points might be 
 noticed : What are the palings made of ? How many are there? 
 How are they held up ? What do they stand upon ? What 
 colour are the bricks ? What else are bricks used for? What 
 
 
 
 
 
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 is the man called who builds the wall ? How does he get 
 the wall upright ? What sort of lines do the rows of bricks 
 make ? &c. These are merely suggestions as to the manner 
 in which interest may be aroused and the general intelligence of 
 the class increased. 
 
H 
 
 The Teaching of Drai 
 
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Infant Schools 
 
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 How many sides has the window in fig. 31 ? What is the 
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 window for ? Why is glass used ? Why would not wood do ? 
 Question on the number of panes, position of the lines, shape 
 of the corners, &c. 
 
 
10 
 
 The Teaching of Drawing 
 
 Slanting Lines 
 
 These are more difficult to draw, and at first should only be 
 short. They greatly increase the variety of the patterns and 
 the skill of the children, as they are now compelled to do with- 
 
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Infant Schools \J 
 
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 The Teaching of Drawing 
 
 
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CHAPTER III 
 
 STANDARD I 
 
 Syllabus Drawing, freehand and with the ruler, of lines, 
 angles, parallels, and the simplest right-lined forms, such as some 
 of those given in Djre's Drawing Book. (To be drawn on 
 slates.) 
 
 The syllabus for this standard is not very difficult, and at 
 first sight may appear rather monotonous. It will require on 
 this account great variety of questioning, and copious illustra- 
 tions showing the practical application of the examples drawn. 
 When taught with intelligence the work is very interesting and 
 popular with the children. 
 
 The teacher will require : - 
 
 i. Large Blackboard with a dull surface. 
 
 2. Chalk, sharpened to a chisel point. 
 
 3. Large T-Square, not less than three feet in length, 
 divided into feet and inches. One with the blade screived on 
 the stock is preferable, especially for using with the set-squares. 
 
 4. Demonstration Sheets. These save the teacher's time, 
 and enable the pupils to see at once the object they are going 
 to draw. If the sheets are not provided, a sketch of the copy 
 should be placed at one corner of the board previous to the 
 commencement of the lesson. 
 
 The children will require : 
 
 1. Slates about ten inches by seven inches, one side of 
 which must be plain. 
 
 2. Slate-Pencils of good quality (the bad ones scratch the 
 slates and break easily), which should always be well sharpened 
 and used for drawing only. When less than three inches in 
 
24 Tlie Tend ling of Drawing 
 
 length, they should not be used unless with a holder, as a short 
 pencil cannot be used with freedom. 
 
 3. Rulers. These should be marked in inches, and if used 
 for this standard only, halves and quarters will be the only sub- 
 divisions needed. They should not exceed nine inches in 
 length, the edge should be bevelled, the scale marks and 
 figures should be clear and distinct, with the inch marks run- 
 ning quite across the ruler from edge to edge. 
 
 Introductory Lesson 
 
 Before children can begin to use the ruler, it is absolutely 
 necessary that they should thoroughly understand the meaning 
 of the various marks upon it. This may be made not only an 
 instructive, but also an exceedingly interesting lesson to young 
 children. The questioning must be smart and definite, and 
 accompanied with plenty of practical applications of the various 
 points elicited. The following lesson is suggestive of the 
 manner in which the subject should be dealt with. 
 
 It must be carefully borne in mind that the children are 
 young, and only beginning, and are therefore capable of re- 
 ceiving information in but small quantities, and when expressed 
 in the clearest and simplest language. Similar lessons will be 
 found to be frequently necessary in the early stages of teaching 
 the subject. 
 
 What is this ? ' // is a ruler' 
 
 (Insist upon the answer being given in the form of a 
 sentence as far as possible.) 
 
 What can you tell me about its edges ? ' They are 
 straight? 
 
 Show a round ruler. Elicit that the ruler used for drawing 
 with is flat. 
 
 Why is it flat ? ' // can be kept firmly on the slate' 
 
 Elicit other examples of flat surfaces. 
 
 Are the two flat surfaces of the ruler alike ? ' No? 
 
 What is the difference between them ? ' One side has marks 
 and figures upon it.' 
 
 Are the marks all alike ? 
 
 How many long marks are there ? 
 
Standard I 25 
 
 The teacher should now draw a representation of the ruler 
 on the board, and place the long marks upon it, as indicated on 
 the children's rulers. 
 
 How many parts do the long marks divide the ruler into ? 
 
 Note. This is a very important question, and the difference 
 between the marks and the parts should be clearly shown, as it is 
 a very common error for children, even in the higher standards, to 
 confuse the marks with the parts which they separate. If there be 
 any difficulty fold a strip of paper into as many parts as there are 
 on the ruler, cut them up, and let the children count them. 
 
 What do you notice near the marks ? ' Figures! 
 
 Name the figures. Explain that the figures indicate the 
 number of parts that the ruler js divided into, and that each of 
 these parts is called an inch. 
 
 How many inches make a foot ? Show a foot ruler. 
 
 How many feet high is the door ? 
 
 Take other illustrations, and let the objects be rapidly 
 measured after the children have first estimated the distances. 
 
 How many inches long is the book ? Measure it. 
 
 How many inches can you span? &c. 
 
 How many half-pennies can be placed on the ruler? 
 (Half-penny=i inch in diameter.) 
 
 Now let the children mark several points, a, l>, c, d, on the 
 left hand side of their slates. From a draw a line 2 inches, 
 from b 4 inches, from c 5 inches, and from d 6 inches in 
 length respectively. 
 
 The slates should be shown, and rapidly scanned after each 
 line has been drawn. 
 
 The teacher now returns to the blackboard representation 
 of the ruler, and marks the half- inches. 
 
 How many parts have I divided the inch into ? 
 
 What would you call each part ? 
 
 Hold up your rulers and count each half-inch, pointing 
 them out with your pencils. 
 
 How many half- inches is the whole ruler divided into? 
 
 Now mark points as before, and draw lines of 2^-, 4 h, 6^, 
 and i\ inches in length respectively. 
 
26 
 
 The Teaching of Drawing 
 
 Next mark the quarter-inches, and proceed in a similar 
 manner. 
 
 Smaller divisions should not be taken for this standard. If the 
 children are carefully and systematically taught after this fashion, 
 there will be no difficulty as to the practical use of the ruler. 
 
 Method of Using the Pencil and Ruler The ruler must 
 always be placed with the bevelled edge upwards, and held firmly 
 in position with the fingers well distributed, and placed near the 
 centre of the ruler, as shown in the illustration, and not at the end. 
 
 The pencil should be held sloping at about an angle of 6o, 
 with its point close to the edge of the ruler. In ruling the lines 
 
 be careful to insist that 
 the pupils always rule 
 along the, upper edge, and 
 from left to right or from 
 top to bottom. 
 
 The teacher should 
 show carefully the 
 method of joining two 
 points. Place two 
 points, a and b, on the 
 board, and place the 
 point of the chalk on b ; now place the bevelled edge of the 
 ruler against the point of the chalk, keep the chalk firm, and 
 
Standard I 
 
 27 
 
 move the end of the ruler up until it reaches point a. Hold 
 the ruler firm, remove the chalk to a, and rule the line. This 
 is rather difficult for beginners, but it will save a considerable 
 amount of time and trouble if persevered with at first. Ex- 
 amples should now be given until the children can join the 
 points readily. 
 
 Care must be taken that the points to be joined are not 
 covered up by the ruler. The teacher may now give the defini- 
 tion. A straight line is the shortest distance between two joints. 
 
 The opportunity should be taken here to show that all lines 
 drawn with the ruler are straight lines, no matter what their 
 direction may be, as children frequently confuse the term 
 straight with level and upright. 
 
 Lengthening Lines. To lengthen a line the pencil and ruler 
 should be used in the same manner as in joining two points. 
 Place the pencil on the line, adjust the ruler as in fig. 82, 
 and rule to the required length without showing the joining. 
 
 First Drawing Exercise. The children may now proceed 
 to the first exercise suggested in the 'Illustrated Syllabus,' 
 viz. : To draw a number of parallel lines in various positions. 
 
 1. Horizontal Lines. Mark two 
 points, a and b, one inch and a half 
 from the top of the slate, and 
 through these points rule a line four 
 inches long, as shown in the pre- 
 vious exercise. Set off distances of 
 one inch with the ruler from each 
 end of the line, ab. [Place the ruler 
 for setting off the distances, as 
 shown in fig. 83, with the inch mark 
 on the line ; the distances can then 
 be quickly marked without moving 
 the ruler.] Rule the lines firmly 
 and evenly, and insist upon all 
 leaving the line when ruled. Allow 
 no rubbing out. It is far better to 
 
 leave the line when ruled, even if not quite accurate, than 
 to attempt to alter it by rubbing out, as the children not only 
 
 
28 The Teaching of Drawing 
 
 smudge the slate, but waste time by getting behind with their 
 work. 
 
 Commendation must be freely distributed, as little children 
 especially are stimulated to greater emulation by judicious 
 praise. Four or five lines only should be drawn at first, or the 
 exercise becomes wearisome. A short lesson with plenty of 
 questions and illustrations is the most profitable. 
 
 Questions of the following character are suggested. 
 
 How many lines are there ? 
 
 What sort of lines are they ? ' They are straight lines' 
 
 What is a straight line ? ' The shortest distance between two 
 points.' 
 
 How long is each of the lines ? 
 
 What else can you tell me about them ? ' They are all the 
 same length.' 
 
 Explain the term 'equal.' 
 
 What position are the lines in ? ' Level.' 
 
 Explain the meaning of ' level,' and show how the surface of 
 water keeps level even when the vessel containing it is tilted to 
 one side. 
 
 Tell me something else that is level. ' The floor.' 
 
 Elicit numerous other examples. 
 
 What else can you tell me about the lines, besides being 
 straight, equal, and level? ' They are the same distance apart. 1 
 
 Explain the term ' parallel.' 
 
 What is parallel to the floor ? The ceiling.' 
 
 Educe plenty of examples, such as opposite walls, edges of 
 books, slates, desks, boards, windows, railway lines, &c. 
 
 The definition of parallel lines may now be given. 
 
 The term horizontal may be used as well as level ; children 
 use it quite as readily. The meaning of horizon must be 
 clearly given, and if the children live near, or have been to the 
 sea-side, they will have no difficulty in realising what the 
 horizon is. 
 
 All the terms used should be put on the board, and copied 
 by the pupils, but it is not desirable to write up definitions 
 for young children. Frequent questioning is more interesting, 
 and secures the desired result just as well. 
 
Standard I 29 
 
 2. Vertical Lines. Show that lines may be in other posi- 
 tions besides being level by referring to the walls, roofs, &c. 
 Draw upright or vertical lines in a similar manner to that 
 adopted for the horizontal lines in fig. 83. 
 
 84 85 
 
 3. Oblique Lines. Draw in a similar fashion to the pre- 
 ceding, and show that they may slope either way. It will pro- 
 bably be easier for the children to turn the slate into a sloping 
 position with a corner towards them in doing this exercise. 
 
 The floor and the walls give two useful comparisons for 
 horizontal and vertical lines. The use of the plumb line by 
 workmen should be referred to, and it should be used to test 
 whether objects in the room, or lines on the blackboard, are 
 vertical. 
 
 It is now very good practice to let the children draw parallel 
 lines by judging the distance with the eye only. To do this, 
 let them first mark the points for the left-hand end of the lines 
 only before ruling. 
 
 Freehand Drawing of Parallel Lines. The children will 
 now be fairly familiar with the ruler and the various terms re- 
 lating to lines, and may proceed to the real difficulty, viz. the 
 drawing of straight lines without the aid of the ruler. In teach- 
 ing, it is undoubtedly much easier to do the ruled copy first, 
 and then proceed to the freehand. At examinations the free- 
 hand is generally required to be drawn first. 
 
 The pencil should be held freely, not close to the point, and 
 making an acute angle with the slate. The points for the first 
 line should then be marked, and the child taught to guide his 
 
30 
 
 The Teaching of Drawing 
 
 pencil by noticing the top of the slate. Then, after carefully 
 taking the pencil across from point to point without marking 
 the slate, the line should be lightly drawn across without join- 
 ings or stopping. The hand must not lie upon the slate, but 
 the little finger may just touch to ensure steadiness to the hand. 
 Now mark the position of the next line, and draw it in a similar 
 manner. The lines in the earlier lessons should not be drawn 
 too long. Practice will enable the children to draw longer 
 lines successfully. If the ends of the parallel lines be joined a 
 simple pattern is at once formed, and additional interest is 
 thereby given to the lesson. 
 
 86 
 
 Arrangement of the Drawing". It is perhaps advisable to 
 call attention here to the arrangement of the drawing on the 
 slates. Some inspectors prefer the ruler and freehand drawings 
 to be both on the same side of the slate, others require each 
 drawing to fill the slate. The latter plan is much more difficult, 
 as the lines run to a considerable length, 
 but it has the advantage of securing much 
 better and bolder work. 
 
 If the two are required on the same 
 side, divide the slate into two parts by 
 setting off five inches from the top, at 
 each side of the slate, and ruling a line 
 across. Now, if the figure required be a 
 square of four inch sides, let the children 
 draw the first line half-an-inch from the 
 dividing line, commencing about one and 
 a half inches from the left : hand side of the 
 slate. This will ensure the drawing being placed nicely on the 
 slate, thus adding considerably to its appearance, and also 
 
Standard I 
 
 31 
 
 training the children to place their work symmetrically. If the 
 freehand drawing be the same figure, first draw the top line 
 ah the square above forming a guide. 
 
 When, however, only one drawing is required on each side, 
 reserve the plain side of the slate for the freehand, and work 
 the ruled drawing on the other side. The position of the draw- 
 ing on the slate must always be thought out before beginning. 
 A six-inch square placed as in fig. 88 is certainly more effec- 
 tive than one placed as in fig. 89. 
 
 88 
 
 Angles. These should now be taken and drawn in various 
 positions, both freehand and with the ruler, and arranged on 
 the slates according to the methods suggested. 
 
 Acute 
 
 Right 
 
 Obtuse 
 
 The children must be able to recognise and draw the angles 
 in any position. 
 
 
32 
 
 The Teaching of Drawing 
 
 91 
 
 G) 
 
 In explaining the three kinds of angles it is advisable to 
 commence with the right angle, and show that it is the corner 
 made by the upright wall meeting the level floor, and that the 
 largest angle of the set-square will exactly fit it. Numerous 
 examples should now be elicited and tested with the set-square. 
 The fact should be pointed out that all right angles are 
 equal, irrespective of the length or position of the lines forming 
 them. The terui perpendicular may now be explained, and 
 the difference between vertical and perpendicular pointed 
 out, that whereas vertical means upright and refers to one posi- 
 tion of the line only, perpendicular means that a line is at right 
 angles to some other line and may be in any position. This 
 is an exceedingly common error, and should be clearly ex- 
 plained and well illustrated. A perpendicular line may now 
 be defined as a straight line at right angles to another straight 
 line. 
 
 Acute and Obtuse angles 
 should be defined as being re- 
 spectively less or greater than a 
 right angle. An open book fur- 
 nishes a ready illustration ; open 
 it at a right angle and test it 
 with the set-square, and then 
 obtain the acute and obtuse 
 angles. The fact should be con- 
 stantly before the pupil that the 
 
 lengths of the lines forming the 
 
 angle do not regulate its size. 
 
 Construction of the right 
 angle. On paper the set-square 
 should always be used, but on 
 slates it will probably be found 
 more convenient to use the ruler 
 only, as the slate frame prevents 
 the set-square from being used 
 easily. To construct a right 
 angle with the aid of the ruler only, first draw ab (fig. 91). 
 Now place the ruler so that one of the marks showing the 
 
 CO 
 
 <> 
 
 m 
 

 Standard I 33 
 
 inches, which runs right across the ruler at right angles to its 
 edges, exactly coincides with the line ab A perpendicular 
 may now be drawn of any given length. It is most essential 
 that the teacher should see that the line on the ruler exactly 
 coincides with the line first drawn. 
 
 The Square 
 
 Directly the construction of the right angle is under- 
 stood, its combinations may at once be proceeded with. 
 The square affords a large number 
 of exercises, as a great variety of ^ 
 simple patterns may be made from 
 it. The position of the starting line 
 should receive careful attention ; 
 this will, of course, depend upon the 
 size of the square to be drawn. The 
 remarks on the ' arrangement of the 
 drawing,' figs. 87, 83, and 89, will 
 make clear what is necessary to be 
 done. The teacher must always see 
 that the starting line is properly placed. To draw the square 
 commence with line ab, placed as previously directed : now 
 place the ruler as in fig. 91 and obtain ad and be. Make 
 them equal to ab, and complete the figure by joining d with e. 
 Plenty of questions should be given as the drawing proceeds, 
 which should be recapitulated and supplemented at the end of 
 the lesson. 
 
 What sort of a line is ab ? ' Straight a?id also horizontal? 
 
 Then, if ab be horizontal, what will be the position of ad} 
 1 Vertical: 
 
 What other line in the figure is vertical ? 
 
 What else do you notice about ad and be ? ' They are parallel: 
 
 In what position is de ? 
 
 If ad be at right angles to ab, what else may be said about 
 it ? ' 7/ is perpendicular to ab: 
 
 How many right angles does the figure contain ? 
 
 How many equal sides ? 
 
 What is the figure called ? 
 
 D 
 
34 
 
 The Teaching of Drawing 
 
 Then a square is a figure with four equal sides and four 
 equal angles. 
 
 Particular attention must be given to the firmness and even 
 thickness of the lines, and to the accuracy of the joinings at the 
 angles. 
 
 The square should now be drawn freehand, following the 
 same method, but starting from the middle line as suggested 
 in fig. 87. 
 
 Dictation of Drawing. This is an exceedingly useful 
 exercise, as it keeps all the class together, stimulates the intelli- 
 gence, compels the children to think and act promptly, and 
 affords an excellent method of testing whether the work has 
 been thoroughly mastered. The following examples will show 
 what is meant : the teacher can, of course, vary them in an 
 infinite variety of ways. 
 
 1. Mark a point near the bottom of the slate one inch from 
 the left hand side. From this point draw a horizontal line, five 
 inches long. From each end of the line draw upright lines 
 four inches long. Join the ends of these lines. 
 
 2. Draw a vertical line four inches long down the middle 
 of the slate. From the top of this line draw a line to the left 
 at right angles to it, and two inches long. Find the middle of 
 the vertical line with your ruler. Join this point with the 
 end of the two-inch line. 
 
 3. Draw a square of six-inch sides. Find the middle of each 
 side with your ruler. Join the middle point of the bottom 
 side of the square with the middle point of the side parallel to it. 
 
 Diameters and Diagonals. The diameter of a square is a 
 line joining the centres of the opposite sides. 
 
Standard I 
 
 35 
 
 In drawing the ruled examples, bisect the sides with the aid 
 of the ruler. In the freehand the sides of the square must be 
 carefully bisected by trial. 
 
 The diagonal joins the opposite cortiers, and is much more 
 difficult to draw, the tendency being to curve the line outwards 
 from the hand. 
 
 94 
 
 The pencil should be carried across from corner to corner 
 without touching the slate before putting in the line. It will 
 assist the beginner if the slate be turned so that the diagonals 
 would be in a horizontal position. It is not, however, a good plan 
 to allow the children to turn their slates or papers to any great 
 extent, as after practice they can draw the line just as readily 
 in one direction as another, and greater power and freedom in 
 using the pencil is acquired by keeping the paper in the same 
 position. 
 
 Lines Intersecting at Right Angles 
 
 Fig. 95. First draw the vertical line. Bisect it and draw 
 
 95 
 
 ie horizontal line, using the ruler to get the right angle as in 
 fig. 91. For the. freehand proceed in a similar manner. 
 
 Fig. 96. The square shown in dotted line should be very 
 
 u 2 
 
36 
 
 The Teaching of Drawing 
 
 lightly drawn, and the diagonals inserted. In the freehand 
 example, the square should then be carefully cleaned out. If, 
 however, the length of the lines were given, then first draw ab, 
 sloping as nearly as possible in the given position, and obtain 
 the other line at right angles to it, in the same manner as in 
 the preceding figure. 
 
 Fig. 97. Draw the dotted square, insert the diameters and 
 diagonals, and for the freehand clean out the parts shown in 
 dotted line, taking care to leave all the lines of equal length. 
 
 97 9* 
 
 
 
 a 
 
 kT 
 
 \ 1 
 N j 
 
 1 
 
 
 
 aX 
 
 
 -a. 
 
 
 "hr 
 
 1 
 
 Fig. 98. Draw the square, set off the widths either from 
 the centres, a, of the sides, or from the angles, whichever may 
 be most convenient : the distance between the lines and the 
 size of the square will determine this. For the freehand, the 
 best plan will be to set off the distance on each side of the 
 point a, and then draw the lines. 
 
 Fig. 99. Draw the square, set off equal distances on each 
 side from the angles, and join the points. This figure is 
 occasionally set to be drawn without the 
 aid of the square. It then forms a most 
 difficult exercise. The best way to pro- 
 ceed is to fix point a in the middle of the 
 slate. Incline the slate and mark poiots 
 b and c in the same line as a, and equi- 
 distant from it. Through b and c draw 
 parallel lines. Obtain de at right angles 
 to be, and make ad and ae equal to ac 
 and ab. Through d and e draw lines at right angles to 
 the other lines. Or the small square formed by the intersec- 
 
Standard I 
 
 37 
 
 tion of the lines may be drawn first, and its sides produced 
 equally on each side. 
 
 The Bisection and Trisection of the Right Angle 
 
 These problems should now be taken. The right angle 
 may be bisected by completing the square and drawing the 
 diagonal ; afterwards cleaning out the portions in dotted line 
 (fig. 100). A better and easier plan is to use the 45 set-square. 
 First, obtain the right angle, and then use the ruler and set- 
 square as shown in fig. 101. 
 
 100 
 
 101 
 
 To trisect the right angle the set-square with the angle of 
 30 should be used, as it is the only really quick and accurate 
 method by which the operation can be performed. The only 
 point that requires careful watching is to see that the lines are 
 drawn true from the angle. The method of procedure is as 
 
 102 
 
 103 
 
 follows. Draw the right angle as large as the space will allow. 
 Place the ruler as in fig. 102, but not too close to the 
 
 
38 
 
 The Teaching of -Drawing 
 
 line. Adjust the set-square with the angle of 30 as shown, 
 and rule a line. Now reverse the set-square (still keeping the 
 ruler firmly in its place), place it with the angle of 6o in 
 the right angle, and rule the second 
 line (fig*. 103). This problem should be 
 practised by the pupils several times, 
 until they can do it readily and quickly. 
 For freehand, this is an exceed- 
 ingly difficult copy. The simplest plan 
 is to estimate the widths between the 
 lines, by marking points a and b, and 
 drawing from them short lines to the 
 angle. If the distances appear correct, 
 then produce the lines. Children require to perform this 
 operation a number of times before they can estimate the 
 distances with accuracy. 
 
 105 
 
 The Rectangle 
 
 This figure will present no fresh difficulties to the pupils 
 after the square has been dealt with. 
 
 Various exercises are now 
 given, many of which have been 
 set for examination. The teacher 
 can multiply these in a variety 
 of ways. It is not so necessary 
 for the pupils to practise a large 
 number of exercises, as to 
 thoroughly understand the best 
 methods of obtaining lines in 
 particular directions with ease and accuracy. 
 
 The dotted lines show the construction necessary to obtain 
 the lines of the figure. They should not be drawn by the 
 pupils. 
 
 Fig. 139. The square in this position is much more diffi- 
 cult to draw. It is necessary to obtain the diagonals first. Draw 
 ab of the required length. Bisect it with the ruler, and draw 
 cd at right angles. Make cd equal to ab, and join the ends of 
 
Standard I 
 
 39 
 
 114 
 
 nS 
 
 [/ 
 
 \ 
 
 
 / 
 
 
 122 
 
 
 
 
 
 
 
 
 
 
 
 
 l\^ 
 
 
 H9 
 
 / 
 
 \ 
 
 \ 
 
 / 
 
 123 
 
 116 
 
 124 
 
 
 1 /\ 
 
 1/ \ 
 
 
 106 
 
 
 107 
 
 
 108 
 
 
 109 
 
 ^/ 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 10 
 
 
 III 
 
 
 112 
 
 
 "3 
 
 / 
 
 
 
 X 
 
 
 
 
 
 
 
 \ 
 
 17 
 
 125 
 
 126 
 
 
 
 127 
 
 
 
 128 
 
 
 129 
 
 K 
 
 
 \ 
 
 
 / 
 
 
 t) 
 
 
 ^ 
 
 
 '\ 
 
 
 / 
 
 
 N 
 
4 The Teaching of Drawing 
 
 *3 131 132 
 
 the lines. The construction lines should not be rubbed out in 
 these figures. 
 
 Fig. 140. Draw the diagonals as before, and complete the 
 square. To obtain the lines ac and bd t the distances, eg and gf 
 
 140 
 
 must be bisected with the ruler, and the lines drawn perpendi- 
 cular to ef If the diagonals are given, the dimensions of the 
 sides of the square are not known, and cannot be directly 
 bisected with the ruler. Care must be taken to see that ac and 
 bd are drawn exactly perpendicular to ef. 
 
Standard I 
 
 4* 
 
 The interior of the square may be filled up in a variety of 
 
 ways. 
 
 141 
 
 142 
 
 Fig. 145. Draw a square. Insert the diameters, and 
 afterwards clean out the part shown in dotted line. 
 
 Fig. 146. Draw a rectangle with its sides in the propor- 
 tion of three to two. Divide the longer sides into three, and 
 145 146 147 
 
 r 
 
 P 1 I 
 
 t I I 
 
 I 1 I 
 
 I I I 
 
 t 
 
 I 1 1 
 
 the shorter into two equal parts. Draw the lines cutting the 
 figure into six equal squares. Clean out the parts shown by 
 dotted lines. 
 
 Fig. 147. This may be done as shown by the dotted lines, 
 or the two bottom squares may be drawn first, the centres of 
 their top lines found, and the top square constructed. For 
 freehand the first method is much better, as the correct 
 proportions of the squares are more easily obtained. 
 
 148 149 150 
 
 l" "] ~] } I 1 1 
 
 1 1 , 
 
 1 < 
 
 _.-;_- -| ^-.-j 1 
 
 f T ' 1 1 
 
 , ' 1 L. 1 , 
 
 The construction lines show the method in the above 
 figures. 
 
42 The Teaching of Drawing 
 
 Memory Drawing 
 
 This is a valuable aid in every standard towards securing 
 really intelligent work. The best plan to adopt is to let the 
 pupils draw from memory the copy taken in the previous lesson. 
 This need not be a long exercise, and it will test whether the 
 methods used have been thoroughly understood, as well as 
 strengthen the pupil's powers of observation. In the upper 
 standards special attention should be paid to knowledge of 
 the analysis of the copy. It is not at all important that the 
 pupil should remember every little detail \ it is the power of 
 blocking in the masses correctly that needs cultivation. 
 
43 
 
 CHAPTER IV 
 
 STANDARD II 
 
 Syllabus. The same as for Standard I, but on paper. 
 The teacher will require two large set-squares in addition 
 to the apparatus for Standard I. 
 The children will require : 
 
 i. Paper. This should be of the regulation size, n by 
 7 \ inches, with a smooth unglazed surface. There is a 
 diversity of opinion as to which is the more convenient form to 
 use, books or paper. Many teachers prefer to use loose sheets, 
 as they are more easily manipulated, while on the other hand 
 books are decidedly cleaner, and as a rule children are proud 
 of a well filled book. 
 
 2. Pencils. The most suitable pencils are the hexagonal- 
 shaped, as they do not roll off the desks. Cheap pencils are 
 
 not necessarily the most economical ; 
 pencils with crumbling leads or hard 
 wood only produce bad work and 
 cause vexation to both teachers and 
 scholars. The marks of various 
 makers differ in degree of hardness, 
 H and F in some are as soft as HB 
 in others. On the whole HB when 
 not too soft is the most useful 
 pencil to adopt. Pencils must always 
 it is impossible to secure accurate 
 is attended to. A sharp knife is the 
 best instrument to use, although some of the pencil sharpeners 
 produce a fair point. 
 
 Fig. 151. A shows the form the point should take ; when 
 cut as in B the point breaks almost directly. It is a very useful 
 
 be kept well pointed, as 
 and neat work unless this 
 
44 The Teaching of Drawing 
 
 plan to point the pencil at both ends, as the pupil is then pro- 
 vided with a good point throughout the lesson. 
 
 Indiarubber. This should be white and flexible. If the 
 piece be cut in halves along its length it is more useful, as it 
 bends easier, and there is less waste. It should not be used 
 for the ruler drawing, and very sparingly for freehand in the 
 lower standards. 
 
 Set-squares. Those having angles of 45 and 6o are the 
 only ones needed. They should be of good size, large enough 
 to draw 6-inch lines, and about ^ inch thick j they will not then 
 readily break. 
 
 Directions. The same methods of procedure as given for 
 Standard I are equally applicable here. The only additional 
 points to be illustrated will be the improved constructions 
 obtained by the use of the set-squares. The same kind of 
 oral questioning must accompany each lesson, and additional 
 skill in answering and giving illustrations should be required. 
 
 The character of the line used should receive special 
 attention, as bad habits formed at the beginning are exceed- 
 ingly difficult to eradicate. For the ruler work a good, bold, 
 firm line should be adopted, so that the figure stands out well 
 from the construction lines, which should be put in as lightly as 
 possible. In the freehand, which will probably need more 
 time than the ruler work, the sketching in must be done very 
 lightly and carefully j the pupil should always first indicate the 
 ends of the lines before drawing them, and after passing the 
 pencil carefully between them several times to obtain a general 
 idea of the direction, finally draw the line with one clean, light 
 stroke. The teacher must keep a sharp watch to see that the 
 pencil is held properly. The fingers must not be too near the 
 point, nor in a cramped position. When the copy has been 
 carefully sketched in, the construction lines should be rubbed 
 out, the whole figure cleaned with the indiarubber, and after- 
 wards finished with a clean even line. By lining in, it is not 
 meant that the line should be blackened over (thus frequently 
 spoiling the drawing), but carefully putting in an even line and 
 improving the shape and finish of the copy. Many condemn 
 the use of indiarubber entirely in this Standard, but with care 
 
Standard II 
 
 45 
 
 it may be advantageously used to clean up the copy. The 
 cuffs of the pupils' coats should be turned up, and not allowed 
 to rub over the lines drawn, or to soil the paper. Cleanliness 
 must be strictly enforced, or the work will be a continuous 
 source of vexation to the teacher. 
 
 Ruler Work 
 
 Parallels. Place the ruler in a vertical position, and hold 
 it firmly with the thumb and third finger of the left hand. 
 Now adjust the set- square as shown, placing one edge in a line 
 
 with one of the inch marks on the ruler, and taking care to 
 impress upon the pupil the necessity of keeping the other 
 edge touching the ruler throughout its length. Keep the 
 set-square in position by pressing it firmly with the first and 
 second fingers, and rule a line. If the set-square be now 
 slipped with the right hand to the next inch mark while the 
 ruler is still held in position with the left hand, parallels one 
 inch apart will be obtained. Repeat the exercise with parallels 
 2 inches and \ inch apart. 
 
4 6 
 
 The Teaching- of Drawing 
 
 Vertical and oblique parallels may now be drawn in a 
 similar manner. Attention should be directed to the fact that 
 while one edge of the set-square gives horizontal lines, the 
 other edge will give oblique lines, but not the same distance 
 apart. 
 
 The teacher will find that it will amply repay for the trouble 
 taken, to teach the uses of the set-squares at this early stage ; 
 as not only can the figures be drawn more accurately, but the 
 difficulty will be overcome for the other standards ; and the 
 work of Standard III will be made easier, more interesting, 
 and more pleasurable to the pupils. Constant vigilance, care, 
 and patience must be exercised when the set-squares are first 
 used ; the method of using them must be repeatedly shown on 
 the blackboard, and every pupil must be supervised to see that 
 the proper way of handling them is thoroughly comprehended. 
 A very common error to guard against is the attempt to draw 
 the lines without keeping one edge of the set-square touching 
 the ruler. The children may also be shown that it is not abso- 
 lutely necessary for the set-square to be of this particular shape ; 
 any right-angled figure, such as a slate or book, will also 
 give parallels and perpendiculars. 
 
 Perpendiculars. Exercises in setting up perpendiculars 
 from points in lines in various positions, such as those suggested 
 in fig. 153, should now be given. Dictated exercises may be 
 used here with advantage. 
 
 All right angles should now be set up, bisected, and tri- 
 sected by using the set-squares. 
 
 The reason for these processes may be demonstrated here 
 
Standard II 
 
 47 
 
 with advantage. Describe a large circle on the board, and 
 draw two diameters at right angles to each other. Fit the set- 
 square into each of the four angles formed, and show that each 
 is a right angle. Now explain that as we use long measure to 
 determine the length of an object, avoirdupois to determine the 
 weight, and other measures to determine content, time, area, 
 &c, so we use a measure to determine the size of an angle. 
 Each one of these right angles is divided into 90 parts by lines 
 drawn from the angle, and the width of the very sharp angle 
 thus formed is called a degree. This may be easily illustrated 
 by describing a large circle on paper and dividing it into four 
 right angles. Divide one of the right angles into nine equal 
 
 divisions, and subdivide one of these divisions into ten, thus 
 showing the actual size of a degree. If the space between the 
 lines be blackened in as shown in the angle of io, fig. 154, 
 it will be more readily comprehended. Now take three set- 
 squares, place them with their smallest angles fitting into the 
 right angle. The reason for using the set-square for trisecting 
 a right angle will at once be seen. The number of degrees in 
 the small angle may be elicited, and if two set- squares be 
 removed it will be found that the larger angle of one set square 
 will exactly fit in place of the two, thus giving the angle of 6o. 
 In the same manner two of the 45 set-squares may be shown 
 
 
4 8 
 
 The Teaching of Drawing 
 
 to fit the same right angle, and consequently one of them would 
 bisect it. 
 
 Introduction of Curves and the Drawing of Common 
 Objects. The Illustrated Syllabus suggests that : 'In order 
 to interest the children it is advisable to teach them to draw as 
 early as possible from actual objects, such as the doors, windows, 
 furniture and apparatus of the school- room. It will also be 
 found quite possible and very desirable to go beyond the fore- 
 going standards in teaching. Thus freehand drawing of bold 
 curves may be introduced in Standards 
 I and II ; and exercises may be ad- 
 vantageously given in all standards in 
 drawing from memory.' 
 
 With regard to the drawing of 
 common objects, they should only be 
 drawn in the flat, and from the teacher's 
 directions ; they then form a valuable 
 introduction to the scale drawing of 
 Standard IV. Examples similar to the 
 end elevation of a desk, fig. 156, the 
 block letters, and many of the simple 
 objects suggested in the Infants' course 
 form good examples. The teacher, 
 however, should carefully work out the 
 measurements beforehand, so that the 
 drawing may not appear distorted. 
 
 Freehand curves may be easily introduced without inter- 
 fering with the other work. The squares and oblongs already 
 drawn can be utilised as a framework for the curves. The 
 cleverer children will in many lessons be able to insert the 
 curves while the others are finishing the ordinary copy. The 
 following examples illustrate a few of the ways in which this 
 may be carried out. The same copies may also be utilised 
 for the work of Standard III at the commencement of the 
 year. 
 
 The drawing of simple patterns should be followed up 
 here as frequently as possible, as it encourages originality 
 among the children and is a pleasing variation from the other 
 
157 
 
 
 r 
 
 \ 
 
 
 V 
 
 \ 
 
 j 
 
 ) 
 
 Standard II 
 158 
 
 49 
 
 159 
 
 160 
 
 161 
 
 162 
 
 163 
 
 164 
 
 165 
 
 166 
 
 167 
 
 168 
 
 
50 The Teaching of Draiving 
 
 169 170 171 
 
 
 178 
 
 
 
 
 1 
 
 79 
 
 
 
 
 
 
 
 A 
 
 r 
 
 ^ 
 
 r 
 
 r 
 
 ^ 
 
 r 
 
 (S 
 
 J 
 
 V 
 
 J 
 
 V 
 
Standard II 51 
 
 work. If the children are allowed to colour the pattern, as 
 suggested on page 5, a wonderful degree of interest will be 
 created in the work. Examples such as those given in the 
 Infants' course, figs. 45-70, are suitable for this purpose. The 
 squared paper of ordinary exercise books answers very well for 
 drawing upon. 
 
 E 2 
 
52 The TeacJung of Drawing 
 
 CHAPTER V 
 
 STANDARD III 
 
 Syllabus. (a) Freehand drawing of regular forms and 
 curved figures from the flat. 
 
 (b) Simple geometrical figures with rulers. 
 
 These right-lined figures to be drawn freehand and also ivith 
 rulers. 
 
 These requirements then resolve themselves into three 
 parts. 
 
 I. Freehand drawing of curved figures, which I have divided 
 into three stages. 
 
 II. Freehand drawing of right-lined forms. 
 
 III. Drawing of geometrical figures with rulers. 
 
 The same apparatus will be required as for Standard II. 
 
 I. FREEHAND DRAWING OF CURVED FIGURES 
 
 This is by far the most important and also the most difficult 
 part of the course for this Standard, and will require a greater 
 amount of time than the geometrical drawing. The pupil must 
 be trained to rely more upon his own powers. Hitherto the 
 figures dealt with have been regular in form, and the proportion, 
 or relation which one part of the drawing bears to the other, has 
 been obtained by the help of the ruler, or from definite instruc- 
 tions furnished by the teacher. The pupil must now be shown 
 how to analyse and understand the principles of construction 
 upon which the copy is based, and how to obtain the proper 
 proportions between its various parts. If these important 
 principles are well grounded at this stage, the freehand and 
 
Standard III 53 
 
 model drawing of the upper standards, upon which so much 
 depends, will be executed with much greater correctness, ease, 
 and pleasure. 
 
 First Stage. As the pupils are now thoroughly familiar 
 with the drawing of rectangular forms, it will be found much 
 easier to introduce curved forms by using these rectangular forms 
 as aids. The curves should not be drawn very large at first, as 
 simple curves when too large are very awkward for the beginner 
 to draw ; nor is it advisable to spend too long a time over 
 them, as, though they are very necessary, and give excellent 
 training in freedom of hand and knowledge of form, they are 
 somewhat uninteresting to the pupil. They should be drawn 
 about the size suggested on the figures, and the construction 
 lines, which must be indicated very lightly, may be allowed to 
 remain, the most important point at this stage being to secure 
 good curves. 
 
 Figs. 180-190. The pupils must be shown from the black- 
 board how to obtain the curves with one careful sweep, after 
 the pencil has been carried several times over the paper, so 
 that the general direction of the curve may be obtained before 
 marking it in. On no account must the pupil be allowed 
 to draw the line thickly or in little bits. Adhere as far as pos- 
 sible to the rule already laid down viz., to draiv from left to 
 right and from top to bottom. 
 
 Some teachers prefer to use slates in the first instance, but 
 this is open to great objection and is an encouragement to 
 careless work, as alterations may be made so readily ; whereas 
 one of the most important points to inculcate is that when a 
 line is drawn it should not need much alteration, and must 
 remain. The knowledge that the line cannot be easily removed 
 compels the pupil to think where it must be placed, and thus 
 gives confidence and begets carefulness. 
 
 Second Stage. In the next series of examples the construc- 
 tion lines must be carefully cleaned out, and the figure, after 
 being correctly sketched, should be rubbed out until only a 
 faint line is visible. The drawing should then be carefully 
 lined in with a sharp pencil ; and here it is again pointed out 
 that the lining in is for the purpose of obtaining an even, con- 
 
54 The Teaching of Draiving 
 
 180 181 
 
 3* V 
 
 182 
 
 183 
 
 3" 
 
 186 187 
 
 188 
 
 [89 
 
 190 
 
 ^ 
 
 . Y 
 
 r\ 
 
 Y 
 
 r 
 
 \ 
 
 ^J 
 
 A 
 
 v; 
 
 y 
 
Standard III 55 
 
 tinuous line, and an improvement in the shape and finish of 
 the copy. 
 
 The pupil should be taught here how to divide a line into 
 three equal parts, a much more difficult process than dividing 
 it into two. The following method given by Mr. Taylor in his 
 excellent book on ' Elementary Art Teaching ' is exceedingly 
 
 191 
 
 useful. If AB be the line to be trisected, then place a finger 
 of the left hand on the line at the same time with the pencil 
 which is to mark the first division ; by this means the equality 
 of the three parts may be more easily judged. 
 
 Figs. 192-200 are all based on the circle, and should be 
 drawn without the aid of squares. The light lines show the 
 necessary construction. Care should be taken to see that the 
 semicircles run into each other at their junction with a con- 
 tinuous line without showing any angle. About six inches is a 
 convenient size for the longest line in these examples, which 
 should all be carefully lined in when drawn. 
 
 Third Stage. Before beginning the next series of examples, 
 which are of the same character as examination tests, the pupil 
 must be taught how to measure, by means of the pencil, 
 objects which are not accessible. This is a most useful and 
 necessary exercise, and should be continually used to ascertain 
 the relationship between the various parts of the copy. Great 
 care and patience will be needed on the teacher's part to see 
 that the method is clearly understood, as the pupil's future pro- 
 gress is largely dependent upon this. Directly the method has 
 been mastered, the power of self-reliance is greatly increased, 
 and it becomes quite exceptional to find the proportion of the 
 figure inaccurate, 
 
56 
 
 The Teaching of Drawing 
 
Standard III 
 
 $7 
 
 Begin by measuring objects in the room such as windows, 
 boards, &c. that can be seen in a similar position by the bulk 
 of the class : taking care always to ask the children to estimate 
 first the relative sizes by means of the eye, and afterwards 
 verify them by measuring with the pencil. 
 
 Suppose the example selected be a window, then the 
 method of proceeding would be somewhat as follows : 
 
 Which is the greater, the height or the width of the 
 window ? 
 
 How much greater is the height than the width ? 
 After obtaining approximately accurate replies, show how to 
 verify with the pencil. 
 
 Hold the pencil horizontally at arm's length, close one eye, 
 and let the end of the pencil be held in a line with the side 
 (A) of the window (fig. 201). 
 Keep this end steady, and slip the 201 
 
 thumb along the pencil until it is 
 in line with the other side (B) of 
 the window. The distance between 
 the end of the pencil and the 
 thumb nail will represent the actual 
 width of the window as seen by the 
 
 pupil. (Take care to see that the &\ 
 
 pencil is held at right angles to the 
 arm.) Let the pupils hold up 
 their pencils, still keeping the thumb 
 in position. The teacher will then 
 see at a glance whether the distance 
 has been correctly gauged. Now 
 step this distance vertically up the 
 
 window. The pupils will readily see that this method fur- 
 nishes them with a ready means of testing the proportions of 
 their drawing. After a few other measurements of various 
 objects, the best plan 
 comparing them with 
 follows : 
 
 Draw AB (fig. 202). Compare it with the height of the 
 board. Lengthen the line to C 
 
 is to take lines on the blackboard, 
 the board and with each other as 
 
58 
 
 The Teaching of Drawing 
 
 
 202 
 
 
 c 
 
 
 
 D 
 
 B 
 
 
 r 
 
 
 
 A 
 
 
 
 Where is point B? 'A little below the half' 
 How do you know this ? 
 Compare CD with AC. 
 
 How many times can CD be 
 set off on AC? 
 
 Then what part is CD of 
 AC? l A little less than one- 
 third.' 
 
 Compare BE with AC l A 
 little more than half 
 
 Similar exercises should fre- 
 quently be given at the com- 
 mencement until the method is 
 thoroughly comprehended. In 
 all cases let the comparison be 
 made first with the eye and after- 
 wards verified with the pencil. 
 
 A typical lesson is given 
 here to show how to apply the 
 method advantageously. Such lessons are frequently required 
 at the examination. 
 
 Apparatus. Demonstration sheet or a drawing of the figure 
 to be placed before the class, pencils, paper, &c. 
 What is the copy like ? ' A leaf 
 What shape is the leaf? ' Like a triangle! 
 What line shall I draw first ? ' The upright line through the 
 middle' 
 
 Now that I have drawn the height, what shall I want to know 
 next ? ' The ividth.' 
 
 Where is the leaf widest ? * At the bottom! 
 Compare AB (fig. 203) with the height. After eliciting a 
 number of answers, let the pupils measure AB with their pencils 
 and verify their answers by stepping the distance up the height 
 line. It will be found to go three times and a little over. Now 
 require the answer to be given in this form : ' AB is a little less 
 than one-third of the height.' Divide your line into three equal 
 parts as previously shown, and mark the first division, a, 
 fig. 204. Now, if we make be and bd a little less than ab, the 
 
Standard III 
 
 59 
 
 correct width of the copy will be ascertained. Join e with d 
 and c t keeping the lines very light. 
 
 I would point out here the extreme undesirability of cutting up 
 the height line into halves, quarters, &c, and constructing a frame- 
 work from these parts. In actual drawings the proportions are 
 very rarely exact parts of the upright line. These divisions should 
 only be used, as in this case, as guides. 
 
 Now draw the stalk, and lines ad and ac, thus producing a 
 general resemblance to the leaf. 
 
 203 
 
 The remainder of the copy is very difficult. The attention 
 of the pupils should be directed to the following points. 
 Notice the number of bends in the side of the leaf, and place a 
 light mark to show where they come, as at points /, g, h. If 
 the pencil be held in a line with e and d, it will be apparent as 
 to how much of the copy projects outside of the triangle. 
 Also notice that the bottom curves are slightly larger than the 
 others. The left side should then be very lightly indicated, 
 and examined carefully before drawing in firmly, the other side 
 
6o The Teaching of Drawing 
 
 drawn to correspond, and the copy afterwards cleaned and 
 lined in 
 
 The advantage of proceeding in this manner is that the 
 pupil is drawing with the head as well as with the hand. It 
 will be noticed that nothing has been told, every step being 
 obtained from the pupils. A copy taught thus takes consider- 
 able time at first, but the time will have been well spent, and 
 the teacher will be amply repaid for the trouble taken. A few 
 copies thoroughly taught in this fashion will be found to be of 
 more value than weeks of unintelligent mechanical copying. 
 This example forms a capital test for memory drawing. 
 
 Figs. 205-209 are examples of lines springing from a 
 central stem. The dotted lines show the method of construc- 
 tion, and the figures denote the order in which the lines should 
 be drawn. Very great care should be bestowed upon the 
 junctions of the side lines with the stem : they should run into 
 the main line easily, gradually forming part of it. This will 
 need constant illustration on the blackboard. 
 
 Fig. 205. First find the position of a and b, and draw 
 lines starting from the centre line as shown at the side (A). This 
 will prevent the joining line from showing a tendency to run 
 through, instead of into, the main line as shown in (B). Draw 
 a line to get the level of the two bottom curves. Ascertain the 
 width of be as shown in the foregoing lesson, and draw the left 
 hand curve first. Now balance this with the corresponding 
 curve on the right. On 710 account must one half of the copy 
 be drawn first : this is a most mischievous plan and should 
 never be allowed. Now mark point e and draw a line through 
 it. Fix the position of/ and g, and draw the top curves. 
 
 Fig. 206 shows an example of alternate radiation. Mark the 
 points a, b, c, d first, and draw the curves as in the last example, 
 commencing with number i. Notice that each curve bends 
 down more as the bottom is approached, somewhat similar to 
 the branches of a tree. 
 
 In all cases always work from the copy placed before the 
 class, so that the pupils may see and understand the reasons 
 for the processes carried on. 
 
 In Figs. 219-231 the necessary construction lines are indi- 
 
Standard III 
 
 61 
 
 205 
 
 206 
 
 207 
 
 208 
 
 209 
 
62 
 
 The Teaching of Drawing 
 
Standard III 
 
 63 
 
 cated by the dotted lines, and those figures which are more 
 difficult are shown in their various stages. At each of these 
 steps the drawings should be carefully examined, the method 
 given in the sample lesson being followed out in all cases. If 
 thought desirable some of these copies may be left at any of 
 the stages shown, as they are rather more difficult than is 
 usually expected from this Standard, although they are given in 
 the syllabus, and form excellent examples to teach from. 
 Figs. 229-231 are also suitable for the earlier stages of 
 Standard IV freehand. 
 
 The work of the lower standards is very rarely tested by 
 cards instead of by the large sheets. If, however, this be done, 
 the general rule is to make the drawing as large as the paper 
 will allow, taking care to leave a fair margin, as this adds to the 
 appearance of the drawing. 
 
6 4 
 
 The TeacJiing of Drawing 
 
 225 
 
 226 
 
Standard III 
 
 65 
 
 231 
 
66 The lead ting of Drawing 
 
 II. FREEHAND DRAWING OF RIGHT-LINED FORMS 
 
 This is a continuation of the freehand work of Standard II, 
 and is not very difficult when the children have learned how to 
 estimate the relative lengths of the lines of the figures. The 
 knowledge of proportion which they have already obtained is 
 now especially useful. In the following examples the pupils 
 must be able to see the proper direction of lines which are 
 partly hidden, and also the proper method of drawing the 
 figures, 
 
 Figs. 232, 233, 234, 240, and 242 are all examples of one 
 figure overlapping a portion of another. The hidden parts of 
 the lines marked a are shown by dots. 
 
 Figs. 235 and 237. Draw the base. Find the position of b, 
 by comparing be with bd. Draw the altitude, compare it with 
 the base, and complete the triangle. The other vertical lines are 
 drawn from the middle points of the sides. 
 
 Fig. 236. Draw the square first, after comparing its height 
 with the height of the triangle, so that the figure may be pro- 
 perly placed on the paper. Draw ef and obtain the equilateral 
 triangle fgh. Draw the sides fg and// to meet the base of the 
 square produced. 
 
 Fig. 238. Draw the square and produce its base. Compare 
 np with the base of the square, and draw pr. Compare //// 
 with ftp, and draw the other side of the triangle. 
 
 Fig. 241. Begin with lines ab and ed. 
 
 Fig. 242. Draw the rectangle bede. Find points f, g, /i, / 
 and through them draw the lines for the other rectangle. 
 
 Fig. 243. Draw ab and find the position of e. Draw ed 
 and^, comparing u and bf with ae, and complete the figure. 
 
 Proceed similarly with the other figures, in all cases insist- 
 ing upon a careful study and testing of the figure by measuring 
 with both eye and pencil. Many of the examples for ruler 
 drawing will furnish other suitable exercises. 
 
Standard III 
 
 6 7 
 
 
 242 
 
 h 
 
 c 
 
 <x 
 
 
 .2 
 I 
 
 
 
 
 d 
 
 e 
 
6S 
 
 The Teaching of Drawing 
 
 III. DRAWING OF GEOMETRICAL FIGURES WITH 
 RULERS 
 
 This is generally the most attractive part of the work of 
 this Standard, and forms an excellent preparation for the geo- 
 metrical work of the higher standards, as a high degree of 
 neatness and accuracy is demanded. A knowledge of the 
 methods of constructing the triangle, square, rectangle, rhom- 
 bus, pentagon, hexagon, octagon, and figures based upon them, 
 together with simple bordering patterns, such as frets, &c, is 
 necessary. 
 
 It is most important that the pupil should be acquainted 
 with the proper method of drawing these figures, and the plan 
 given in the following lesson should be rigidly adhered to. If 
 this course be adopted the pupils will soon be able to measure 
 up a copy for themselves, and decide upon the size and con - 
 struction necessary. 
 
 The cards given at the examination usually contain two 
 figures which have to be drawn larger. This prevents unin- 
 telligent copying, and requires the pupil to possess a knowledge 
 of the construction necessary to draw the example. The paper 
 should be divided into two parts as in fig. 245, and one figure 
 placed in each half. 
 
 244 
 
 2 2 - - 
 
 / 
 
 a 
 
 
 4 
 
 / 
 
 
 4 
 
 
 / 
 
 . , .' 
 
 s 
 
 4 
 
 1 5 
 
 1 
 
 4 
 
 A 
 
 The following lesson will best illustrate the way in which 
 the figures should be taught. 
 
 Apparatus. The board should be placed as in fig. 245, and 
 divided into two equal portions by a line ab. It will then cor- 
 respond with the paper upon which the pupils are drawing. A 
 
Standard III 69 
 
 copy of the figure without construction lines should be placed 
 before the class. This will correspond with the card which the 
 pupil will be required to work from at the examination. It will 
 be sufficient for the present if the teacher 
 dictates the sizes of the lines to be drawn. 
 Both teacher and pupils will also need 
 rulers and set-squares. 
 
 The teacher will explain that he is 
 going to make his drawing a little larger 
 than the copy, and that it must be placed 
 in the top half of the board. 
 
 1. Place the ruler on the copy and 
 rule the continuous lines as shown by 
 the dots on fig. 244. The pupils will 
 
 then see that the copy is constructed upon three parallel 
 horizontal lines, intersected by vertical parallels forming a 
 number of squares. 
 
 2. Measure ab. Suppose it to measure half an inch ; then, 
 if the copy has to be enlarged, ab on the pupil's drawing might 
 be made three-quarters of an inch. 
 
 Note. The teacher should have his ruler marked so that four 
 inches on his ruler represent one inch on the pupil's ruler. 
 
 3. Draw a very faint line of indefinite length about one inch 
 from ab (fig. 245), and set off on it as many spaces of three- 
 quarters of an inch each as there are squares required (in this 
 case six). Fix the position of the first point a (fig. 244) care- 
 fully, so that the copy may be well placed on the paper. About 
 one inch from the margin will do in this case. 
 
 4. Set off very carefully at each end of the line two spaces 
 of three-quarters of an inch each, giving the points, b, c, e, and/; 
 using the ruler as shown in fig. 91. Rule be and cf very 
 lightly. 
 
 5. Place the ruler on ad, and with the set-square draw the 
 vertical lines forming two rows of squares. 
 
 Note. The pupils should follow the teacher step by step. 
 
 6. Now thicken in the pattern with a good firm line, ruling 
 the lines as directed. First the lines marked 1, then 2, next 3, 
 
-jo The Teaching of Drawing 
 
 then 4, and complete by ruling 5. It is very important to insist 
 upon the ruling being done in this manner, as it secures rapidity 
 and uniformity, and the pattern will always be symmetrical at 
 each stage of the copy. 
 
 7. The pupils should now be shown that the pattern may 
 be continued to any length, and illustrations of its application 
 in the decoration of oilcloths, papers, carpets, stonework, &c, 
 given. The bottom half of the paper should now be filled 
 with the same pattern drawn to a different scale. 
 
 Notes.- 1. Many teachers prefer to rule the construction lines 
 in dotted line. This gives a very good appearance if the line is 
 carefully ruled with light and even strokes, as the pattern stands 
 out well from the construction. A very faijit line is much quicker, 
 and can probably be done better by the class as a whole. 
 
 2. No construction lines are to be removed, as the line of the 
 copy will be spoiled, and it is essential that the method of obtain- 
 ing the figure should be apparent. It is not advisable to give out 
 indiarubbers, except towards the end of the course, and then only 
 for the purpose of trimming up the copy if necessary. 
 
 3. The squares as a rule should not be of less than three-quarter 
 inch sides. 
 
 Figs. 246-259. These are all based upon two lines of 
 squares. 
 
 The dotted lines show the necessary constructions, which 
 should be worked out in a similar manner to fig. 244. The 
 figures indicate the order of thickening in the pattern. 
 
 Figs. 260-270. These figures are constructed upon three, 
 four, and five lines of squares, and can be easily followed 
 from the construction lines. 
 
 Figs. 271-281 are based on the square, rectangle, &c. The 
 dotted lines indicate the method of construction. Various 
 exercises of a similar character may easily be devised by the 
 teacher. 
 
 The copy without the construction lines should in all cases 
 be placed before the class, and the method of construction 
 elicited before beginning. The pupils should be taught to 
 measure up the copy, and as far as possible to enlarge the 
 various^ parts proportionately. For example, suppose it were 
 
Standard III 
 246 
 
 71 
 
 
 1 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 -- 
 
 
 
 
 2 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 247 
 
 / 
 
 mm y " TT-TI n T-n" v~\ \~~r~ 
 
 3 \ 1 1 1 . 
 
 -- ,- 1 ; ! - --7 i 
 
 I I I I I 
 
 lil t I I 1 . I 
 
 
 f 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 1 
 
 4 
 
 3 
 
 
 
 
 
 ' 
 
 
 
 
 
 i 1 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 1 i 
 
 
 2 
 
 
 
 
 249 
 
 
 
 
 
 If 
 
 / 
 
 
 
 / 
 
 
 
 \ 
 
 / 
 
 
 
 ' ! 
 
 1 
 
 4 
 
 5 
 
 
 
 
 
 
 \ 
 
 
 
 
 1 
 
 3 
 
 250 
 
 I 1/ I 
 
72 
 
 The Teaching of Drawing 
 
 253 
 
 / 
 
 257 
 
 258 
 
 259 
 
 
 
 
 260 
 
 
 
 
 t 
 
 f 
 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 i 
 
 
 
 1 
 
 in 
 
 ... 
 
 1 
 
 1 
 
 261 
 
 * 
 1 
 
 
 
 1 
 
 _J 
 
 
 
 4.. 
 
 
 
Standard III 
 
 73 
 
 262 
 
 / 
 
 
 1 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 
 z 
 
 
 4 
 
 
 
 
 
 
 
 
 
 ;3 
 
 2 
 
 . 3 
 
 
 
 
 
 
 
 1 
 1 
 
 203 
 
 
 
 
 1 
 
 
 I 1 
 
 1 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 / 
 
 
 
 
 
 1 
 
 t 
 
 
 1 1 
 t ' 
 
 1 I 
 
 
 
 
 264 
 
 265 
 
 i v \ x'i / : !x ! 
 
 r - yv - 1 >nt - - - -a\- - r - TV - r 
 
 1 / ;\ . /i\ 1 /'X , /\ X 1 
 
 266 
 
 1 1 1 , 
 
 1 1 11 
 
 1 1 1 1 
 
 1 1 1 11 
 
74 
 
 The Teaching of Drawing 
 267 
 
 2 
 
 1 1 1. 
 
 t \ i 
 
 i !. i 
 
 9 
 
 / 
 
 26S 
 
 XX 5 XX NX XiX XIX XX XX 
 
 k~- XV T m XX "yrtv" ~~ XX* 7 ""A >dVv^"">TV~ X jfK xx I 
 
 L^-A-S.X XjhJpi X^ - ' X-^r X x x^ 
 
 X : X : X 1 X : X X X 4 X X X X2 X /z X 
 
 209 
 
 270 
 
 1 1 1 
 1 
 
 1 > 
 1 
 
 _ il 
 
 ' ! 
 1 1 1 
 
 required to make fig. 275 half as large again ; then, if cd=2 inches 
 and tf=half an inch, the pupil would make the dimensions 
 three inches and three-quarters of an inch respectively. 
 
 Figs. 271-276. First draw the squares shown in dotted 
 line. Set off the distances marked ab from each angle. Rule 
 in the pattern with a good firm line, 
 
Standard III 
 
 7$ 
 
 271 
 
 272 
 
 273 
 
 
 a, b 
 
 1 
 
 1 
 
 
 
 
 
 ^ 
 
 
 
 \ 
 
 1 
 
 
 
 j 
 
 a b 
 
 a b 
 
 
y6 The Teaching of Drawing 
 
 Note. In figs. 273 and 275 care must be taken to see that the 
 lines pass exactly through the centre. 
 
 Fig. 277. Draw the diagonals and complete the square, and 
 then set off the distance ab from each angle. 
 
 Fig. 279. This is rather difficult for children to see at first, 
 but if the teacher places the ruler on the copy and marks in 
 the dotted lines, they will at once perceive that the copy is 
 obtained by dividing each side of a square into three equal 
 parts and emphasizing portions of the lines. 
 
 Fig. 281. Draw the diagonals and obtain the square as in 
 fig. 277. To obtain the middle points of each side of the 
 square, place the 45 set-square with its longest edge on the 
 side of the figure, as shown. Keep the ruler firmly in position, 
 and slip the set-square into the position shown by the dotted 
 lines, so that its longest edge is now on the centre of the square, 
 and mark in the points a and b. Reverse the set-square, still 
 keeping the ruler in its place, and obtain c and d. 
 
 Note. This is a very important method, as when the square is 
 constructed from the diagonal the side cannot be bisected easily, as 
 its length is not known. It has also the advantage of being 
 quickly performed, and gives the pupils increased power in the use 
 of the set-square. 
 
 Triangles. These are classified in two ways, either accord- 
 ing to their sides or to their angles. When named from their 
 sides they are called : 
 
 1. Equilateral. Three equal sides. 
 
 2. Isosceles. Two equal sides. 
 
 3. Scalene. All the sides unequal. 
 
 When named according to their angles they are called : 
 
 1. Right-angled. When one of the angles is a right 
 angle. 
 
 2. Acute-angled. When each angle is less than a right 
 angle. 
 
 3. Obtuse-angled. When one angle is greater than a right 
 angle. 
 
 Notes. 1. These two ways of denoting triangles should be 
 frequently explained and defined. 
 
Standard III 
 
 77 
 
 2. It will be quite sufficient for the pupils to test the size of 
 the angle with the set-square in determining whether it be a right 
 angle or not. 
 
 The terms base and apex or vertex should be explained. 
 
 The equilateral triangle, fig. 282. Draw ab the required 
 size. Place the 6o set-square on the ruler with the angle of 
 6o at a, as shown by the light line, and draw ac. Keep the 
 ruler in position, reverse the set-square, and draw be. This is 
 much more expeditious and accurate than bisecting ab, drawing 
 a perpendicular, and cutting it with a distance equal to ab to 
 obtain the point e. 
 
 282 283 
 
 If the figure stands upon its angle, as in fig. 283, then place 
 the ruler and set-square as shown, and draw ab and ac as before. 
 Make ab and ac the required length, and join b with c. 
 
 284 285 286 
 
 d a c d 
 
 a, c o d a c 
 
 The isosceles triangle, figs. 284, 285, 286. Draw the base 
 
78 
 
 The Teaching of Drawing 
 
 ab and obtain the centre c. Set up the altitude to the required 
 height, and draw the sides. 
 
 The right-angled triangle will need no comment- It 
 might be pointed out that it may also be isosceles like the 45 
 set-square. 
 
 Zigzags. Fig. 287 forms a good exercise on the equilateral 
 triangle. Draw two parallel lines a little wider apart than the 
 
 287 
 
 if 
 
 
 d 
 
 
 f 
 
 /60 
 
 
 a 
 
 c 
 
 
 e 
 
 
 given copy. Mark point 0. Place the ruler on ac, and with 
 the 6o set-square draw ab. Reverse the set-square and draw be, 
 then cd, de, ef, &c, reversing the set-square for each line. 
 
 Fig. 288. This is another example of the same character. 
 Draw two parallels as before and obtain the single zigzag abedef 
 
 g, making ag 
 
 as in the last figure Now fix the position of 
 
 slightly larger than the copy. Draw gh with the set-square in 
 
 the same manner as ab, and complete the zigzag ghlmno as 
 
 before. 
 
Standard III 
 
 79 
 
 The previous examples are based upon the equilateral 
 triangle. If, however, the lines are not drawn at an angle of 
 6o, then vertical lines 
 should be drawn as in 
 fig. 289, and the zigzag 
 completed by drawing a 
 series of alternate dia- 
 gonals. 
 
 The Hexagon. This 
 is a very important and 
 
 interesting figure, as so many pretty and useful exercises may 
 be based on it. It affords excellent practice with the set- 
 square, and will do more to accustom the pupil to ready mani- 
 pulation of this useful instrument than any other exercise. 
 
 I. Standing on its base, fig. 290. Draw ab, say one and a- 
 half inches in length. Adjust the set-square as shown in position 
 A, and draw be. Place the set-square as in B and draw af. 
 Make be and af both equal to ab. With the ruler on ab slip 
 the set-square from A to point/ as shown by the dotted line, and 
 
 290 
 
 draw fe. Reverse the set-square and obtain cd. Make/? and cd 
 equal to ab. Join ^and e. Now let the pupils draw hexagons 
 of various sizes until the figures can be quickly and deftly con- 
 structed. If the required hexagon be a large one, then place 
 the ruler on af and obtain fe in the same manner that af was 
 obtained from ab, &c. In all cases it will be necessary for the 
 class to draw the figure line by line with the teacher, and a strict 
 
80 The Teaching of Drazving 
 
 watch must be kept to see that each child always places his 
 set-square on the ruler. 
 
 Various diagonals, &c, may be drawn across the figure, form- 
 ing fresh exercises, as in figs. 291-293. 
 
 As an exercise in ingenuity the pupil may now be shown 
 how to complete the hexagon without measuring the sides, as 
 in fig. 294. 
 
 Draw ab of the required length. 
 Obtain be and ad with the set- 
 square. Reverse the set-square 
 and draw of and be. Place one 
 edge of the set-square on ab and 
 draw a line through o parallel to 
 ab, cutting off the sides of and be 
 equal to ab. From/ and c draw fe 
 and cd parallel to ad and be respec- 
 tively, and cutting the lines be and 
 ad in e and d. Join e with d. 
 II. When standing on an angle, fig. 295. Mark the point a 
 and rule a faint line xy through it. With the ruler on the line, 
 and the set- square with its angle of 30 placed as shown, 
 draw ab and af the required length. Keep the ruler in its posi- 
 tion and draw be andy? at right angles to xy and equal to ab. 
 Draw ed and cd parallel to ab and af respectively by slipping the 
 set-square from its first position across to point e. If the set- 
 square be not large enough, then place the ruler on ec. 
 
 Fig. 296. This is a common test, and if worked as shown, 
 from the hexagon, presents no difficulty whatever. 
 
Standard III 
 
 81 
 
 The lesson should be given somewhat after the following 
 manner. 
 
 A drawing of the figure without any construction lines 
 should be placed before the class. If the pupils be each pro- 
 vided with a copy it will be advantageous. 
 
 i. How many points has the figure ? ' Six.'' 
 
 If I join them, how many 
 sides will the figure have ? 
 
 What do we call a figure 
 with six sides ? ' A hexagon.' 
 
 Elicit illustrations, such as 
 nuts in machinery, bees'-cells, 
 patterns, &c. 
 
 2. Draw a hexagon roughly 
 on the board, and join the 
 alternate corners. 
 
 What figure is formed ? 
 1 An equilateral triangle.' 
 
 Why is it called equi- 
 lateral ? 
 
 Join the remaining corners. The pupils will now see that 
 the figure formed is the drawing required. 
 
 3. Measure the distance between a and b on the given copy, 
 and explain that as the drawing has to be a little larger each side 
 
 G 
 
82 
 
 The Teaching of Drawing 
 
 of the hexagon must be enlarged. For example, if ab be one 
 and a-half inches on the copy, then on the drawing it should be 
 made about one and three-quarters of an inch or two inches in 
 length. 
 
 4. Draw xy and mark a point a in the centre. 
 
 Which angle of the set-square must be used ? ' The smallest? 
 
 Now, step by step, obtain the hexagon as in fig. 295, eliciting 
 the reason for each step. Join the alternate angles /, b, d, 
 giving the equilateral triangle fid. Complete the figure by 
 drawing the intersecting triangle ace. 
 
 Notes. 1. Be careful to draw the hexagon either very faintly 
 or in dotted line. 
 
 2. Let the pupils draw exercises of different sizes until the 
 method is well understood. 
 
 The Octagon. This forms an exercise in the use of the 
 45 set-square. 
 
 Draw ab one inch long. Arrange the set-square as shown 
 (A) : draw ^and ah> making each line one inch in length. Keep 
 
 297 
 I e 
 
 the ruler in position, and with the vertical edge of the set-square 
 draw cd and kg (B). Keep the ruler still on the base, and with 
 the sloping edge of the set-square draw gf and de. If the set- 
 square be not large enough, place the ruler on gd. Vertical 
 lines from a and b will determine the points / and e. Join / 
 with e. 
 
 Join the alternate corners as in fig. 298, and two intersecting 
 squares will be produced. 
 
Standard III 
 
 83 
 
 The intersecting squares may, however, be more easily 
 obtained by the method shown in fig. 299. 
 
 1. Measure the diagonal ab on the copy, and decide upon 
 the size to which it should be enlarged. For example, if the 
 diagonal measured two inches, then three inches would be a 
 suitable size for the enlargement. 
 
 2. Draw the diagonals ab and ca\ and complete the square 
 adbc. 
 
 3. Place the set- square on ad and draw ef parallel to it. 
 Obtain gh in a similar manner. Make ef and gh equal to ab, 
 and draw the square egfh. 
 
 The Pentagon. This figure cannot be drawn accurately 
 without the use of the compass or the protractor, and should 
 really not be set as a geometrical figure for this Standard, as 
 it cannot be correctly drawn with the ruler only. Various 
 mechanical devices have been given, none of which are very 
 satisfactory, as they are after all only approximations. 
 
 The most accurate device is to use the protractor, but as 
 this may not be readily obtainable the teacher can easily cut 
 out in paper angles of 108 , and use these to draw the angles 
 of the figure. The paper angle must be placed so that its edge 
 is exactly on the base ab with the angle of 108 at b (fig. 300). 
 Place a little tick c to mark where the line has to be drawn. 
 
 G2 
 
84 
 
 The Teaching of Drawing 
 
 Remove the paper and rule the line. Make the side equal to 
 ab. Place the paper at a and draw ae, then at e and draw ed, 
 Join d with c. 
 
 The proportions given on fig. 301 will give a sufficiently 
 accurate pentagon of a convenient size. Let ab = 2 in. Draw 
 
 cd perpendicular to ab from the middle point c, and make it 
 3 J inch long. Set off d? = i inch. Draw fg parallel to ab, 
 and. make ef and eg each = if inch. Draw af, bg, fd, 
 and gd. 
 
 Note. In this case the pupils must have the proportions given 
 them. 
 
25 
 
 CHAPTER VI 
 
 FREEHAND DRAWING. STANDARDS IV, V, VI, AND VII 
 
 If the methods of obtaining the proportions of the different 
 parts of the copy, and the drawing of the leading and the con- 
 taining lines have been well taught in Standard III on the 
 methods shown in figs. 203-231, the freehand drawing of the 
 higher standards becomes an easy and pleasant task. The 
 main points that will now require attention are : 
 
 (1) Greater degree of difficulty in the examples. 
 
 (2) Increased power in analysing and blocking in the copy. 
 
 (3) More skill and finish in the lining in of the drawing. 
 And here I would again point out the necessity of strict atten- 
 tion being paid to the lining in. On no account must the 
 pupil be allowed to hurriedly blacken over the lines of the 
 drawing. A careful, clean sketch shows much better and more 
 artistic work than a carelessly lined in drawing. The primary- 
 object of lining in is to improve the shape, and to give finish 
 to the work. 
 
 It has been thought desirable to take the whole subject of 
 Freehand in one chapter, as it is quite impossible to divide the 
 subject into standards by any arbitrary rule. A selection of 
 suitable copies including those given in the 'Illustrated 
 Syllabus,' and many that have been set as examination tests 
 are appended for the teacher's guidance. 
 
 Sample lessons are also given, and those copies which illus- 
 trate important principles, or present special difficulties, are 
 shown in various stages to indicate the methods by which they 
 should be taught. In some cases the dotted lines are sufficient 
 to indicate the construction. The figures in all cases indicate 
 the order of drawing the lines. 
 
86 The Teaching of Drawing 
 
 The following arrangement of the examples given is sug- 
 gested : 
 
 Standard IV. Figs. 302-329. 
 Standard V. Figs. 330-356. 
 Standard VI. Figs. 357-376. 
 Standard VII. Figs. 377-383. 
 
 Standards VI and VII are frequently examined from cards 
 instead of large copies placed before the class, and practice 
 must therefore be given in both methods of testing. The 
 pupils when drawing from cards must never be allowed to draw 
 the example the same size as the copy. It should always be 
 either enlarged or reduced ; generally the instruction is to 
 make the copy fairly fill the paper. 
 
 The time taken for the drawing must be borne in mind, 
 especially towards the examination ; fairly rapid work should be 
 encouraged, but on no account must the pupils be allowed to 
 finish their drawings to time at the sacrifice of accuracy in the 
 shape. A portion well drawn and correctly planned is far more 
 valuable than an incorrectly finished exercise. 
 
 The following lesson indicates the way in which the 
 examples should be taught : 
 
 (1) Place a drawing of the figure before the class, and pro- 
 ceed to question generally as to what it is called, what grows 
 like it, and ask for illustrations of its application in metal scroll 
 work of various kinds. Explain that the drawing is obtained 
 by selecting the important lines only of the object from which 
 the idea is taken ; the details and little irregularities are rejected, 
 not being suitable for the required purpose. 
 
 (2) Commence with the upright line and mark in the 
 middle point, as the half is very useful for purposes of compari- 
 son, even though no line may pass through it. 
 
 (3) Mark the point a where the bottom curve commences, 
 judging the distance with the eye. Find point b by measuring 
 with the eye and pencil. 
 
 Where is it? * A little above the half of the line? 
 What do we want to know next ? ' The position of 
 point c? 
 
Standard IV 
 
 87 
 
 Find the width of the curve on the right and mark point d. 
 
 Is point e as far from the centre line as point d? 
 
 (4) After marking in point e proceed to draw the bottom 
 spiral, taking care to keep the curve continuous throughout. 
 The first time of drawing a spiral the pupils may, if thought 
 well, draw the dotted lines shown on fig". 303 as guides for 
 the curves. They should, however, be discarded afterwards, as 
 
 303 
 
 all aids of this character tend more or less to limit the pupil's 
 confidence and freedom in drawing bold curves. 
 
 (5) Draw the top spiral in a similar manner, first marking 
 in points g, h, /, m. 
 
 (6) Now show how the parts 1, 2, and 3 branch off from 
 the other lines. Notice that they form a continuous line with 
 the previous part of the curve as in A> not as in B (fig. 304). 
 
88 
 
 The Teaching of Drawing 
 
 Attention must also be directed to the fact that the spiral 
 gradually decreases towards its centre, od is slightly less than 
 
 304 
 
 en, and bp less than od (fig. 302). This point may be easily 
 illustrated by rolling a piece of paper so as to form a spiral. 
 
Standard IV 
 305 306 
 
 89 
 
90 
 
 The TeacJiing of Drawing 
 
 310 
 
Standard IV 
 
 91 
 
 311 
 
 312 
 
92 
 
 The Teaching of Drawing 
 313 
 
 . l_ 
 
 314 
 
3i6 
 
94 
 
 The Teaching of Drawing 
 
 318 
 
Standard IV 
 319 
 
 95 
 
 320 
 
96 
 
 The Teaching of Draiving 
 
Standard IV 
 
 97 
 
9 8 
 
 The Teaching of Draiving 
 
 \ ( ' 
 
 329 
 
Standard V 99 
 
 STANDARD V 
 
 The figures suggested for this Standard are arranged more 
 with reference to their form and the principles which they illus- 
 trate, than to the order in which it may be most desirable to 
 teach them. It will probably be found more interesting to 
 intermix the vases shown in figs. 332-338 with the other 
 copies, than to draw them in the order in which they are given. 
 These vases are v typical shapes, possessing great beauty of 
 contour, and are those which are most commonly used in model 
 drawing. They afford excellent practice in the drawing of bold, 
 symmetrical curves. As vases when placed in a vertical position 
 present a somewhat similar appearance to all the class, it will 
 be found to be of considerable assistance to the model drawing 
 if the pupils have previously practised the vases as freehand 
 exercises ; the same method of working being followed out in 
 both model and freehand. 
 
 Attention should be directed to the fact that all the vases 
 given are based on the oval that is, one end of the body is 
 larger than the other, like an egg. This form gives a much more 
 elegant shape than either the circle or the ellipse would do. 
 
 The method of drawing is shown in stages and by the aid 
 of dotted lines. The following steps refer particularly to 
 fig. 334, but are also generally applicable to most vases. 
 
 1. Draw the centre line, ab. 
 
 2. Find the position c of the widest part of the vase. 
 
 3. Compare the greatest width with the height, and set it 
 out, de. 
 
 4. Draw the diameters of the mouth and foot of the vase, 
 fg and hk, comparing them with the greatest width, de. 
 
 5. Carefully sketch in the oval for the body, afterwards re- 
 moving the parts which are not needed. 
 
 6. Draw the ellipses for the mouth and foot. 
 
 7. Mark the narrowest part of the neck, ?m. 
 
 8. Draw the curve uniting the mouth with the body. 
 
 9. Suggest the thickness as shown in fig. 330. It will be 
 necessary to make enlarged drawings on the board of the details 
 
 h 2 
 
IOO 
 
 The 
 
 Teaching of Drawing 
 
 connected with the mouths and feet of vases. For example, the 
 mouth of fig. 334 is suggested in the following manner. The 
 edge being rounded off, the thickness is only visible at each side. 
 
 33o 
 
 V" 
 
 The foot of fig. 338 should be drawn as in fig. 331. The 
 outer ellipse should be shown going behind the inner ellipse, 
 as in A, not like B or C. 
 
Standard V 
 
 ioj 
 
io2 The Tear] ling of Drawing 
 
 336 
 
Standard V 
 337 
 
 103 
 
104 The Teaching of Drawing 
 
 Fig. 339 is an excellent example for teaching from, as it 
 affords practice in analysing and blocking in a copy. It is 
 shown in three stages of development, and should be taught in 
 the following manner : 
 
 i. Draw an upright line, ab. 
 
 2. Draw cd just below the point a. 
 
 3. Compare ed with ab. 
 
 4. After marking the position of c and d, fix the points / 
 and g t and draw the curves cf and dg. 
 
 5. Find the position of h and draw a line through it. 
 
 6. Mark the points / and m, comparing hi with ec. 
 
 7. Draw the curves from / and m, taking care to let them 
 run into (/and dg, so as to form a continuous curve from /to / 
 and from g to m. 
 
 The leading lines of the figure are now obtained, and the 
 drawings should be carefully examined before proceeding any 
 further. When this stage has been correctly drawn the pupils 
 may go to the stage marked B. 
 
 8. Mark the width of the middle leaf at its widest part, no. 
 
 9. Draw the middle vein, noticing that the point of the leaf 
 bends over to the right. 
 
 10. Draw the sides of the leaf, taking care to let the lines 
 run into cf and dg gradually. 
 
 11. Mark the width at^ and q, and draw the curve. 
 
 12. Draw the lines rs and tu at right angles to cf and dg, 
 and put in the top curves of the flower. 
 
 13. Unite / and m with the bottom curve as is shown on the 
 left hand side of fig. B. This is rather a difficult curve, and 
 requires great care. 
 
 14. The leading lines and masses of the figure being now 
 completed, the drawings should again be carefully examined, 
 after which the figure may be finished as in C. 
 
 15. Mark the position of v and w, and draw the short curve 
 first. 
 
 16. Draw the bottom curve of the flower as shown on the 
 left side of C. 
 
 17. Put in the stems and complete the figure. 
 
Standard V 
 
 105 
 
io6 
 
 The TeacJdng of Drawing 
 
Standard V 
 342 
 
 107 
 
io8 
 
 The Teaching of Drawing 
 343 
 
Standard V 
 
 345 
 
 109 
 
 346 
 
no 
 
 The Teaching of Drawing 
 347 
 
 348 
 
 \e 
 
Standard V 
 
 in 
 
 35i 
 
112 
 
 The Teaching of Draiving 
 352 
 
Standard V 
 
 "3 
 
U4 
 
 The Teaching of Drazving 
 
 354 
 
Standard V 
 356 
 
 US 
 
 1 2 
 
u6 
 
 The Teaching of Drawing 
 
 STANDARD VI 
 
 Increased attention must be paid to the finish of the draw- 
 ing, as in this and the next Standard the work leads up to the 
 work required for the Elementary Drawing Certificate. If the 
 pupils have been well grounded through the previous standards, 
 they will now find no special difficulties here. 
 
Standard VI 
 
 117 
 
 360 
 
1 1 8 The Teaching of Drawing 
 
 361 
 
3^3 
 
120 
 
 The Teaching of Drawing 
 364 
 
Standard VI 
 
 121 
 
122 
 
 The Teaching of Drawing 
 
 367 
 
123 
 
 37o 
 
124 
 
 The TeacJiing of Drawing 
 
Standard VI 
 
 125 
 
 373 
 
 374 
 
1 26 The Teaching of Drawing 
 
Standard VI 
 
 12 J 
 
 376 
 
128 
 
 The Teaching of Drawing 
 
 STANDARD VII 
 
 .The pupils should now have reached a stage of proficiency 
 requiring much less help from the teacher, and should them- 
 selves be able to apply the principles taught in the previous 
 standards. A few examples are given as an indication of the 
 character of the tests. Accuracy and finish should receive 
 great attention. Second Grade cards form very suitable 
 examples for the work of this Standard. 
 
 377 
 
Standard VII 
 378 
 
 129 
 
130 
 
 The Teaching of Drawing 
 379 
 
Standard VII 
 380 
 
 1*1 
 
 K 2 
 
132 The Teaching of Drazving 
 
 381 382 
 
 Fig. 382. Attention is here directed to the method of ob- 
 taining the flutes on curved surfaces. As the pupils will have 
 done some solid geometry, they will easily understand the way 
 in which this common form of decoration is obtained. The 
 semicircle shows half the plan of the vase at the top of the 
 fluted part. If the semicircle be divided into as many equal 
 portions as there are flutes required, ard projectors drawn as 
 shown, the correct widths for the flutes will be obtained. The 
 left hand side shows the necessary construction. 
 
 Figs. 383 and 372 show a small piece of foliage, and indi- 
 cate the way in which the plant should be drawn from nature. 
 The method of obtaining the serrated edges is shown on the 
 bottom leaf of the laurel in fig. 383, half being left plain to 
 show the way in which the leaves should be sketched. The 
 veins should be kept light and delicate, gradually dying away 
 as they approach the edge of the leaf. 
 
Standard VTT 
 
 33 
 
 383 
 
1 34 The Teaching of Drawing 
 
 CHAPTER VII 
 
 SCALE DRAWING. STANDARD IV 
 
 Syllabus. Simple scales and draiving to scale. 
 
 Drawing to scale will be limited to the following subjects : 
 
 To draw and take dimensions from a scale of feet and 
 inches. 
 
 To draw a plan or other figure on squared paper from a 
 sketch having dimensions marked on it. 
 
 To enlarge or reduce plane figures to scale. 
 
 These requirements may be conveniently divided into four 
 parts. 
 
 i. The measurement and drawing of lines, and the con- 
 struction and use of scales. 
 
 2. The drawing of objects to various given scales on plain 
 paper. 
 
 3. The drawing of objects on squared paper. 
 
 4. The enlarging and reducing of given drawings. 
 
 The apparatus necessary for the teacher will be : large set- 
 squares 45 and 6o, a 3 ft. slip or T-square marked in inches 
 as in Standards I and II, and a blackboard squared on one 
 side with red lines one inch apart. 
 
 The pupils will require plain drawing books or paper 1 1 by 
 7J inches, set-squares, indiarubber, &c, as in the previous 
 standards, and in addition squared paper ruled very faintly 
 with lines one-eighth of an inch apart. If every fifth line be 
 ruled heavier it is of considerable assistance in counting. 
 
 An H pencil. 
 
 A 9-inch ruler marked with twelfths and eighths. 
 
Scale Drawing. 
 
 Standard IV 
 
 135 
 
 The following diagram represents a convenient scale ruler for 
 this subject. Ordinary rulers, such as are used for arithmetic, 
 &c., are not very suitable, as the edges get notched -and the 
 divisions obscured by ink. Good hard-wood scales may now be 
 obtained very cheaply. The teacher will find it better to keep 
 a set purposely for scale work. It is not advisable to procure 
 any scales that are not properly figured. The first unit on the 
 
 384 
 
 "["I'M" 
 
 
 
 
 
 
 
 
 
 
 \1k 6 3 
 8 7 
 
 
 
 6 
 
 1 
 
 5 
 
 2 
 
 4 
 
 3 
 
 3 
 
 4 
 
 2 
 
 5 
 
 1 
 
 6 
 
 
 
 7 8 
 
 2 4-68 
 
 
 
 
 
 
 
 
 J, 1,1, 
 
 scale ought always to be marked zero (o), as distances can then be 
 measured from it without fear of mistake. Suppose, for exam- 
 ple, the distance of 2 ft. 7 in. is required to be set off to a scale 
 of one inch to a foot, then the space marked AB (from the 2 
 to the 7), fig. 384, will be the required distance. In the same 
 manner other distances may be marked off directly ; 5 ft. 9 in. 
 would be represented by the distance between 5 and 9 on the 
 scale. On an ordinary ruler the pupil would have to calculate 
 the distance by counting up the inches and parts. 
 
 Compasses. If thought desirable, a pair of compasses or 
 dividers may be used. They are not, however, necessary for 
 this Standard, as all the dimensions can be more accurately 
 taken by the pupils from the scale ruler. 
 
 In giving a lesson the teacher should in all cases have either 
 the object to be drawn or a drawing of it before the class. This 
 subject is a valuable means of stimulating general intelligence, 
 and is always popular with children, as its practical application 
 is so apparent to them. 
 
 The subject will be treated in the four sections mentioned 
 at the beginning of the chapter, but the construction of plain 
 scales should not be attempted until the pupils have obtained 
 a thorough mastery of their instruments. The easiest plan is 
 to commence with sections two and three that is, the drawing 
 of objects to scale on plain paper, and the exercises on squared 
 paper working the two concurrently. 
 
1 36 
 
 The Teaching of Drawing 
 
 Introductory Lesson. 1. Refer to Standard I geography, 
 where the pupils have already acquired the idea of representing 
 long lines by taking shorter units, when drawing plans of the 
 room, school, &c, and illustrate this by plans, maps, &c, drawn 
 to various scales. Explain that this is ' Drawing to Scale,' and 
 show that it is not only necessary to draw large objects to a 
 smaller scale, but in the case of small objects such as the 
 parts of a small instrument or the wheels of a watch--it would 
 be necessary to make the drawing to a larger scale. 
 
 2. Give mental exercises on the repre- 
 sentation of lines of various lengths to 
 different scales, such as : 
 
 If the door be eight feet high, how long 
 will the line be to represent it, if one inch 
 stands for one foot 7 
 
 If half an inch and two inches 
 respectively represent one foot, how long 
 then ? 
 
 3. Measure up the outline of some 
 simple object, such as a door or window, 
 make a rough dimensioned sketch on a 
 corner of the board, as in figure 385, and 
 from this draw to a scale of 1" to i' o v . 
 
 4. Explain the method of representing 
 the dimensions ; that feet are represented 
 
 by ('), and inches by ("), and that 3' 6" reads 3 feet 6 inches. 
 The 8' o" in fig. 385 represents the distance between the 
 arrowheads a and b, and the 3' 6" between the arrowheads 
 c and d. 
 
 5. Commence with the base line. 
 
 How long is it ? ' Three feet six inches.'' 
 
 What distance niust be taken to represent it if the scale be 
 one inch to one foot ? ' Three inches and six- twelfths' 
 
 Then set off from your rulers from the three inches to the 
 six- twelfths. 
 
 How high is the door? 
 
 What distance shall we mark off from the ruler ? ' From 
 o to 8.' 
 
Scale Drawing. Standard IV 137 
 
 What kind of an angle do the 1 sides make with the bottom 
 of the door ? ' A right angle? 
 
 How, then, must the sides be drawn ? ' With the set- 
 square' 
 
 6. After the outline of the door is completed, draw it again 
 to a scale of two inches to one foot, and if time permits to a 
 scale of half an inch to one foot. 
 
 Show that the three drawings represent the same object, 
 and that the relative proportions of the parts are maintained 
 in each. 
 
 This should be followed by the measuring up and draw- 
 ing of a window or some such object in a similar manner to 
 the previous one. 
 
 x * The pupils will then have a clear understanding of what 
 drawing to scale - really means, and will readily comprehend the 
 reasons for the various processes which follow. 
 
 Note. The teacher will mark arbitrary divisions on his ruler 
 to represent inches, such as 4 in. to stand for 1 in. It is a very 
 useful plan to mark the ruler so as to correspond with the pupil's 
 ruler ; each line that the teacher measures will then correspond 
 exactly with that measured by the pupils. 
 
 As this book is intended for the teacher's use, the section 
 dealing with the construction and use of scales, although the 
 most difficult, is taken first, as it is essential that the teacher 
 should thoroughly understand the principles upon which scales 
 are constructed and the method of using them before teaching 
 the subject. 
 
 SECTION I 
 
 The construction of simple scales. The scales required in 
 this Standard are what are known as plain scales that is, scales 
 showing equal divisions and from them we get two dimensions 
 such as feet and inches, or miles and furlongs, &c. 
 
 Before constructing any scales, explain that the scale is used to 
 measure distances on the drawing, and illustrate this by measuring 
 on plans and maps from the scales given on them. As scales 
 are perfectly useless unless accurate, very great care should be 
 
n8 
 
 TJie Teaching of Drazving 
 
 fa ^ 
 
 taken in their construction ; a sharp pencil should be used, and 
 the divisions marked off with exactness. This is about the 
 most difficult operation that has to be done in this Standard. 
 The method to be adopted will be best 
 
 seen from the following example : 
 
 Construct a scale of i inch to ifoot, show- 
 ing feet and inches, long enough to measure 
 4 feet. From this scale draw a line 2 //. 
 9 in. long. 
 
 1. Ascertain how long the line must be 
 that will represent 4 feet. 
 
 2. Draw a line 4 inches long, and mark 
 the inch divisions on it from the ruler. 
 
 3. Rule the parallel line above it and 
 ' about one-twelfth of an inch from it, and very 
 
 carefully mark in the short vertical lines 
 fjhowing the divisions. 
 
 4. Figure the scale as shown, and be 
 careful to insist upon the first division being 
 marked zero (o). 
 
 5. Explain that we have now marked 
 the units. (If 1 inch represents 1 foot, 
 then the inch is the unit.) The sub-divisions 
 of the unit will be shown on the left hand 
 side of the (o). 
 
 6. Now if 1 inch represents 1 foot, 
 what distance will represent 1 inch ? One- 
 Hvelfth: 
 
 Take the end of the ruler which is 
 divided into twelfths, place it carefully on 
 the first division, and mark in first the 
 half-inch, then the quarters, and afterwards the twelfths. 
 
 Note. Be careful to insist upon the vertical lines being ruled. 
 This may be done with the set-square if thought desirable. For the 
 first exercise it will probably be sufficient to mark in the quarters only. 
 
 Os 
 
 isM 
 
 7. Figure the sub divisions 3, 6, 
 right and inches at the left. 
 
 9, 12, and print feet at the 
 
Scale Drazving. Standard IV 139 
 
 8. Write under the drawing ' Scale=i" to 1' o".' 
 
 9. Explain and show the advantage of figuring the first 
 division (o) by the second part of the question, viz : ' to draw 
 a line 2 ft. 9 in. long' The pupils will see that from the 2 to the 
 9 is the distance required, and that when the scale is correctly 
 numbered, the figures will always indicate the distance. Let 
 the pupils come out to the board and show other distances 
 thus : 3 ft 7 in., the right-hand forefinger on the 3 and the 
 left-hand finger on the 7, &c. 
 
 10. Thicken in the bottom line and every alternate division 
 for the sake of clearness. 
 
 The representative fraction should be explained, as it helps 
 to a better understanding of the subject. 
 
 If 1 inch stands for 1 foot how much smaller is the line 
 drawn than its actual size ? ' One-twelfth of the real size.' 
 
 Then T V is the representative fraction, and shows that the 
 real object is twelve times larger than the drawing of it. 
 
 If half an inch represents 1 foot what is the representative 
 
 . _ \ inch 1 inch 1 
 
 fraction? *- e - = -. , as 
 
 1 loot 12 inches 24 
 
 If 1 inch stands for 1 yard, what is the fraction? 
 1 inch 1 
 
 36 inches ~" 36' 
 
 Other similar questions will easily make this point clear. 
 
 Scales of two inches , half an inch, and one and a- half inches 
 to the foot should now be drawn, as shoivn in figs. 387, 388, 
 389- 
 
 Note. The eighths of an inch will give the twelve sub-divisions 
 for the scale of \\" to i' o." 
 
 A variety of ways in which these problems may be set are 
 given, and should be frequently and carefully practised. 
 
 Fig. 390. Construct a scale of three-quarters of an inch to 
 one yard, to show 5 yards 1 foot. 
 
 What is the unit? ' Three-quarters of an inch.' 
 
 What does it stand for? * One yard.' 
 
 If the scale is to measure 5 yards 1 foot, how many units 
 must be set off? 'Six.' 
 
140 
 
 CM 
 
 r ! 
 
 *) 
 
 ^c 
 
 Ot 
 
 o CM 
 
 I 
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 The Teaching of Drawing 
 
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Scale Drawing. Standard IV 
 
 141 
 
 How long will the line 
 
 Orn 
 
 be ? ' 6 inches 
 inches' 
 
 Rule a line 
 
 x j i?ich=^\ 
 
 4 
 
 inches 
 
 long, and set off on it six 
 spaces of three-quarters of 
 an inch each. 
 
 Note. These dimensions 
 may, of course, be set off with 
 the dividers, if preferred. Our 
 own experience is that they 
 are not necessary, and that 
 the pupils mark off the divi- 
 sions more accurately and 
 quickly from their rulers. 
 
 Figure the scale and 
 write yards at the right hand. 
 
 If three-quarters of an 
 inch represents 1 yard, 
 what will represent 1 
 foot ? ' A quarter of an 
 inch' 
 
 Mark in and figure the 
 Sub-divisions, and complete 
 the scale. 
 
 Now indicate the dis- 
 tance required, 5 yards 1 
 foot, as shown above. 
 
 Fig. 391. Draw a 
 scale of 5 ft. 7 in. to a scale 
 of 1" to i' o". 
 
 Fig. 392. Draw a 
 scale 0/2! 6" showing inches. 
 Let 1 \ inches stand for 1 
 foot. 
 
 Fig. 393. Draw a 
 scate to measure 5 miles, 
 showing furlongs. Let 1 
 inch represent 1 mile. 
 
 <0 -r 
 
 <o 
 
 a cvj 
 
 ^O 
 
 Ch 
 
 ?M 
 
 rO 
 
 ^o 
 
 K-; 
 
 CM 
 
 H 
 
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142 The Teaching of Draiving 
 
 Notice that the end of the ruler marked with eighths will give 
 the furlongs. 
 
 The following exercises, most of which have been set for 
 examination, should now be worked. 
 
 i. Draw a scale of 1" to i' o" and draw from it a line 3' 4" 
 long. 
 
 2. Construct a scale of half an inch to one foot, and drazv a 
 line from it 3 ft. 6 in. long. 
 
 3. Draw a scale of one and a-half inches to one foot, and 
 show on it 2 ft. 2 in. 
 
 4. Draw a scale of % ft. 3 in. Let two feet be represented by 
 one inch. 
 
 5. Draw a scale of two inches to one foot, and mark off a dis- 
 tance showing 2 feet 3 inches. 
 
 6. If two and a quarter inches represent a longer line on a 
 scale of one inch to one foot, what is the actual length of the line 
 represented ? 
 
 SECTION II 
 
 The drawing of objects to scale on plain paper. This 
 naturally follows the construction of scales. 
 
 A dimensioned sketch of the object must be placed before 
 the class, as in fig. 394. 
 
 Commence with the base line, first ascertaining its length. 
 Complete the rectangle abed. Set off af and de each four 
 twelfths (o to 4), and rule the lines eg and fh with the set-square. 
 This is preferable to setting off the measurement on each side, 
 as time is saved and dexterity in manipulation acquired. These 
 lines should be either dotted or ruled with a very light line. 
 
 The points / and ;;/ must now be found, de + Im -\-fa = 1 foot. 
 
 Then el -(- mf=i foot 6 inches, and el=g inches. 
 
 Set off el and /;;/ each nine-twelfths and draw A? and ;;// 
 with the set-square as before, making them the required length. 
 Set off fq four-twelfths, and complete the figure by carefully 
 thickening in the outline. 
 
 Ail construction lines must be left in to show the method of 
 procedure ; hence the necessity for fine lines. 
 
Scale Drawing. Standard IV 
 
 143 
 
 The figure when finished should stand out boldly from the 
 construction lines. 
 
 Note. The pupils should be shown how to obtain the dimensions 
 of the parts which are not figured. For instance, in fig. 394, 4 in. 
 is only given once, as it is evident at a glance that the other widths 
 are the same ; again, el is easily found from the other given 
 dimensions. 
 
 394 
 d C 
 
 T 
 
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 1 
 1 
 1 
 
 o 1 
 
 I ! 
 
 1 j 
 
 V4"-. j 
 
 ..A ;* 
 
 CVJ 
 
 I 
 
 / 
 
 I 
 
 % 2-0" ->* 
 
 Scale = 1" to i' o". 
 
 A few typical examples are given to illustrate the methods 
 of treating the figures ; for additional exercises the ordinary 
 books, such as ' Longman's Drawing to Scale ' {2d.) will furnish 
 an abundance of suitable examples. 
 
 Generally speaking, the bulk of the figures may be solved 
 either by enclosing the figure in a rectangle, as in fig. 394, or 
 working from a centre line. If the sides of the figure are 
 inclined to one another, one of these two plans must be adopted. 
 As a rule, working from a centre line is the neatest and 
 most workmanlike method. In the following examples the 
 construction lines are dotted, and show the method of work. 
 Explanations are also given where thought necessary. 
 
144 
 
 1 
 
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 trig 
 
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 395 / 
 
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 396 
 
 
 
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 a 
 
 
 
 
 
 
 Scale = t" to i' o" 
 
 
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 Scale 
 
 
 
 1" to x' 0". 
 
 
 397 ^^ 
 
 J 
 
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 1 
 
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 Scale = 1" to 1' 0". 
 
 
 
 
 Scale = 2" to 1' 0". 
 
 
 
 
 b 
 
 Fig. 395. Draw the vertical line 2| inches long. Set off 1 
 inch from the top and set out the horizontal line with the set- 
 square. Make each side -^ inch and complete the figure. 
 
 Fig. 396. Draw the top line. Set off 2$ inches and draw 
 ab. Complete the top, set off -^ inch from each end, and 
 with the set-square draw the outer lines of the legs. The 
 completion is now easy. 
 
 Fig. 397. Draw the box first. For the lid set off ad and erect 
 aperpendicular. To get the thickness of the lid, place the ruler 
 on cd and draw perpendiculars at c and d with the set-square. 
 
 Fig. 398. Draw ab 2\ inches long. At a draw the perpen- 
 dicular ac 4 inches. Set off 1 'inch from the top and with the set- 
 square draw de parallel to ab. At b erect a perpendicular. Draw 
 /parallel to de. The rest of the figure presents no difficulty. 
 
Scale Drawing. Standard IV 
 
 145 
 
 
 
 
 
 
 399 
 
 
 
 
 
 
 fw 
 
 
 T r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 u 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 
 $ 
 
 
 
 
 
 
 
 
 
 
 - 1 ^ ^ 
 
 1 
 <c 
 
 401 
 
 Scale = 3" to 1' o". 
 
 a<- 3 
 
 Scale = 1" to 1' o". 
 
 Fig. 399. Draw ab. Set off 2 inches and draw the dotted 
 line at the top. Set off \ inch for the lines at c and d, and draw 
 them parallel to ab. For the line at e set off inch (i| inches 
 =^ foot). For the palings set off distances of T \ inch. 
 
 Fig. 400. Draw ab 2^ inches long. (A scale of 3" to 1' o" 
 is a scale of j, so that each line will be \ of its real size.) Find 
 the centre c, and draw cd \\ inches long. Draw ef parallel to 
 ab, and make de and df each \ inch. Draw ea and /^. To 
 obtain bg, produce ab and make the produced part 2 inches 
 long. Draw kg perpendicular to M, and complete. 
 
 Fig. 401. Draw ab 3 inches long, and at the centre c draw 
 the perpendicular cd = 7 inches. Through */ draw ef. Draw <w 
 and </ The rest of the figure is easily followed. The width 
 of the rails must be set off on the centre line, and not on the 
 oblique sides of the easel. 
 
146 
 
 The Teaching of Drawing 
 
 402 43 
 
 1 
 
 
 1 
 
 
 
 1 
 
 
 1 
 
 J 1 
 
 Scale 
 
 [ l" to i' o' 
 
 Scale = 2" to i'o' 
 
 Figr. 402. This 
 
 figure requires very care- 
 ful drawing. Begin with 
 the line ab 3/0 inches 
 long. Draw the centre 
 line cd, on it set off 
 1 {% inches, and draw 
 the line ef, parallel to ah 
 and equal to it. Set off 
 1 T \ inches on the centre 
 line above ef, and drawdfe 
 and df Set off ^ inches 
 from a and b, and rule in 
 the sides. For the holes 
 draw a horizontal line T 8 2 inch above ab, set off the width, and draw 
 the vertical lines 5 the lines to g, &c, are obtained with the 45 
 set-square. For the thickness of the roof, draw lines at e and /at 
 right angles to ed and df, on these lines set off the thickness, and 
 rule the lines parallel to ^and ^ with the set-square. The width 
 of the struts must be obtained in the same, manner. Draw hi. 
 At h draw a perpendicular, and on this set off yV inch. 
 
 Note. This is a very important point. The pupils should be 
 shown why the thickness must be set off at right angles to the 
 side, and not on the vertical nor horizontal lines. 
 
 Fig. 403. The sketches given are not always drawn to scale j 
 the pupil should be taught to draw from the figured dimen- 
 sions, and must not necessarily expect the drawing to look 
 like the sketch given in the question. In this figure first draw 
 the rectangle shown in dotted lines, and set off the distances 
 from each corner. The length and breadth must first be 
 calculated from the dimensions given. 
 
Scale Drawing. 
 
 Standard IV 
 
 H7 
 
 SECTION III 
 
 Drawing on squared paper. This is the easiest portion of 
 the course, and is on that account frequently taken before the 
 other sections. It only requires accurate counting and care in 
 ruling. The following example will illustrate the proper method 
 of working. 
 
 Draw the given figure on squared paper. Let the side of 
 each square represent half an inch. 
 
 1. First count up the greatest length and breadth of the 
 figure, so that it may be placed to advantage on the squared 
 paper and not crammed into a corner. The given figure is 
 \o\ inches by 8^ inches, and will therefore require 21 squares 
 in one direction and 17 in the other. 
 
 a o 
 
 2. Count about 20 or 25 lines from the top of the paper, and 
 mark the points a and b with small dots 12 squares apart and 
 about equidistant from the centre of the space in which the draw- 
 ing is to be placed, as in fig. 405. In the same manner indicate 
 the points c and d, and rule in the rectangle abed with a. firm bold 
 line, so that the drawing stands out well from the chequered lines. 
 
 This is much better than marking the whole figure in with dots 
 before ruling, as when a line is ruled in, the position of the lines 
 adjoining it can be more readily fixed. The dots must on no account 
 be made large, or they will show after the lines are ruled. 
 
 l 2 
 
148 
 
 The Teaching of Drawing 
 
 3. Obtain e andyj and rule in. 
 
 4. The points m and / are obtained as follows : gh 
 2 inches + inch + J inch = 3 inches. Therefore dm 
 1 inch. Complete the right hand side. 
 
 405 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 r 
 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 11 
 
 
 
 v\ 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 P 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 '''.772 
 
 
 
 h 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 b 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5. Find the middle (x) of cd and mark in/ and ^, each two 
 squares from the centre. Count up 7 squares from x and 
 mark the points r and s. Rule in qs and fir, dotting the upper 
 portion. From r count 4 squares and rule in st. Mark u and 
 rule z/z>. Join v with 5-. Notice that V is not at the corner of a 
 square. The figure when completed should show a clear bold 
 line of uniform thickness throughout. 
 
 The same plan must be followed out with regard to the 
 following examples, always taking care to estimate the size and 
 position of the figure on the paper before starting. India- 
 rubbers should not be used at all. 
 
 Note. The plain paper examples may be used as exercises for 
 the squared paper, and vice versa. 
 
Scale Drawing. Standard IV 
 
 149 
 
 406 
 
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 ?-9-'--- 
 
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 rO 
 
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 C\J 
 
 
 
 
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 I 
 
 a * 
 
 Fig. 406. Let the side of each square equal 2 inches. 
 
 Fig. 407. Let the side of each square represent 3 inches. 
 First obtain ab and the two side lines ac and bd. From the 
 centre of ab count up 14 squares, and mark f. This point 
 will fall on the middle of the side of the square, and must be 
 carefully marked. The rest of the figure presents no difficulty. 
 
 Fig. 408 Let the side of each square represent 1 inch. Mark 
 in abed, 20 squares by one square. Find the centre, and mark 
 point e, 20 squares above. Mark points /and g over a and b. 
 
 Fig. 409. Let the side of each square equal 1 inch. 
 Draw ab, and get the centre line. Notice that the bottom of 
 the handle will come to the middle of the side of the square. 
 
The Teaching of I) rawing 
 
 Fig. 410. Let the side of each square represent 2 inches. 
 Draw the beam at the top 24 squares by 2 squares. Fix the 
 position and width of the posts, count 48 squares down, and 
 rule the ground line and posts. Now mark the position of 
 the ropes at the top. To obtain the seat, count 10 squares 
 up from the ground and 3 squares from each post, and rule 
 in the bottom line. Complete the seat, and mark one square 
 from each end for the position of the ropes. Notice that the 
 ropes are not vertical. 
 
 Fig. 411. Let the side of each square represent 2 inches. 
 Fix the point a in the centre of the base, and draw the bottom 
 part of the figure. Count up 42 squares from a, and from this 
 point set out 8 squares on each side of the centre line, giving 
 points b and c. For d, count 8 squares above be, rule in bd 
 and cd, and complete the roof. Mark points e and /, and 
 complete the opening. For the point g set off 6 squares on 
 each side of ;;/. Draw the sloping sides. 
 
Scale Dr diving. Standard IV 
 
 151 
 
 SECTION IV 
 
 Enlarging or reducing a given figure. In enlarging 
 and reducing simple figures it will be found much neater and 
 easier to teach the pupil to measure the lines with the scale, 
 and then calculate the required length, rather than to measure 
 or divide by means of compasses or dividers. Suppose, for ex- 
 ample, it is required to draw a rectangle with its sides half as 
 long as those of the given figure. Instead of bisecting, let the 
 pupil measure each of the sides. He will find them 2\ inches 
 and 1^ inches respectively, and will at once know that the 
 required figure will have sides of ij inches and | inch. 
 
 412 
 
 As a general rule it will be found that most figures will 
 scale, and their dimensions can be readily calculated. Small 
 dimensions can neither be correctly divided nor accurately set 
 off by children with ordinary compasses. 
 
 The following lesson will illustrate the method suggested 
 above : 
 
 Draw the bell 'tent (fig. 413), making the lines three times as 
 long as those of the given figure. 
 
 1. Commence by drawing the base line of indefinite length, 
 and mark in the point a and the centre line am. 
 
 2. Now place the ruler on the base line, and measure ab. 
 Suppose it to scale inch, then the pupil will set off 2\ inches 
 on each side of the centre. 
 
52 
 
 The Teaching of Drazving 
 
 Note. The proper method of doing this must be explained 
 clearly. If the distance be less than i inch, then place the o of the 
 scale on a and read off to the left. If over i inch and less than 
 2 inches, then place i on a and read off as before. If over 2 inches 
 and less than 3 inches, place 2 on a, &c. 
 
 3><A 
 
 3. Measure bd. Suppose it to scale y^ inch, then 
 inch = 2 inches must be set off. Draw bd and ce at 
 
 right angles to be, and complete the rectangle bced. 
 
 4. Scale bfi set off thrice the distance, and draw//$ and gl. 
 
 Note. It is better to scale the longer distance bf than the 
 shorter distance af, as the measurement is likely to be more 
 accurate. 
 
 5. Measure am. If it measures i inches, then the pupil 
 will set off 4.5 inches. Draw dm and em. 
 
 6. With the set-square draw hn and In, parallel to the lines 
 dm and em respectively. 
 
 The figure should be carefully thickened in, and all the con- 
 struction lines left either dotted or very thin. The pupils should 
 be taught to thicken in lines like bd, dm,fh, &c, when first ruled, 
 as it saves time and is likely to produce neater work. 
 
 Fig. 414 Draw the given figure ivith lines three times the 
 given size. 
 
 Find the dimensions as in the previous figure, 
 
Scale Drazving. Standard IV 
 
 153 
 
 1. First draw abed, then the chimney. 
 2-. Find position of e, and draw ef parallel to cd with the set- 
 square. Joiny?. 
 
 3. Measure up and draw the door. 
 
 4. The window must be obtained as shown by the dotted 
 construction lines. Measure nh and set it off at g. Now 
 measure nm, and set off at /. From g and / draw lines parallel 
 to ab. Measure gh, set it off, and rule a perpendicular hm. 
 Obtain the other side of the window in a similar manner. 
 
 4^5 
 a 
 
 Fig. 415. Draw the figure with lines half the size of those 
 given. 
 
 I. Begin with line bc > and then rule the centre 
 line ad. 
 
154 
 
 The Teacliing of Drawing 
 
 2. If ab equals if inches, then the pupil will set off | inch 
 on each side of a. 
 
 3. Complete the rectangle beef. 
 
 4. Measure ad, set off half the distance, and complete the 
 figure. 
 
 Examination Tests 
 
 Two papers are given to show the character of the tests the 
 children may expect There are usually two problems to be 
 drawn, and great attention should be given to the proper 
 arrangement of the examples so as to show to advantage on 
 the paper. 
 
 Test-paper A (to be tvorked on plain paper) 
 
 1. Draw a scale of 1^ inches to 1 foot, and from it draw a 
 line to represent 2 ft. 4 in. 
 
 2. Draw figure 416 with lines twice the length of those 
 
 
 
 416 
 
 
 
 
 \ 
 
 
 /I 
 
 
 - 
 
 
 
 
 
 
 
 
 / 
 
 
 \ 
 
 
 
 
 
 
 
 
 
Scale Draiving. Standard IV 
 
 55 
 
 Test-paper B (to be ivorked on squared paper) 
 i. Draw fig. 417 from the given dimensions, letting the 
 
 side of each square equal 1 inch. 
 
 2. Draw fig. 418 from the given dimensions, letting the 
 
 side of each square equal 3 inches. 
 
 ! 
 
 1 
 
 
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 1 
 I 
 
 417 
 
 V 1 
 
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 7 
 
 
 
 
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 - 
 
 
 
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56 The Teaching of Drawing 
 
 CHAPTER VIII 
 
 PLANE GEOMETRY. STANDARDS V AND VII 
 
 Syllabus, Standard V. Geonietrical figures with instru- 
 ments and to scale. 
 
 This section will include such problems as the division of 
 a given line into a number of equal parts by trial with the 
 dividers, and also by construction ; the drawing of lines parallel 
 and perpendicular to given lines by means of the set-squares, and 
 also by construction ; the construction of an equilateral triangle 
 or a square of a given side ; the construction of an angle equal 
 to a given angle ; the bisection of a given angle ; the construction 
 of a triangle, its sides or its sides and angles being given. 
 
 Apparatus. The teacher will require a pair of large chalk 
 compasses about 15 inches in length, in addition to the appa- 
 ratus necessary for Standard IV. 
 
 The pupils will require the same material as for Standard 
 IV, with the addition of pencil compasses. Where expense is 
 no object small dividers are very useful for dividing lines and 
 taking off measurements, but they are not essential. 
 
 Compasses. These should be as good as can be obtained, 
 as it is utterly impossible to expect that children can do neat 
 and accurate work with the wretched instruments that are com- 
 monly supplied to schools. It is not desirable that very deli- 
 cate or expensive instruments should be supplied, as they are 
 very liable to be soon damaged. The best cheap compass with 
 which we are acquainted is known as ' Harris's Patent,' fig. 
 419. It is strongly made, with a good point, and does not 
 get out of order easily, the pencil being held firmly by a 
 screw collar which envelops both jaws. Pencils can be bought 
 to fit the compasses, and should be sharpened so as to form a 
 chisel point, as this lasts longer and gives a much better line. 
 
Plane Geometry. Standard V 157 
 
 The figure to be drawn should be ruled in firmly, so as to 
 show out well from the construction lines, ivhich must not be 
 rubbed out, and should be ruled in either with a very light or 
 dotted line. For children probably a fine continuous line is 
 preferable, as it is more quickly done. Dotted lines do not 
 
 419 
 
 look well unless the dots are kept very even, and to do this 
 takes a much longer time. The page should always be divided 
 by ruled lines into spaces, so that each problem is kept dis- 
 tinctly to itself, and the figure should be worked as large as 
 the space will allow. It will be necessary for the teacher to 
 watch carefully the method of holding the compass, and to 
 insist upon it being held nearly upright and between the thumb 
 and forefinger, as the proper method of using the instruments 
 is an important factor towards obtaining successful work. 
 
 The course required for Standard V embraces the follow- 
 ing points. Elementary constructions relating to : (1) Lines. 
 (2) The drawing of perpendiculars and parallels. (3) Angles. 
 (4) The construction of triangles of various kinds. (5) The 
 square, the rectangle, and the circle. Definitions must be fre- 
 quently given, in order that the pupil may thoroughly com- 
 prehend the questions set. It is not advisable to attempt to 
 learn these definitions by heart ; frequent questioning and 
 illustration will soon enable the class to explain the terms used. 
 The theory of construction and the uses of the different in- 
 struments must also be carefully and frequently explained. 
 
 The following course amply covers the requirements, and 
 most of the figures will explain themselves. Notes are only 
 given where specially needed. Attention is again directed 
 to the necessity of drawing the figures large, in a variety of 
 positions, and of forming numerous exercises from them. A 
 few examination cards are given at the end, which should be 
 arranged upon the paper as directed. Longman's ' Practical 
 
I 5 8 The Teaching of Drazving 
 
 Geometry for Standard V ' will furnish the teacher with a 
 variety of exercises. 
 
 The following problem is worked out fully as an illustra- 
 tion of the points which should be dealt with in a lesson : 
 
 From a given point A, draw a line which shall meet the 
 line BC at an angle equal to the given angle D. 
 
 i Draw two parallel lines on the board with the set-square. 
 Place the 6o set-square as shown in fig. 421, and draw a line 
 ad cutting both the parallel lines. Apply the set-square to the 
 angle at b, and direct the attention of the pupils to the fact that 
 it exactly fits, and therefore the alternate angles must be equal. 
 
 420 421 
 
 Draw another line with the 45 set-square, and show that there is 
 the same result. Now draw two converging lines, and show that 
 the alternate angles are no longer equal. (Explain ' alternate.') 
 
 2. Through A draw AE parallel to BC 
 
 3. At A make an angle equal to T>, and produce the line 
 to meet BC in F. 
 
 4. The angle AFC equals the angle FAF, as has been 
 previously shown, and FAF wa.s constructed equal to D, there- 
 fore AFC must be equal to D, and AF is the required line. 
 
 This is a difficult problem for children, and should be 
 reasoned out as shown above. The parallel line may also be 
 obtained by using the set-square. 
 
Plane Geometry. Standard V 
 
 159 
 
 422 
 
 A 
 
 V 
 
 428 
 
 429 
 
 Figs. 422 and 423. To bisect lines. 
 
 Be careful to see that the bisecting line goes exactly through 
 the intersection of the arcs, and that the arcs are kept equal 
 in length. 
 
 Figs. 424 and 425. To erect a perpendicular from a point 
 in a given line. 
 
 The method in fig. 422 should be used when the point is near 
 the middle of the line, as it is neater and more quickly performed. 
 
 Figs. 426 and 427. -7b drop a perpendicular from a point 
 without a given line. 
 
 The method in fig. 425 is for use when the point is nearly 
 over the end of the line. It can also be used for fig. 426. 
 
 Fig. 428. To draw a line parallel to a given line at a given 
 distance from it. 
 
 Fig. 429. To drawa line parallel to a given line through 
 a given point. 
 
 Fig. 430. Draw a line parallel ti AB through the point C, 
 and on the opposite side of AB draw another line parallel to 
 it and \\ inches from it. 
 
 Notes. 1. All these perpendiculars and parallels should also 
 be obtained by the use of the set-square. 
 
 2. Definitions of the terms 'bisection,' 'intersection,' 'perpen- 
 dicular,' ' parallel ' and ' arc ' should be given here. 
 
i6o 
 
 The Teaching of Drawing 
 
 Fig". 431. To construct an angle equal to a given angle. 
 
 Fig. 432. To bisect a given angle. 
 
 Fig. 433. To divide a given angle into four equai parts. 
 
 Fig. 434. To trisect a right angle. 
 
 Fig. 435. To draw a line that would bisect the angle be- 
 tiveen two converging lines without producing the lines. 
 
 Draw lines parallel to the converging lines and at equal 
 distances from them, as in fig. 428, and bisect the angle thus 
 formed. 
 
 Fig. 436. Find a point in a given line equally distant from 
 the tivo given points A and B. 
 
 Fig. 437.-20 draw a line from the point A to meet BC, and 
 make an angle with it equal to D. 
 
 Figs. 438 and 439. To divide a line into any number of 
 equal parts. Say five. 
 
 The pupils should be conversant with both methods, but 
 the method shown in fig. 439 by using the set-square is the 
 most important, as it is the one in practical use. 
 
Plane Geometry. Standard V 
 
 161 
 
 440 
 
 441 
 
 443 
 
 444 
 
 445 
 
 446 
 
 447 
 
 Construction of angles when their size is given in 
 degrees. Describe a circle, and show that the radius will go 
 exactly six times round it. The explanation of a degree is 
 given on page 47, and should be recapitulated here. If the circle 
 contains 360 , then each of the sixths into which it has been 
 divided must equal 6o. Most of the other common angles can 
 be obtained from the angle of 6o. 
 
 Figs. 440-448. To construct angles of 6o, 120 , 30, 15 , 
 
 45, 75, *5> i35 22 i- 
 
 These may be easily followed from the constructions, and 
 
 most of them can also be obtained by using the set-squares. 
 
 The angle of 30+ the angle of 45 will give 75 , &c. 
 
 Triangles. These have previously been defined and ex- 
 plained in Standard III, and will now only need recapitulating. 
 
 The number of degrees in the various angles will require 
 constant practice, and the pupils must be well drilled in the 
 fact that the three ang/es of any triangle contain 180 . Plenty 
 of examples should be given, such as, when two angles are 
 given to find the third, and, in the case of an isosceles triangle, 
 when the vertical angle is given to find the base angles. 
 
 M 
 
162 
 
 The Teaching of Drawing 
 
 Fig. 449. 71? construct an equilateral triangle on a given base. 
 
 Fig. 450. To cofistruct an equilateral triangle, its altitude being 
 given. Draw the base line first, perpendicular to the altitude. 
 
 Fig. 451. To construct an isosceles triangle, the base and 
 altitude being given. 
 
 % Fig. 452. To construct an isosceles triangle, the base and side 
 being given. 
 
 Fig. 453. To construct a triangle, its three sides being given. 
 
 Fig. 454. To construct a triangle, its base and base angles 
 being given. 
 
 Fig. 455. To construct a triangle similar to a given triangle. 
 
 Fig. 456. To construct an isosceles triangle having its base 
 and vertical angle given. 
 
 This depends upon the previous problem, and is more 
 easily understood when worked as shown. Convert the given 
 angle c into an isosceles triangle by making its two sides equal 
 and joining them. At a and b construct angles equal to the 
 base angles of c. Then the vertical angle d must be equal to c. 
 
 This problem should be practised a number of times until 
 thoroughly understood. 
 
 Fig. 457. Construct a triangle having a base of 3 feet and 
 two angles of 6o and 45 respectively. What is the size of the re- 
 maining angle ? Scale- 
 
 inch to 1 foot. [1S0 - (6o + 45) = 75]. 
 
Plane Geometry. Standard V 
 
 163 
 
 Fig. 458. 71? construct an isosceles triangle with a vertical 
 angle of 30 and a base 0/ 1 inch. What is the size of the base 
 angle ? 
 
 Construct an angle of 30, convert it into an isosceles 
 triangle, and then proceed as in fig. 456. 
 
 Note. Practise this problem with a variety of vertical angles, 
 and notice that to construct an isosceles triangle having base angles 
 of 75 is only another way of wording the above. 
 
 Fig. 459. To construct an isosceles triangle on a given base 
 and having its base angles 30 . 
 
 It is only necessary to construct one angle, the other is 
 more easily measured from the angle already obtained. 
 
 Fig. 460. To construct a square on a given base. 
 
 Fig. 461. To construct a square on a given diagonal. 
 
 Fig. 462. To construct a rectangle, its two sides being given. 
 
 Fig. 463. To construct a rhombus, having a side and an 
 angle given. 
 
 The circle. The various parts should be defined and ex- 
 plained, such as centre, circumference, radius, diameter, chord. 
 
 Fig. 465. To find the centre of a given circle. 
 
 Fig. 466. To complete the circle of which AB is a portion* 
 
 m 2 
 
164 
 
 The Teaching of Drawing 
 
 In the following card the problems should be arranged as 
 indicated below. 
 
 Card I. 1. Copy the angle ABC, and through D draiv a 
 line parallel to AB, 
 
 'C 
 
 2. Draw tivo right lines each 2 feet long to meet at an angle 
 of go . Scale=i\" to i' o". 
 
 3. Describe two circles touching each other with diameters of 
 1 inch and 1^ inches respectively. 
 
 467 
 
 1. To copy the angle, first measure AB. Take BC as 
 radius and describe an arc. Intersect this arc with the dis- 
 tance A C. This method is necessary, as no marks must be 
 made on the cards. 
 
 2. As the scale is i%" to 1' o", each line will be 2 J inches 
 long. 
 
 3. Draw a line and set off the diameters. Find the centre 
 of each diameter and describe the circles. Be careful to see 
 that the circles touch one another. 
 
 Note. If radii of I inch and f inch had been set off, the same 
 result would have been obtained. 
 
Plane Geometry, Standard V 
 
 165 
 
 Card II. 1. Copy the given triangle, and bisect an angle and 
 a side. 
 
 2. Construct a triangle having its base i\ inches, and its 
 angles 45 , 45 and 90 . 
 
 3. Construct an equilateral triangle of 2 feet sides. Scale 
 = i" to i' o". 
 
 Card III. 1. Copy the given line AB and the point C, and 
 through C draiv a line parallel to AB. 
 
 2. Construct a right angle, and bisect it. 
 
 3. Make an isosceles triangle, base 2 inches and angle oppo- 
 site the base 45 . 
 
 Card IV. 1. Construct a square on AB. 
 
 2. Draw two straight lines, each 2\ inches long, which shall 
 meet at an angle of 6o. 
 
 3. Construct a triangle with sides of \\ inches, 2\ inches, and 
 3 inches respectively. 
 
1 66 The TeacJiing of Drawing 
 
 Card V. i. Copy the given triangle, and through the point C 
 draw a line parallel to the base. 
 
 2. Draiv a circle of i inch radius, and divide the circum- 
 ference i?ito four equal parts. 
 
 3. Draw a line 2 \ inches long, and divide it into three equal 
 parts. 
 
 Syllabus, Standard VII. (^ 1.) Geometrical Drawing, 
 more advanced than in Standard V. 
 
 This sectio?i will include the constniction of a triangle similar 
 to a given triangle a?id standing on a given base. The drawing 
 of two ci?'des of given radii touching each other. Construction for 
 circles passing through three given points, or touching three given 
 lines. Tangents to two circles. Construction of 7-egular polygons 
 by any general method, together with their inscribed and circum- 
 scribed dixie. The use of plain scales. 
 
 This subject may be taken instead of section (b.) : The 
 drawing of any common objects, and casts of ornament in light and 
 shade. It is much easier than drawing in light and shade, as it 
 is very difficult to arrange objects and casts with a suitable light 
 in ordinary school- rooms. There is nothing in the above 
 requirements that cannot be easily covered by the pupils in 
 Standard VII, and it has the advantage of giving a more ad- 
 vanced knowledge of the very useful and interesting study of 
 Plane Geometry which has been already begun in Standard V. 
 The pupils also are now better able to appreciate the value of 
 exactness and finish in the work, and are more skilful in the 
 
Plane Geometry. Standard VII 167 
 
 manipulation of their instruments. To give a complete course 
 is beyond the scope of this book, as there are plenty of text 
 books, such as ' Longman's Plane Geometry, Book 14,' which 
 amply cover all the requirements. A number of examination 
 questions are given which will indicate the character of the 
 work. Solutions are given to the more difficult problems, from 
 which it will be seen that there is no special difficulty to be 
 overcome. These, of course, should be worked to a much 
 larger scale. The scales are all drawn half their proper size, 
 and any necessary notes to the problems are given at the end 
 of the solutions. Three questions are usually given for the 
 examination. 
 
 Examination Tests 
 
 1. Draiv a line to touch the two given circles (fig. 468). 
 
 2. Draiv a scale of " to 1' 0'' to show 7 ft. 5 in. (fig. 
 469). 
 
 3. Copy the given triangle at a scale of \" to \' o" on a base 
 of 4 ft. 7 in. (fig. 470). 
 
 4. Describe a rectangle of which AB is one side and CD a 
 diagonal (fig. 471). 
 
 5. Through the point A draw parallels to BC and CD; also 
 from A draw perpendiculars to BC, CD (fig. 472). 
 
 6. Describe an irregular pentagon of which the sides are 2\ 
 inches, 2 inches, \\ inches, 1 inch, and\ inch. The angle ivhich 
 the longest side makes with the shortest side is ioo, and the angle 
 between the two longest sides is 65 (fig. 473). 
 
 7. In a given circle inscribe seven equal touching circles (fig 
 
 474). 
 
 8. Divide a given quadrant into halves, thirds, and sixths 
 
 (fig- 475)- 
 
 9. From three given points A, B, C, draw three right lines 
 equal to one another, to meet in the same point (fig. 476). 
 
 1 o. Construct a trefoil of tangential arcs (fig. 477). 
 
 1 1. About a given circle construct an octagon (fig. 478). 
 
 12. Trisect a given arc (use the dividers). 
 
 1 3. Draiv a scale to show 3 ft. 7 in. when t \ inches represent 
 ifoot(hg, 392). 
 
1 68 
 
 The Teaching of Drawing 
 
Plane Geometry. Standard VII 169 
 
\jo The Teaching of Drawing 
 
 14. Describe a regular pentagon on a base of \\ inches (fig. 
 
 479)- 
 
 15. From two given points, A and B, draiv two circles of 
 
 equal radii touching each other (fig. 480). 
 
 16. From a given point A draivtwo tangents to a given circle 
 (fig. 481). 
 
 17. Construct a triangle with sides 2 ft. 9 in., 2 ft. 3 in., and 
 1 ft. 9 in. respectively. Scale = f to 1' o" (fig. 482). 
 
 1 8. Draiv a scale of r ^th to show yards and feet, and long 
 enough to measure five yards (fig. 483). 
 
 Notes on the Examination Tests 
 
 Fig. 468. As the two circles are copied, their centres are already 
 found. Join the centres, and describe a circle with the difference 
 of their radii. From a draw a tangent ac to the described circle. 
 Produce be to d, and from a draw a line parallel to bd and rule the 
 tangent. 
 
 Fig. 470. The scale constructed in fig. 469 will give the base. 
 
 Fig. 472. The readiest method for obtaining the perpendiculars 
 is to use that shown in fig. 427, as the same arc which was used 
 for the parallels does also for the perpendiculars. 
 
 Fig. 473. Make a rough sketch first, showing the position of 
 the angles. Draw ab. Set out the angles of 6$ and ioo with the 
 protractor, and complete the sides be and ae. 
 
 Fig. 474. The problem does not state that the circles are to 
 touch the given circle. If six circles be inscribed, the seventh will 
 exactly fit in the centre. If the circles had to touch the given 
 circle, then the circumference would require dividing into fourteen 
 equal parts. 
 
 Fig. 476. As the lines drawn from A, B, C are to be equal, they 
 must be radii of a circle ; therefore join AB, BC, and bisect. 
 
 Fig. 477. The arcs are to be tangential that is, if the circles 
 were completed they would not cut each other. Construct an 
 equilateral triangle with each side double the radius of the arc, 
 and with each angle as a centre describe the arcs. For a quatre- 
 foil, construct a square, &c. 
 
 Fig. 482. First construct the scale, and make it long enough to 
 measure 3 feet. As no smaller measurements than 3 inches are 
 required, it will be sufficient to divide the first unit into four parts. 
 
Plane Geometry. Standard VII 171 
 
 Fig. 483. A scale of ^th to show yards means that the unit to 
 be taken is ^th of a yard. The scale has to measure 5 yards, 
 therefore its total length will be B 5 ff of a yaid = 6 inches. Draw a 
 line 6 inches long, and divide it as shown into five equal parts, 
 each of which will represent one yard. Subdivide the first part 
 into three for the feet. 
 
172 The Teaching of Drazving 
 
 CHAPTER IX 
 
 SOLID GEOMETRY. STANDARDS VI AND VII 
 
 Syllabus, Standard VI. Plans and elevations of platte 
 figures and rectangular solids i?i simple positions with sections. 
 (Girls are not required to take solid geometry in either Stan- 
 dards VI or VII.) 
 
 Apparatus. Same as for plane geometry for the pupils. 
 Drawing-boards and T-squares are very useful, but not 
 essential. 
 
 The teacher must also be provided with : 
 
 1. Plane figures, such as the triangle, square, rectangle, 
 circle, &c, cut out in cardboard black is preferable to white, 
 as chalk marks can be made on it. 
 
 2. Models of the Solids used, some of which should be cut 
 to show the sections. These can be bought in sets, or the 
 teacher, if fond of tools, may construct them in wood. The 
 easier plan, however, is to make them of cardboard by develop- 
 ing the surfaces. It is a capital exercise for each pupil to make 
 his own set of models in this manner, as it encourages manual 
 dexterity and gives a thorough familiarity with the various 
 models a most important acquirement in this subject, as it 
 is impossible for pupils to represent a solid unless they can 
 imagine its appearance. The method of constructing some of 
 the easier solids is given, as no successful work can possibly be 
 done unless models are well used and handled by the pupils. 
 For rapid illustration, when a variety of sections, &c, require 
 showing, a piece of soap is a useful substitute. 
 
 3. Model to show the position of the two planes. Two 
 small black-boards fastened with a hinge is the most useful. 
 
Solid Geometry. Standard VI 173 
 
 Folded paper or cardboard answers very well when the folding 
 board is not obtainable. 
 
 4. Some wire, to show the projecting lines. 
 
 The principal solid forms and terms connected with them 
 are defined here : 
 
 A cube is a solid figure contained by six equal squares. 
 
 A prism has its two ends equal, similar, and parallel, and 
 each of its sides is a parallelogram. 
 
 Prisms are named from the shape of their ends ; thus, a square 
 prism has a square for each end, a pentagonal prism has a pentagon 
 for each end, &c. 
 
 A pyramid has a plane figure for its base, and each of its 
 sides are triangles, which meet at a point above the base called 
 the apex. 
 
 Pyramids are named from the shape of their bases. 
 
 A sphere is generated by the revolution of a semicircle 
 about its diameter j every part of its surface is equally distant 
 from the centre. 
 
 A cone is generated by the revolution of a right-angled 
 triangle about its perpendicular. 
 
 A cylinder is generated by the revolution of a rectangle 
 about one of its sides. 
 
 The axis is the line passing through the middle of the 
 solid ; when it is perpendicular to the base or ends of the 
 solid, the figure is termed a right prism or pyramid. 
 
 To make Simple Solids from Cardboard 
 
 Figs. 484-490 show the shapes to which the Cardboard 
 must be cut to form the solids. The figures must first be 
 accurately drawn to the required size, and carefully cut out 
 along the outer dark lines. A knife should then be drawn 
 along the inner light lines, taking care not to cut quite through 
 the cardboard. Turn up the surfaces on the opposite side to 
 that which is cut, as this gives a clean unbroken edge. Finish 
 by gumming thin paper over the joints. Other solids may be 
 made in a similar manner, and the teacher thus secures a good 
 
1 74 The Teaching of Drawing 
 
 set of models at little cost. They may be made solid by filling 
 with plaster of Paris. 
 
 Fig. 484 shows the development of the surfaces of the 
 cube ; figs. 485 and 486 of the square prism and pyramid ; 
 figs. 487 and 488 of the equilateral triangular prism and pyra- 
 mid ; figs. 489 and 490 of the hexagonal prism and pyramid. 
 
 Note. The equilateral triangular pyramid is usually termed a 
 tetrahedron. 
 
 Sections. There is generally a little difficulty in showing 
 sections. These may be easily made in cardboard. Suppose, 
 for example, a section is required through the square pyramid. 
 After cutting out the surfaces, turn up the sides and mark in 
 pencil on the edges where the section is required j turn the sides 
 down, and cut off the parts above the section line. Finish 
 the model by turning up the edges and gumming as before. 
 
 The method in this branch of the course is treated rather 
 more fully than in some of the previous portions, as it is felt that 
 solid geometry is the most difficult part for the pupils to under- 
 stand. All the main difficulties and important principles are 
 dealt with, and test problems given at the end. The ordinary 
 books, such as Longman's Book io for Standard VI, and 
 Book 15 for Standard VII, will afford plenty of examples. 
 
 This subject is generally taught in a less satisfactory 
 manner than any part of the drawing syllabus, partly on 
 account of the difficulty of the subject in itself, as, although 
 very little is required, the pupil must imagine the position of 
 the object and reason out the solution. In actual practical 
 work it is really the most useful portion of geometrical draw- 
 ing, as by its aid we represent not only length and breadth, but 
 thickness also. Carpenters, engineers, and mechanics generally, 
 make more use of this branch of drawing than any other. 
 When taught well it is not only very interesting to the pupils, 
 but it affords excellent mental training. Examples of working 
 drawings can easily be obtained to show to the pupils. This 
 arouses their interest, as the practical use of plans and eleva- 
 tions is at once brought before their minds. 
 
 The earlier lessons should be entirely taken up with repre- 
 
Solid Geometry. Standard VI 175 
 
iy6 The Teaching of Drawing 
 
 senting plans and elevations of common objects in various 
 positions. These should be drawn roughly on the blackboard, 
 the pupils working with a slate and pencil. A line should be 
 drawn across to separate the plans from the elevations. This 
 method enables the teacher to deal with a great number of 
 objects, and thoroughly familiarises the pupils with the idea of 
 representing objects in a variety of positions. To begin with 
 definitions and a description of the planes is almost sure to 
 disgust the pupils, and to effectually kill all interest in the 
 subject. 
 
 Three simple rules should be laid down : 
 
 i. The plan of an object is seen when we look vertically 
 downwards upon it. 
 
 2. The elevation is seen by looking horizontally forwards. 
 
 3. Every point in the plan is exactly under the corresponding 
 point in the elevation. 
 
 Let the pupil see the objects, as it is perfectly useless 
 giving theoretical demonstrations unless the pupils can see and 
 carry in their minds the appearance of the model when viewed 
 from different positions. This may be varied by taking some 
 common object that the pupils are familiar with, and questioning 
 as to its appearance when seen from various positions, without 
 showing the model. This cultivates and trains the mental 
 powers in the very important faculty of remembering what is 
 seen. Figs. 491-512 show the plans and elevations of a 
 number of objects suitable for the earlier lessons. These 
 should be drawn approximately correct, as previously suggested. 
 The pupils' attention should be directed to the fact that one 
 drawing shows only two dimensions, as length a?id breadth, and 
 that the two drawings are necessary to show the height as well. 
 
 When the pupils have thoroughly grasped the idea of what 
 plans and elevations really represent, then the teacher may 
 show how these drawings may be accurately constructed from 
 definite statements. 
 
 The vertical and horizontal planes may now be explained, 
 and their relation to one another illustrated. To do this, fold 
 a piece of paper at right angles, and place it on a board or 
 table adjoining a wall, so that one half of the paper rests on 
 
Solid Geometry. Standard VI 
 
173 
 
 The Teaching of Drawing 
 
 504 
 
 503 
 
 1 1 1 1 1 1 U 1 1 1 1 1 1 1 1 1 
 
 ^s. 
 
 D 
 
 DD 
 
 505 
 
 506 
 
 J 
 
 V 
 
 EC': 
 
 507 
 
 n 
 
 / 
 
 508 
 
 \ 
 
 509 
 
 \J 
 
 -frx 
 
 511 
 
 512 
 
 r\ 
 
 w 
 
 510 
 
Solid Geometry. Standard VI 
 
 179 
 
 the table and the other half against the wall (fig. 5 1 3). Explain 
 that any perfectly flat surface is called a plane. Illustrate by 
 reference to the carpenter's plane and its uses. There are 
 two plane surfaces here, one upright and the other level ; the 
 upright one is called the vertical plane, and the level one 
 the horizontal plane. The angle which they make with one 
 another is a right angle, and the line where the two planes 
 intersect is called the intersecting line. 
 
 Place a small box or any simple object on the horizontal 
 plane, and trace its shape, abed, on the paper. This will evi- 
 
 5i3 
 
 
 
 514 
 
 
 A 
 
 
 1 
 
 3' 
 
 
 
 a 
 t 
 
 t 
 
 t 
 
 
 
 b 
 
 
 
 c 
 
 z 
 
 
 dently show the length and breadth of the box, and, as it 
 shows the space covered by the box on the horizontal or 
 ground plane and its distance from the vertical plane, it is its 
 plan. Next, with a long pencil, trace the outline on the 
 vertical plane, A'B'a'fr. This shows the height, and, as it 
 represents its appearance when looked at horizontally forwards, 
 it is its elevation. If the paper be now held up, the plan and 
 elevation will be seen, as in fig. 514, one exactly under the 
 other, 
 
 N 2 
 
i So 
 
 The Teaching of Drazvzng 
 
 SOLIDS STANDING ON THEIE FACES 
 
 Lesson I. A problem similar to the following may now be 
 worked out on the blackboard. 
 
 A cube stands on tlie H.P. with two of its faces parallel to the 
 V.P. Draw the plan and elevation when the back face is 
 6 inches in front of the V.P. 
 
 Note. The contractions H.P. and V.P. will be used in future 
 for horizontal and vertical planes respectively. 
 
 i. Place the paper showing the planes as in fig. 513. Now 
 elicit the position in which the cube is to be placed and its 
 distance from the V.P. Trace its plan. Remove the cube 
 and show the plan. 
 
 2. Draw the intersecting line XY on the board ; let the 
 pupils show it on the paper, and explain its use. Draw a line 
 . 6 inches below the intersecting 
 
 line, parallel to it, and equal to 
 an edge of the cube. Con- 
 struct a square abed on this 
 line, and show that this square 
 corresponds with the traced 
 plan. 
 
 3. Replace the paper and 
 cube, and trace the elevation 
 on the vertical plane. Remove 
 the cube, and show the plan 
 and elevation. 
 
 4. Draw projectors from 
 the plan on the board. Elicit 
 the height of the cube, and 
 complete the elevation. 
 
 5. Show that the con- 
 structed drawing corresponds 
 with the traced one, and ex- 
 plain that it would be inconvenient to draw with the planes at 
 right angles to each other, although the pupil must continually 
 bear this in mind while working. 
 
 a 
 
 
 b 
 
 y 
 
 
 \ 
 
 A 
 
 c 
 
 
 & 
 
 
 Q 
 
 , 
 
 b 
 
Solid Geometry. Standard VI 
 
 181 
 
 6. Letter the figures, and explain that the same point always 
 keeps the same letter. If A be a point on a figure, then a will 
 be its plan and a' its elevation. Find the points at first by 
 referring to the model. 
 
 7. Let the class repeat the drawing to a suitable scale. 
 Lesson II. Arrange the planes as before, place a cylinder 
 
 standing with its end on the H.P. and proceed as follows. 
 (Work out each step on the board as it is elicited from the class.) 
 
 What position is the cylinder in ? 4 Standing o?i its base. 1 
 
 In what direction must 
 I look to see the plan i 5 
 
 ' Vertically downwards' 
 
 What shape do I see if 
 I look down on the cylin- 
 der ? ' A circle? 
 
 I must now decide 
 where to draw the circle ; 
 how shall I find this out ? 
 * By measuring its distance 
 from the V.jP.' 
 
 Draw a line at right 
 angles to XYand set off the 
 distance eb. Measure the 
 diameter ab of the cylinder, 
 and describe the circle. 
 
 What does the circle 
 represent ? ' The plan of 
 the cylinder? 
 
 Why ? * Because it is 
 the space the cylinder covers on the ground? 
 
 Could it represent the plan of anything else? 'Sphere 
 cone, &c? 
 
 Where must the elevation be drawn? i Above XV a/id 
 exactly over the plan? 
 
 In what direction must I look to see the elevation ? 
 
 What shape do I see then ? ' A rectangle? 
 
 Project the width from c and d. Measure the height, and 
 set it off on the board. 
 
182 
 
 The Teaching of Drawing 
 
 Letter points c' and d '. 
 Where is b' ? 
 
 Lesson III. Place the cube with its sides making angles 
 with the V.P., and point out that its exact position with 
 reference to both planes must always be stated. Now write 
 a problem on the board as follows : Draiv the plan and 
 
 elevation of a cube with one of its 
 
 faces i?i the H.P., its nearest corner 
 
 i inch from the V.P., and with one 
 
 side making an angle of 30 with it. 
 
 1. Question out every step with 
 regard to its position. 
 
 Is it on its face or edge ? 
 Place the model on the plane. 
 Is it in the required position ? 
 
 'No: 
 
 Why not ? ' Because its sides do 
 not make 30 with XY' 
 
 Place it in position with the aid 
 of the 30 set-square. 
 
 2. What shape will the plan be ? 
 1 A square: 
 
 Draw a line at 30 with XY, 
 and on it construct a square. 
 
 How many sides are seen in the elevation ? ' Two: 
 Do they appear to be squares ? Why not ? 
 
 3. Project lines from each angle of the plan. 
 Elicit the height, and complete the elevation. 
 
 4. Where will b be in the elevation ? Mark it. 
 
 Why not at the bottom ? ' Because the bottom is not visible 
 in the plan: 
 
 Elicit the position of the other angles in the same way. 
 Frequent reference to the model will be found necessary, as 
 it is rather difficult for the pupils to find these points at first. 
 
 5. Thicken in the visible lines, and explain that the line 
 from c, not being visible, should be dotted. 
 
 Notes. 1. The teacher will find it easier to take simple positions 
 of the rectangular solids first, and afterwards proceed to the more 
 
Solid Geometry. Standard VI 183 
 
 difficult ones. The square prism, box, &c. should now be treated 
 in a similar manner. 
 
 2. The projectors should be shown with very fine lines, and 
 care must be taken to see that they are drawn at right angles to 
 XY. To do this when the ruler and set-square only are used, 
 place the ruler above XY, and with the set-square draw one pro- 
 jector, say from a ; now place the ruler below the figure, and with 
 the set-square rule parallels to the projector already drawn. 
 
 SOLIDS STANDING ON AN EDGE 
 
 Three positions require illustration : I. When the edge is 
 perpendicular to the V.P. II. When the edge is parallel to 
 the V.P. III. When the edge is neither perpendicular nor 
 parallel to the V.P. 
 
 I. Edge perpendicular to the V.P. 
 
 This is perfectly simple. The three figures given below 
 illustrate what is necessary in this case. 
 
 II. Edge parallel to the V.P. 
 
 The pupils will soon discover that when the model is in this 
 position its elevation cannot be determined directly, as the edges 
 
1 84 
 
 The Teaching of Draivin 
 
 521 
 
 d 
 
 of the ends are in an oblique position, and consequently do not 
 show their true size. The true size of the edges can only be 
 determined when the end is parallel to the V.P. Hence we 
 get this general principle, that when the axis of the solid is not 
 at right angles to the V.P. y a third view showing the true shape 
 of the end must be obtained first. 
 
 The following example illustrates the mode of working : 
 Draw the plan and elevation of a cube standing on one edge 
 with its axis parallel to the KP, and with two of its adjacent 
 faces making equal angles with the H.P. 
 
 I. Elicit its position, and place the cube on the planes as 
 required. Now show that if we turn it round at right angles 
 all its dimensions can be ascertained. 
 
 2. As two of the 
 adjacent faces of the 
 cube make equal angles 
 with the JT.P, they will 
 be at angles of 45 . 
 With the 45 set-square 
 draw B'A' and B'C, 
 make them the required 
 length, and complete the 
 square. Then A' B'CT>' 
 will represent the true 
 shape of the end. Ob- 
 tain the plan ACGE 
 as in fig. 518. 
 
 3. If the plan and 
 elevation thus found be 
 each turned at right 
 angles, the required 
 
 plan and elevation will be obtained. In actual practice it is 
 not necessary to draw the light-lined plan A CGE. It is put 
 in here, as experience shows, that the pupils can readily grasp 
 the idea that the required plan eacg is simply the plan EACG 
 turned at right angles. 
 
 Project horizontally from A' and D'. Set off the width 
 fd', and complete the elevation. 
 
 a' 
 
 
 \cv: 
 
 
 
 
 
 
 
 
 a 
 
 
 
 B i 
 
 V 
 
 
 
 r 
 
 pf 
 
 
 c 
 
 
 
 
 cl 
 
 
 f 
 
 
 A 
 
 
 ^^>. 
 
 C 
 
 
 a, 
 
Solid Geometry. Standard VI 
 
 185 
 
 4. Let the pupils look at the model and notice the shape 
 of the plan. It will be found .to correspond exactly with the 
 elevation. This is always the case when either the cube or 
 square prism have their axes parallel to the V.P. Project 
 vertically for the plan, and obtain the width as shown. 
 
 Note. The pupils should first draw the elevation and plan as 
 shown in light line, and then turn them at right angles ; and after- 
 wards obtain the plan and elevation without using the first plan, 
 transferring the widths directly from the intersecting line as shown 
 by the arcs. 
 
 Figs. 522 and 523 show similar positions of the square and 
 triangular prisms. 
 
 All four views are shown for the sake of clearness. Re- 
 member that the required plan is the light-lined plan turned at 
 right angles, and that after the principle is understood the first 
 plan may be dispensed with and the widths transferred directly 
 from the intersecting line. 
 
 III. Edge neither perpendicular nor parallel to the V.P. 
 
 Draiv the plan and elevation of a cube standing with its edge 
 in the If. P., and with its axis making a?i angle of 30 with the 
 V.P. 
 
 This is a rather more difficult position than is usually given 
 
1 86 
 
 The Teaching of Draivin 
 
 524 
 
 to Standard VI. The principle is exactly the same as that used 
 in the previous problems, so that it is included here for the sake 
 
 of completeness. It 
 is more usual to give 
 the plan, and require 
 the elevation to be 
 drawn from it. 
 
 1. Draw the ele- 
 vation and plan when 
 the end is parallel to 
 the FT as before. 
 
 2. Place the plan 
 so that its axis makes 
 30 with the V.T. ; 
 ADC then becomes 
 adc. 
 
 3. Project hori- 
 zontally from A' and 
 D' for the heights. 
 
 4. Use the model well, and project from d and h, giving the 
 top and bottom edges. Thicken these lines in when obtained, 
 as it helps to keep the figure clear. Complete the front vertical 
 face by projecting from a and c to the line from A'. Finish 
 the back face, showing the unseen edges with a dotted line. 
 
 The square prism should be similarly dealt with. 
 
 This problem may be worked more quickly by the device 
 which is constantly used in more advanced solid geometry, 
 viz., changing the position of the intersecting line and assuming a 
 fresh vertical plane. The problem may then be solved by using 
 three figures instead of four. The method is as follows : 
 
 1. Obtain the elevation and plan as before (fig. 525). 
 
 2. Instead of moving the plan, move the intersecting line 
 XY, so that it makes the required angle with the edge of the 
 plan, X Y. If we now imagine the figure to be turned so 
 that X Y is horizontal, the plan acge will be in the required 
 position. 
 
 3. Project as before from d and h at right angles to X Y . 
 
Solid Geometry. Standard VI 
 
 187 
 
 Set off fi'd' and/'h' equal to B D', and thicken in d'h' and b'f 
 for the top and bottom edges. Complete the front face, making 
 
 a' and c' the same distance above X Y that A' and C are 
 above XY 
 
 4. Complete the back face, and thicken in as before. 
 
 PLANE FIGURES 
 
 These will present no special difficulty after solids have been 
 dealt with. Use cardboard figures to illustrate the various posi- 
 tions. A door opened at various angles shows the varying 
 width. 
 
 Two positions require special attention : I. When the figure 
 is vertical and makes an angle with the vertical plane like an 
 open door. II. When the figure makes an angle with the 
 horizontal plane like a trap door when opened. 
 
 I, A square standing vertically upon one edge makes an angle 
 0/4$ with the V.P. Draw its plan and elevation (fig. 526). 
 
 The same principle must be used as in the preceding pro- 
 blem, viz., to draw the plan and elevation when the figure is 
 parallel to the V.P. 
 
 1. Draw the elevation a'B'C'd, and the plan aB, when the 
 square is parallel to the V.P. 
 
i88 
 
 The Teaching of Draiving 
 
 2. Turn the plan through an angle of 45 to position ab. 
 This will be the required plan. 
 
 3. Project from b, and obtain the required elevation a'b'c'd'. 
 
 a 
 
 1 
 
 $' 
 
 B' 
 
 d 
 
 
 0' 
 
 c' 
 
 
 
 
 B 
 
 
 \t6 
 
 b 
 
 The same square has its diagonal vertical. Draw its plan 
 and elevation {fig. 527). 
 
 1. Draw the elevation a'B' CD' and the plan a BC when 
 the diagonal B D' is vertical and the figure is parallel to the 
 V.P. 
 
 2. Turn the plan aBC into position abc. 
 
 3. Project from b and c to the required heights, giving the 
 elevation a'b'c'd . 
 
 II. A square rests with one edge on the H.P. at right angles 
 to the V.P. Its surface makes an angle of 45 with the H.P. 
 Draiv its plan and elevation (fig. 528). 
 
 1. Draw the plan aBCd, and the elevation a'B', when the 
 surface is horizontal. 
 
 2. Turn the elevation a'B' through the required angle to 
 position a'b' . This will be the elevation of the door. 
 
 3. Project from b' to the plan, giving abed the required 
 plan. 
 
 The same square has one of its diagonals at right angles to 
 the V.P. Draw its plati and elevation (fig. 529). 
 
Solid Geometry. Standard VI 
 
 8 9 
 
 1. Draw the plan aBCD with the diagonal BD at right 
 angles to the V.P., and the elevation a'B'C. 
 
 c' 
 528 529 
 
 6, 
 
 a 
 
 '/l5 
 
 
 & 
 
 
 d 
 
 c 
 
 r 
 
 
 
 
 
 c 
 
 l I 
 
 ) 
 
 9 
 
 2. Turn the elevation to position a'b'd, 
 
 3. Project from the elevation as before for the plan. 
 
 SECTIONS 
 
 The plan and elevation of an object do not always convey 
 all the information necessary to construct it. The plan and 
 the elevation of a house will not show the position and thick- 
 ness of the floors, nor would the plan and elevation of a fly- 
 wheel show the shape and thickness of the arms. 
 
 To supply information of this character, drawings showing 
 the shape of the object when supposed to be cut through at 
 various places are given. These drawings are called sections. 
 
 Sectional plans and elevations are all that are usually 
 required from this Standard. The true shape of the section, 
 which is really the most important, is not usually asked for. 
 The difference should be explained to the pupils, and they 
 should be encouraged to draw the true shape for practice. The 
 sectional plan is the appearance of the object when viewed 
 vertically downwards from above ; the sectional elevation is 
 its appearance when looked at horizontally forwards ; the true 
 
190 The Teaching of Dr diving 
 
 shape is seen when the section is viewed at right angles to the 
 plane of the section. 
 
 To illustrate these it is necessary to have either models cut 
 in various sections or else made in cardboard, as suggested at 
 the commencement of the chapter. As no fixed section will 
 illustrate every variety of cut, a piece of soap is very useful for 
 this purpose. 
 
 The line of section should be indicated by figures to avoid 
 confusion, and the section should be ruled with lines put in 
 with the 45 set-square about one-eighth of an inch apart. 
 This will be quite close enough, and permits of the lines being 
 ruled evenly and carefully. Close section lines are confusing, 
 and cannot be done neatly by the pupils. If the set-square be 
 slipped an eighth on the ruler for every line, perfect uniformity 
 of space between the lines will be secured. The appearance of 
 a neatly ruled section will amply repay the pupil for the trouble 
 bestowed on it. 
 
 Figs. 530 and 531. The plans are given of two cubes cut by 
 a plane passing through 1, 2. Draw the elevation. 
 
 The construction lines show what has to be done. The 
 portions below the section line should not be projected, as they 
 are supposed to be cut away. The true shape in fig. 530 
 would be a rectangle having 12 for its base and its height equal 
 to the height of the cube. It may be shown at right angles to 
 12 as in 12 ab, or by the side of the elevation as in i'V a" b '. 
 
 Figs. 532 and 533. Elevations of cubes are given. Draw 
 the sectional plans made by a plane passing through iV. 
 
 The portions above the section lines are not projected, as 
 they are supposed to be removed. In fig. 533 the true shape 
 is shown as well. 
 
 Fig. 535. The plan of a cube cut by a vertical plane passing 
 through 1, 2 is given. Draw the sectional elevation. 
 
 This is rather more difficult. First obtain the elevation of 
 the cube as in fig. 524. The section should then be found in 
 the following manner. Point 1 is on line ae, therefore its eleva- 
 tion will be on a'e'. Point 2 cuts the edges ab and ad, therefore 
 its elevation will be the points marked 2', on lines a'b' and ad'. 
 If each point of the section be traced out and marked in this 
 way very little difficulty will be found. 
 
Solid Geometry. Standard VI 191 
 
192 The Teaching of Drawing 
 
 Fig. 536. The elevation of a cube is given. Draw the 
 sectional plan when cut by a plane passing through i f $'. 
 
 As the plan of the cube when in this position is of the same 
 shape as its elevation, it can at once be projected. For the 
 section proceed as follows : Point i' is on line a'e', therefore 
 its plan will be on line ae. Point 2' is on line b'f and the line 
 behind it d'h', therefore its plan will be on bf and dh. Join 
 the points already found. It is evident that 3' cannot be 
 projected, because the ends of both plan and elevation are in 
 the same straight line. The true shape of the end must be 
 drawn, and 3' projected to it, giving 3'W as the width of the 
 cut on the end. Set off 3 3 equal to 3" 3'. The corners b 
 and d are not shown thickened in, as they would be cut away. 
 
 Fig. 537. The plan of a square prism cut by a section plane 
 1 3 is given. Draw its elevation. 
 
 The elevation of the prism will be the same shape as the 
 plan. Project points 1 and 2 for the section as before. Point 
 3 must be dealt with in the same manner as in fig. 536. 
 
 Fig. 538. The elevatio?i of a square prism is given. Draw 
 its plan when cut by a section plane passing through i f $'. Care- 
 fully project the plan of the prism. Trace out each point, 
 marking it when found by a small dot. Thicken in the figure, 
 and shade the section. 
 
 Fig. 539. The plan of two steps is given, each of which is as 
 high as it is wide. Draw the elevation when cut by a plane 
 passing through 1, 3. 
 
 This is rather confusing to young pupils. First project the 
 two steps and rule in. Remember that in the section, 1 and 2 
 are on the top step. Point 3 is on the bottom step, and must 
 only be projected to it. 
 
Solid Geometry. Standard VI 
 
194 
 
 The Teaching of Drawing 
 
 Examination Tests. Two problems are usually given on 
 each card, which should be arranged on the paper as shown 
 in fig. 540. The figures given in the tests should be drawn 
 about three times the given size. 
 
 1. AB, BC are the elevations of hvo straight lines parallel 
 to the V.P. Draw their plans. 
 
 1. 2. 
 
 2. The given figure is the plan of a cube. Draw its elevation, 
 and the elevation of the section made by a plane passing through 
 AB. 
 
 Problem 1 presents no special difficulty. Remember that 
 the true length of a line is shown when the elevation is parallel 
 to the V.P.,or when the plan is parallel to the H.P. AB and 
 BC in the question represent the true lengths of the lines. 
 
 54o 
 
 a' 
 
 
 
 
 
 
 
 
 
 
 
 
 b 
 
 
 
 
 
 a 
 
 
 
 
 
 
 
 c 
 
 a 
 
 
 
 
 
 
 
 b^ 
 
 
 
 
 b' 
 
 
 
 c 
 
 1 
 
 ) 
 
 c 
 
 
 
 / 
 
 \ 
 
 
 b 
 
 
 / 
 
 #\ 
 
 
 / 
 
 A 
 
 
 
 a 
 
 
 
 
 / 
 
 
 
 
 
 /a, 
 
 
 
 
 
 
 
Solid Geometry. Standard VI 
 
 195 
 
 In problem 2 the elevation will be of the same shape as the 
 plan. The points 1 and 2 cannot be projected to the eleva- 
 tion, and the true shape of the end must be drawn. If the 
 points be projected to this end the widths of the section will 
 be shown by the lines a x a x and b x b v Make a! a' and b' b' 
 equal to these widths. 
 
 3. AB and CD are the elevations of two squares having two 
 sides parallel to the V.P. Draw their plans. 
 
 4. The given figure is the elevation of a squa?-e prism. Draw 
 the section when cut by a plane passing through 1,2. 
 
 5. Draw the plan of the cube of which the given figure is the 
 elevation. 
 
 6. The given lines represent the elevations of two squares each 
 of which has a diagonal parallel to the V.P. Draw the plans. 
 
 7. The elevation of a square prism 2\ inches long is given. 
 Draw the plan. 
 
 8. The given figure represents the elevation of a cube. Draw 
 its plan when cut by a plane passing through 1, 2. 
 
 9. Three steps are given in elevation. Draw the plan, and 
 the plan of the section made by the line AB. The steps are 33 
 feet wide. Scale=}y" to 1' o", 
 
 o 2 
 
196 
 
 The Teaching of Drazving 
 
 /6 
 
 /i 
 
 10. The plan of hvo slabs each 1 inch thick is given. Draw 
 their elevation. 
 
 11. The plan of a square slab 1 inch thick surmounted by a 
 cube is given. Draw the sectional elevation when cut by a vertical 
 plane AB. 
 
 12. The given figure represents the plan of a square prism. 
 Drazv its elevation. 
 
 1 3. Draw the elevation of the square prism, and the elevation 
 of the section made by the vertical plane 1 2. 
 
 14. AB is the plan of a line parallel to the H.P. and 1 
 inch above it. Draw its elevation. 
 
 15. CD is the plan of a line 3 inches long. Drazv its 
 elevation. 
 
 16. The given figure is the plan of a cube. Drazv its sec- 
 tional elevation when cut by a plane passing through 1,2. 
 
 17. The given figure shows the plan of hvo steps in each of 
 which the zvidth equals the height. Drazv the elevation zvhen cut 
 by a vertical section through AB. 
 
Solid Geometry. Standard VII 
 
 19; 
 
 Syllabus. Standard VII. Plans and elevations of rectan- 
 gular and circular solids, ivith sections. 
 
 The work of Standard VI must be continued in an in- 
 creased degree of difficulty. Rectangular solids, both singly 
 and combined, must be drawn in more difficult positions. In 
 dealing with the circular solids great care must be taken to 
 keep the construction lines, which are rather numerous, neat 
 and distinct. In setting off the widths for the elliptical ends, 
 the greatest exactness must be insisted upon, or it will be found 
 impossible to secure good curves. When the points for the 
 curve are obtained, it must be very lightly sketched in first, and 
 thickened in after an accurate shape has been obtained. 
 
 Any number of points may be taken in the curve. It is con- 
 venient to take either 8 or 12, as the circle can be readily 
 divided into either of these parts by means of the set-squares. 
 
 A few typical positions of the circular solids are shown, with 
 some examination tests to show the character of the work 
 required. 
 
 Figs. 541-548 show easy positions of the circle, cylinder, 
 and cone. 
 
 54i 
 
 542 
 
 543 
 
 544 
 
 k. 
 
 545 
 
 rS 
 
 546/ 
 
 / 
 
 \ 
 
 -^547 
 
 
 548 
 
 \y 
 
 
 
 ^ 
 
 J 
 
 
 
 r 
 
 s 
 
 
 
 
 
 
 
 
 
 j 
 
 v. 
 
 j 
 
 
 
 
 1 
 
198 
 
 The Teaching of Drawing 
 
 Figs. 549-556 show easy sections of the cylinder, cone, 
 and sphere. In fig. 549 the true shape, as well as the plan of 
 the section is shown. 
 
 \^J \ 
 
 Figs. 557 and 558. Draw the plan and elevation of a 
 circle : 1. With its plane vertical and making an angle of 45 
 with the V.P. 2. With its plane perpendicular to the V.P. and 
 inclined at 6o to the H.P. 
 
 t. The plan will evidently be the line ab inclined at 45 
 to the V.P. Its elevation will be an ellipse having its longer 
 diameter c'c' equal to ab and its shorter diameter a'b ' . As, 
 however, an ellipse cannot be accurately drawn when only four 
 points of its curve are given, four additional points in the circle 
 will be taken. The same method as that used in fig. 521 and 
 the following figures is used here, viz. drawing the true shape of 
 the figure. In the case of the circle it is neither necessary nor 
 advisable to put in the whole of the figure on account of the 
 multiplicity of lines, the semicircle giving all the necessary 
 measurements. 
 
Solid Geometry, Standard VII 
 
 199 
 
 On ab describe a semicircle and divide it into 4 or 6 parts, 
 as at E, C and F. From E, C and i^draw perpendiculars to 
 ab giving widths across the 
 circle at those points. (The 
 complete circle is inserted 
 here, the unnecessary part 
 being in dotted line.) 
 
 From a, e, c, /, b project 
 to the V. P. Set offVV equal 
 to ab, and draw a'b' midway 
 between c' and c' . On each 
 side of a'b' set off the dis- 
 tance e~E, giving the points 
 e'e and /'/'. Through the 
 eight points thus obtained 
 draw the elliptical elevation. 
 
 2. The elevation will be 
 a line at 6o to the H.P. 
 For the plan proceed in 
 a similar manner to that 
 
 shown in the preceding figure. After projecting from the 
 points, draw ab at any convenient distance from xy, and set 
 off the widths from the semicircle on each side of it. 
 
 Fig. 559 shows the plan and elevation of a cylinder when 
 its axis is inclined to the V.P. The method is only a repetition 
 of that explained in fig. 557. Two circles are projected and 
 joined. 
 
 Fig. 560 shows the plan and elevation of the cylinder when 
 its axis is inclined to the H.P., and also a second elevation 
 when the cylinder is viewed from the left at right angles to its 
 former position. 
 
 Note. The second elevation will be readily followed if the 
 figure be turned so that V P' is horizontal. The first elevation 
 then becomes the plan for the second, and the lines are merely 
 repetitions of those in fig. 559. 
 
 Fig. 561 shows the plan and elevation of a cone, with its 
 axis inclined at 30 to the H.P. and parallel to the V.P. Also a 
 side view similar to that shown in fig. 560. 
 
200 
 
 The Teaching of Drawing 
 
Solid Geometry. Standard VII 201 
 
 Fig. 562 shows the plan and elevation of the cone when 
 lying on its side with its axis parallel to the V.P. Notice that 
 the cone must first be drawn in an upright position, and then 
 turned so as to bring the side into the H.P. for the required 
 elevation. 
 
 Fig. 563 shows the plan of the sphere cut by the section 
 plane iV. 
 
 Fig. 564 shows the elevation of the sphere when cut by a 
 vertical plane 1 2. 
 
 Fig. 565 shows the sectional plan and true shape of a 
 cylinder when cut by the plane iV. All oblique sections of 
 the cylinder are ellipses or portions of ellipses. After drawing 
 the plan of the cylinder, draw the centre line \p. Point 1 will 
 be the extremity of the longer diameter of the ellipse. Describe 
 a semicircle on the elevation, showing half the shape of the 
 end, and draw 2V. On each side of p set off the distance 2V, 
 giving 2 2, the width of the section on the end of the cylinder. 
 Through the centre a of the semicircle draw ab, and produce 
 it to meet the section line at 3'. Project from 3' to the plan, 
 giving the points 3, 3, where the section will be widest. The 
 
202 
 
 The Teaching of Drawing 
 
 curve might now be drawn, but its accuracy will be better 
 secured by fixing at least two more points. Mark point 4', 
 and project horizontally and vertically. Set off the distance 
 cd on each side of the centre line, giving the points 4, 4. 
 Through the points obtained draw the curve. The true shape 
 is easily followed from the construction lines. Project at right 
 angles to the section, and draw the centre line. The widths 
 will be exactly the same as in the plan. 
 
 * Fig. 566 shows the elevation of a cylinder cut by a vertical 
 plane 12. After obtaining the elevation of the cylinder, pro- 
 ject from 1 to the middle line of the elevation, giving 1', and 
 from 2 to the end, giving 2V. Produce ab to meet the section 
 line at 3. From 3 project to the elevation, setting off the 
 distance ab on each side of the centre line for the points 3' 3'. 
 Through the points thus obtained draw the curve. 
 
Solid Geometry. Standard VII 
 
 203 
 
 Fig. 567 shows the plan of a cone when cut by the section 
 plane i'a'. When the cone is cut by a plane which passes 
 through both sides, the section is an ellipse. Project from i' 
 and 2', giving points 1 and 2, the length of one diameter of 
 the ellipse. Take point 3' on the section line, and suppose a 
 horizontal section to pass through this point. The plan of this 
 section would be a circle, and if 3' be projected to this plan 
 two more points 3, 3 in the section will be obtained. Take 
 other sections, and proceed in a similar manner. Draw the 
 curve through the points obtained. 
 
 Fig. 568 shows the elevation of a cone cut by a vertical 
 section through 1, 2. After obtaining the elevation of the cone, 
 project points 1 and 2, giving iV the width of the section. 
 Next obtain the height. From the centre draw a line at 
 right angles to the section, and with as centre describe a circle 
 
204 
 
 The Teaching of Drawing 
 
 touching the section. From a project to a', and from a' draw 
 a line representing the elevation of the circle described. A 
 projector from 3 will give 3', the top of the section. To obtain 
 other points in the curve, mark 4, describe a circle passing 
 through it, project the elevation of this circle at b\ and from 
 the points 4, 4 project for 4V. Other points may be obtained 
 in the same way. This section is called the hyperbola. 
 
 Fig". 569 shows the plan of a section made by the plane 
 iV parallel to the side of the cone, also the true shape of that 
 section. Project the points 1' and 2', giving 11, the width, and 
 2, highest point of the curve. To find other points in the curve, 
 take any number of points, as 3' and 4', and draw horizontal 
 section lines through these points. Obtain the plans of the 
 
 569 
 
 circles of which these lines are the elevations. Project from 
 points 3' and 4' to the plans of these circles, giving the points 
 3, 3 and 4, 4, and draw the curve. For the true shape project 
 at right angles from each point of the section, draw a centre line, 
 and set off , i // i" equal to 1 1, 3" 3" equal to 3 3, &c. The curve 
 drawn through these points will be that known as the parabola. 
 
Solid Geometry. Standard VII 
 
 205 
 
 Examination Tests. Solutions or references are given 
 where needed. All the figures must be copied to a much 
 larger scale. 
 
 1. The given figure repre- 
 sents the plan of a right cylin- 
 der, with an axis of \\". 
 Copy the plan, and draw the 
 sectional elevation. 
 
 2. The elevation of a cube 
 surmounted by a sphere is given. 
 Copy the elevation, and draw 
 the plan, showing the section 
 made by AB. {Fig. 563.) 
 
 4. The given figure shozvs 
 the elevation of a cone. Draw 
 the plan and plan of section 
 made by AB. {Fig. 567.) 
 
 3. AB and BC are the ele- 
 vations of two circles. Dratv 
 the plans. 
 
 5. The given figure is the 
 plan of a cone with a section 
 passing through its centre. 
 Draw the elevation. {Fig. 570.) 
 
 6. The given figure is the 
 elevation of a cylinder. Draiv 
 its plan, and the plan of a 
 section made by A B. {Fig. 571.) 
 
206 
 
 The TeacJiing of Drawing 
 
 7. The elevation of a cone 
 is given. Draw its plan. {Fig. 
 
 562.) 
 
 8. The given figure is the 
 elevation of a cube with a hemi- 
 sphere placed upon it. Draw 
 the plan, and show the section 
 on AB. {Fig. 572.) 
 
 S 
 
 9. The figure is the plan of 
 a circular slab 2 inches thick, 
 with a cube of 2-inch edges placed 
 centrally on it. Draw the ele- 
 vation, and show the section 
 made by AB. {Fig. 573.) 
 
 10. The figure is the plan 
 of a cube pierced by a cylin- 
 drical tube. Draw the eleva- 
 tion, and show the section on 
 AB. {Fig. 574.) 
 
Solid Geometry. Standard VII 
 
 207 
 
2c8 The Teaching of Drawing 
 
 CHAPTER X 
 
 MODEL DRAWING. STANDARDS V AND VI 
 
 Syllabus. Standard V. Drazvingfrom simple rectangular 
 and circular models, and easy com??ion objects. 
 
 Model drawing requires both greater skill in teaching and in- 
 creased dexterity in drawing from the teacher. In freehand 
 drawing all draw the same view, hence class teaching has been 
 easy ; but in model drawing class teaching can only be used to 
 demonstrate the principles, and to show how the model would 
 appear under certain conditions. The fact that every pupil 
 sees a different view of the object necessarily prevents them 
 from clearly comprehending the illustrations drawn upon the 
 board, simply because they do not appear so to them. So that 
 although the board may be used to a great extent, it is abso- 
 lutely necessary, if really good work is to be secured, that there 
 should be a large amount of individual supervision. The 
 teacher will find it necessary to go to each pupil, take the same 
 position, and then show how to obtain a correct representation 
 of the object. Attention to good methods and plenty of 
 practice are the two great secrets of success. As the pupils 
 understand the methods adopted, only the slower ones need so 
 much individual supervision, and if plenty of practice be given, 
 this branch of drawing becomes very attractive, especially when 
 common objects are taken. When the pupils can successfully 
 represent some object with which they are familiar, their interest 
 is aroused and stimulated, as they see some tangible result of 
 this drawing of cubes, cylinders, &c, which must certainly ap- 
 pear somewhat unattractive and monotonous to them if not 
 sufficiently varied. 
 
 The pupils having already acquired the knowledge of how 
 
Model Drawing. Standard V 
 
 209 
 
 to draw straight lines, how to ascertain the various proportions 
 of a copy, and how to apply this knowledge so as to secure an 
 accurate drawing, it is now only necessary to show how this 
 knowledge may be applied to the drawing of objects. 
 
 Introductory Lessons. These should be taken on slates, 
 as their object is to cultivate the observing and reasoning 
 faculties, and to bring clearly home to the minds of the pupils 
 important principles upon which success in model drawing 
 largely depends. The lessons should be short, with plenty of 
 illustrations, and the sketches should be rapidly made. 
 
 First Lesson. The door will form a suitable example. 
 
 1. Let the pupils 
 commence by drawing 
 a vertical line ab to re- 
 present one side (fig. 
 575). Now ascertain the 
 width as compared with 
 the height, and complete 
 the rectangle. 
 
 2. Open the door at 
 an angle, and let the 
 pupils now measure the 
 width as compared with 
 the height. They will 
 discover that the width 
 has decreased and that 
 
 the upright lines must now be drawn closer together (fig. 576). 
 This shows the variation in the width of a plane surface when 
 seen at various angles. 
 
 Second Lesson. Take a piece of cardboard about 2 feet 
 square. Place it so that all can see as nearly as possible the 
 same view. 
 
 1. Let the pupils rapidly sketch it on their slates, noticing 
 that the sides will be vertical and the top and bottom horizontal 
 
 (% 577). 
 
 2. Turn the cardboard at an angle, and let the pupils draw 
 it under fig. 577, step by step from the teacher's direction, and 
 working with him. 
 
 p 
 
2IO 
 
 The Teaching of Drawing 
 
 Draw the nearest vertical edge ab. 
 Is the width the same as in the first drawing ? 
 Measure the width, and compare with the height, 
 other vertical side cd. 
 
 577 578 
 
 Draw the 
 
 Is the top edge now horizontal ? They will not all be able 
 to decide this. 
 
 Let all hold their pencils in a horizontal position level with 
 point a. 
 
 Is the back corner above the pencil? ' Yes.' 
 Then the line must run up. Draw ae to represent the level 
 of the pencil. Notice the angle made by the edge of the card- 
 board with the horizontal pencil, and draw it as nearly as pos- 
 sible. This will give the top edge ac. 
 
 3. Measure the back vertical edge of the cardboard, and 
 compare it with the front. They will discover that it measures a 
 shorter distance. Make cd less than ab, and draw the bottom 
 
 edge bd* 
 
 4. Change the position of 
 the card again, and note that 
 the width appears still less and 
 that ac makes a greater angle 
 with ae than before. 
 
 Another illustration that is 
 very convincing to children is 
 to arrange a board in a hori- 
 zontal position and on it to place three objects of equal height, 
 one at a, another at b, and a third at c. Let the pupils measure 
 
Model Drawing. Standard V 211 
 
 c with the pencil, and apply this distance to b. It will be found 
 that it only covers part of b, and on applying the distance to 
 a a larger portion still is not covered by it. 
 
 The pupils will now T have been familiarised with two most 
 important principles in model drawing : 
 
 1. The varying ividth of a plane surface when viewed at dif- 
 ferent angles. 
 
 2. The stnaller space occupied by an object when it is removed 
 farther back. 
 
 Now hold the card above the eye, and direct attention to 
 the fact that the top and bottom lines appear to run down. 
 Place it level with the eye, and show that the back corner is 
 level with the front. This will enable the pupils to grasp the 
 idea of lines vanishing to the level of the eye. The fact that 
 the top line of the door runs down will be demonstrated directly 
 the pencil is held horizontally level with the front top corner, 
 when the back corner will be found to be below it j and in the 
 same manner if the pencil be held level with the front bottom 
 corner, the back corner will be seen above the pencil, and the 
 bottom line of the door will consequently run up. 
 
 Several short lessons of this character, well illustrated and 
 rapidly drawn, will do more to fix these important truths than 
 the drawing of many models before these ideas are understood. 
 
 After the teacher has drawn the various views on the board, 
 the pupils should always be allowed to make their own repre- 
 sentation of the object. Care should be taken to keep as 
 nearly as possible the same view before all the class. It is 
 very necessary that the teacher should be able to sketch these 
 views correctly on the board, as otherwise much mischief will 
 be done. A little previous practice and forethought will enable 
 almost any teacher who can draw a straight line to illustrate all 
 that is necessary. 
 
 The various models will now be treated separately in typical 
 positions, such as lend themselves to demonstration on the 
 blackboard. After the pupils have gone through these care- 
 fully, they will experience but little difficulty in dealing' with 
 other views. It is very desirable that the ordinary models 
 should be followed up by a judicious selection of common 
 
 p 2 
 
212 The Teaching of Drawing 
 
 objects. Instead of going through all the models first, it will 
 be found far more interesting to combine the drawing of the 
 models with common objects. When the cube and square 
 prism have been dealt with, a box or any similar simple object 
 should be drawn. Children do not associate the drawing of 
 the cube with anything useful, but when able to draw a box or 
 a book they feel that considerable strides have been made. 
 
 Arrangement of the models. In the earlier lessons it is 
 very desirable that, as far as possible, only one view should be 
 drawn, as the teacher's difficulties will be very much increased 
 
 if more than one view has to 
 be dealt with in the same 
 lesson. To secure this, if the 
 class be large several models 
 should be used. This is only 
 necessary when dealing with 
 the model for the first time, as 
 after the pupils have drawn 
 two or three views they will be 
 able to apply the principles 
 to other views without much 
 difficulty. Fig. 580 shows the 
 arrangement for a lesson, a, <, c show the position of the 
 models, which should be large and placed as far from the 
 class as possible, as by that means it is more easy to secure a 
 similar view for all the class. 
 
 THE CUBE 
 
 First Lesson. 1. The easiest position in which to draw the 
 cube is evidently w T hen one vertical face only is visible. Place 
 the models as shown in fig. 580. If only one cube be obtain- 
 able, square boxes, or cubes made of mill board, will make very 
 good substitutes. 
 
 Question rapidly as follows : 
 
 What is the object called ? ' A cube.'' 
 
 How many faces has it ? ' Six.' 
 
 How many edges ? 
 
 czz 
 
 rzi3 
 
 CZZl 
 
 CZZ) 
 
 CZZ) 
 
 CZZ 
 
 CZZ) 
 
 CZZ) 
 
 CZZl 
 
 CZZ 
 
 CZZ) 
 
 CZZ) 
 
 CZZ) 
 
 CZZl 
 
 CZZ 
 
 CZZ 
 
 CZZ) 
 
 CZZ) 
 
 CZZl 
 
 CZZ 
 
 CZZ) 
 
 CZZ) 
 
 CZZ) 
 
 CZZl 
 
 CZZ 
 
 a 
 
 b 
 
 
 
 c 
 
 
 
Model Drawing. Standard V 213 
 
 What is the shape of each face ? 
 What is a square ? 
 
 How many faces can you see ? Two.' 
 What positions are they in ? ' One vertical and one hori- 
 zontal? 
 
 Which face can you see most of? ' The vertical face.' 
 
 What shape is it ? ' A square? 
 
 Draw a square abed of about 4-inch sides. 
 
 2. Beginners generally make the error of drawing the top 
 face too wide. To prevent 
 
 this careful measurement is 5 Sl 
 
 necessary. To assist the 1 _, I 
 
 pupils, place a ruler on the 
 edge cd of the model, and 
 gradually raise it until it is in 
 a line with the back edge ef. 
 Now hold the ruler still, and 
 let the pupils take the vertical 
 distance from cd to the edge 
 of the ruler and compare it 
 with the height of the model. 
 
 Before doing this, let the pupils estimate the distance with 
 their eye. Most of them will be astonished at the difference. 
 Now mark the distance and draw the line ef. 
 
 3. The next point is to decide upon the length of ef Let 
 the teacher place a pencil vertically upon the corner c of the 
 model. 
 
 Which side of the pencil is the back corner ? ' Right.' 
 Mark it on the line ef Now place the pencil on d. 
 Which side of the pencil is the other back corner ? ' Left.' 
 Mark it, and join e and /with c and d. 
 Ought efto be less than cd? ' Yes.' 
 Why ? ' Because it is further away.' 
 
 4. Now show a large drawing previously made in which the 
 back lines are equal to the front, fig. 582. On being questioned 
 the pupils will probably say that 1 is longer than 2. Measure 
 the lines, and show that they are equal. Now explain that we 
 always draw objects not as they really are, but as we see them. 
 
214 
 
 TJic Teaching of Drawing 
 
 All this can be shown from the board, but it will also be 
 necessary to visit each pupil to see that the drawing is generally 
 correct. 
 
 582 533 
 
 1 
 
 9 
 
 Second Lesson. Place the cubes so that three faces are 
 visible (fig. 583). 
 
 1. Begin with ab, the nearest vertical line, and fix its 
 length. 
 
 2. Measure the width of the widest face, and compare with 
 ab. Mark this width, and draw cd. 
 
 3. Compare the narrower vertical face with the wider one 
 and draw ef Before anything else is attempted the horizontal 
 distance between ef and cd should be compared with ab. It 
 will be found to be greater. 
 
 4. Draw a very light horizontal line through a. Hold the 
 pencil in a horizontal position level with point a on the model, 
 and notice carefully the angle made with the pencil by the 
 wider edge ac, and frcm a draw ac making a similar angle. 
 Direct attention to the fact that the wider the side the less this 
 line will slope. 
 
 Find the inclination of ae in the same manner. 
 These lines ac and ae should be carefully verified before 
 proceeding, as the rest of the model depends upon them. 
 
 5. Look at ac, and draw eg slightly converging towards it. 
 From c draw eg converging slightly towards ae. 
 
Model Drawing. Standard V 
 
 215 
 
 6. Recall the exercise in measuring in fig. 579. 
 
 Is cd shorter than ab ? Why ? 
 
 Is it much shorter ? ; No? 
 
 Why not ? ' Because it is not much farther off.' 
 
 Then make cd slightly less than ab, and draw bd. 
 
 Elicit that ef\$ shorter than cd because it is farther back, 
 and draw bf 
 
 Third Lesson. The cube may now be drawn when its 
 vertical faces appear equal as in fig. 584. This will present no 
 special difficulty. 
 
 The lines should be drawn according to the order in which 
 they are numbered. 
 
 584 
 
 Common errors. Fig. 585 shows a very common error, 
 arising from the fact that the teacher has drawn such views in 
 perspective. In this the pupil is supposed to be drawing the 
 cube when looking at something else, an impossible task. The 
 error may be easily demonstrated by holding the edge of the 
 drawing-book horizontally level with a } when the sides of the 
 cube will be seen making an angle with the edge of the book. 
 The pupils are liable to make the error, because the face of the 
 cube is parallel to the front of the desks. The simplest way to 
 avoid the error is to lay down the rule that ab can only be hori- 
 zontal when the pupil is quite in front and sees only that vertical 
 face. From this deduce the rule that ivhen nearly in front ab 
 will be nearly horizontal, &c, 
 
2l6 
 
 The Teaching of Drawing 
 
 Fig. 586 shows another common mistake. Here the lines 
 vanish too much, producing a distorted representation of the 
 
 586 
 
 object. 
 
 The height of the eye and the 
 position of vanishing lines may now 
 be explained. Draw a horizontal line 
 ab on the board to represent the 
 edge of the horizontal plane upon 
 which the model stands (fig. 587). 
 Let the pupils point out on the wall 
 the level of their eye Draw a line 
 cd to represent this. Draw a cube 
 as shown, and explain that the edges, 
 
 if carried far enough, would appear to meet at the level of the 
 
 eye as shown. 
 
 587 
 
 C ct 
 
 a 
 
 The square prism. The only fresh point is that one of the 
 sides is longer than the other. The prism may be easily con- 
 verted into a box, as in fig. 588. 
 
 589 
 
 zf 
 
 . ( _ 
 
 ^ 
 
 
 \a 
 
 
 The square frame is very useful for showing how to 
 obtain the width of the sides. The sides a and b will be seen 
 wider than c and d. To decide what this width should be, 
 
Model Drawing. 
 
 Standard V 
 
 217 
 
 point out that if from c to d equals \ of the distance from a to 
 b, then the thickness of the wood at c and d should be of 
 the thickness at a and b. 
 
 A box, such as that shown in fig. 590, is a suitable model 
 to take next. After drawing 
 the box, and marking the 59 
 
 position of the lid, obtain the 
 keyhole by drawing the dia- 
 gonals for the centre of the 
 side. Through this centre 
 draw a vertical line, and on 
 it place the keyhole. Notice 
 that the half ab will be slightly 
 larger than be, because it is 
 nearer to the spectator. 
 
 A slate may now be attempted. This is a rather difficult 
 object, and at this stage should only be drawn in an easy 
 position. A number of slates can easily be arranged so that all 
 the class may see a similar view. 
 
 1. Draw ab. Obtain the side cd and the points c and d in 
 the same manner as shown in fig. 581. 
 
 59i 
 
 2. Draw the width of the frame as in fig. 589. 
 
 3. For the thickness of the frame draw vertical lines from 
 a and b, and on them mark off the thickness. A common error 
 is to make these lines slope outwards. 
 
 4. It may be left at this stage if thought fit. If where the 
 slate fits the frame be indicated, then direct attention to the 
 fact that this distance is of the thickness of the frame. 
 
 The book. Let the pupils draw a rectangular prism similar 
 to fig. 592 from a copy on the board. Turn it into a book as 
 
2 1 3 The Teaching of Drawing 
 
 shown in fig. 593. They will thus see the principles upon 
 which the book is drawn. 
 
 592 593 
 
 Now put up a sufficient number of books so that all have a 
 similar view, and draw as shown in fig. 594. Notice that the 
 edge of the leaves falls within the cover. If the drawing be a 
 
 594 
 
 large one the thickness of the cover may be indicated. On a 
 small drawing the thickness is better left out for the present. 
 
 Other rectangular objects, such as bricks, &c, may now be 
 taken. Probably a sufficient number are given here for the 
 present. It is not advisable at this stage to draw difficult 
 positions ; a few familiar objects in easy positions interest the 
 pupils more and secure better results. If difficult positions are 
 given at this early stage the pupils cannot make creditable 
 drawings and are more likely to be disgusted at their attempts 
 to represent the object. 
 
 THE CYLINDER 
 
 This is a very important model, as it enters into the formation 
 of such a large number of objects. 
 
 Axis vertical. First Lesson 
 
 1. Draw ab and fix its length. Compare the width of the 
 cylinder with its height, and draw cd. Join a with c, and b with 
 
Model Draiving. Standard V 
 
 d. Examine the drawings at this stage to see that the pro- 
 portions are correct. 
 
 2. Take a circle cut out of cardboard, and show the varia- 
 tions in its shape as the circle is changed 
 from a horizontal to a vertical position. 
 
 3. Draw ellipses on the board, show- 
 ing the most common errors. 
 
 Question on these, elicit the defects, 
 and correct. Fig. 596 is too flat. Fig. 
 597 is made up of two curves meeting 
 and forming angles at a and b. This 
 error is best remedied by drawing the 
 curved portions at a and b first. Fig. 598 
 is not symmetrical. This may be easily tested by holding the 
 drawing so that ab is vertical. ' The defect is then easily 
 detected. 
 
 596 
 
 597 
 
 598 
 
 4. Find the centre of ac and bd, and draw the shorter 
 diameters. Compare the width f/with ac. Draw the rounded 
 portions at a and c as shown in fig. 599. Complete the ellipse. 
 Test it as explained in fig. 598. 
 
 599 
 t 
 
 at 
 
 y 
 
 d L -- 
 
 d b 
 
 601 
 A 
 
 <^zi^> 
 
 5. Take the circular card again and hold it in a horizontal 
 position, level with the eye. Its shape will be a line (fig. 601 A), 
 
220 
 
 The Teaching of Drawing 
 
 Place it lower down, level with the top of the cylinder. 
 Its shape will now be represented by B. Now place it level 
 with the bottom of cylinder, and compare its width with the 
 width when at B. Its shape will now be represented by the 
 wider ellipse C. Hence the bottom of the cylinder must be 
 drawn slightly wider than the top. Why ? ' Because it is more 
 below the level of the eye. 1 It is advisable to draw the rounded 
 ends at b and d (fig. 600). If not, the tendency is to make a 
 corner at these points, as in fig. 597. 
 
 A number of easy common objects should follow this lesson. 
 Let the teacher draw several cylinders on the board, and illus- 
 trate how they may be converted into representations of objects, 
 as in figs. 602-605. 
 
 602 
 
 These may be drawn from the blackboard copies by the 
 pupils, as they form good exercises in freehand as well as model 
 drawing. This is generally a fascinating lesson for children, 
 and may be used as an exercise in memory drawing. They also 
 make good examples for dictated drawing, given as follows : 
 Draw a cylinder half as ivide as it is high. Turn this drawing 
 into a jug, showing a handle and a spout. An exercise of this 
 kind helps to develop the inventive faculties, as a great variety 
 of curves will be produced. It is, however, of no use doing 
 this until after exercises similar to figs. 602 to 605 have been 
 shown. 
 
 Axis horizontal. This is a much more difficult position, 
 and much care must be bestowed upon it. It is easier to adopt 
 two fixed methods. I. When the end of the cylinder is facing or 
 
Model Draiving. Standard V 
 
 221 
 
 nearly facing the pupil. II. When the axis is inclined to the 
 picture plane. 
 
 1. First Lesson. i. Arrange several cylinders before the 
 class so that all see a similar view viz., end nearly facing the 
 pupil. This is easier to draw than when the end is exactly 
 opposite. Rolls of paper or jars will make suitable substitutes 
 if a number of cylinders are not available. 
 
 2. Draw ab and cd (fig. 606). Let the pupils test whether 
 cd be less than ab, and draw the front face. This will be nearly 
 a circle. 
 
 3. Measure the distance from the front edge to the back 
 edge. Compare w T ith cd, set this distance off from ab, and draw ef. 
 
 Why is ef shorter than ab ? ' Because it is farther back.'' 
 Through the centre of <?/"draw gh, and make it a little less 
 than cd. Draw the back curve. These two curves should be 
 similar in shape, but the back one a little smaller than the front 
 one. 
 
 4. Join the two curves. 
 
 Note. When the drawing is lined in, all the portions shown 
 in dotted line should be omitted. 
 
 606 
 
 
 Fig. 607 shows the cylinder when the end is exactly opposite 
 to the pupil. Draw two circles and join them. This is not so 
 easy to demonstrate as fig. 606, as the construction lines of the 
 back circle clash with those of the front one. The back circle 
 is, of course, smaller than that in front. 
 
 II. Axis inclined to the picture plane. This position of 
 
222 The Teaching of Drawing 
 
 the cylinder is the real difficulty, not on account of the actual 
 drawing, but from the fact that it is difficult for the pupil to 
 correctly estimate the angle of inclination. When in this posi- 
 tion it is easier to draw the inclination of the axis first, instead 
 of the longer diameter of the elliptical end. 
 
 i. Arrange the model so that a somewhat similar view is 
 seen by all. It is not now so essential that all should see exactly 
 the same view. Explain the term ' axis,' and mark point a for 
 one end. Through a draw a horizontal line. To get the 
 inclination of the axis, hold the pencil in a horizontal position 
 level with point e, and notice the angle made between it and the 
 top edge ceof the cylinder. Through a draw a/* at this inclina- 
 tion. 
 
 608 609 
 
 Note. This is quite accurate enough for all practical purposes ; 
 strictly speaking, the angle of inclination at a is slightly larger than 
 that at c. It is, however, impossible for the pupil to measure the 
 inclination at the axis, as it is not visible. This angle should be 
 tested repeatedly until the pupil has obtained it fairly accurately. 
 It is a good plan to call several pupils out to the board, and let 
 them draw the inclination which they see. This prevents the lazy 
 ones shirking this most essential step, as if the inclination be in- 
 correct the rest of the model will be wrong. 
 
 2. Through a draw be at right angles to the axis, and fix its 
 length. If the axis and this line be obtained correctly, the rest 
 of the model presents no special difficulty. 
 
 3. Compare the length of the cylinder with be, and set it off 
 
Model Drawing. 
 
 Standard V 
 
 223 
 
 from a. Through / draw ed parallel to be and slightly shorter. 
 Draw ee and bd (fig. 608). 
 
 Notes. 1. In estimating the length of the cylinder, measure 
 from h to / (fig. 609). This is easier than from c to e. Common 
 errors are to make the length too great and the back end too small. 
 
 2. The figure, when in the stage represented by fig. 608, should 
 be carefully examined to see that the proportions are accurate. 
 
 4. Compare the width gh with be, and draw the ellipse. 
 Complete the back in the same manner Remember that the 
 back ellipse is slightly rounder than the front j hi should be a 
 little longer than ee. 
 
 THE CONE 
 
 I. Axis vertical. Commence with the ellipse. Produce 
 ab for the height, and draw the sides (fig. 610J. 
 
 II. Lying on its side. This is a very awkward position, 
 as it requires considerable judgment to estimate the slope of 
 the axis. 
 
 1. Mark a point a for the centre of the base, and through 
 it draw a horizontal line. Hold the pencil so as to be in line 
 with the axis, and with the other hand hold a pencil or ruler 
 horizontally level with a. The angle between the two pencils 
 
 610 
 
 will be the inclination of the axis. The line ab represents the 
 position of the right-hand pencil, the dotted line that of the 
 other. Test this until sure of the inclination, and draw ab. 
 
 2. Through a draw ed at right angles to ab. Determine 
 the length of ed. 
 
224 
 
 The Teaching of Draiving 
 
 3. Compare the width with cd, and draw the ellipse. 
 
 4. Compare ab with cd, and draw the sides. Notice that 
 these lines do not touch the ellipse at d and c. 
 
 Notes. 1. The drawing may be additionally verified by testing 
 the slope of cb. 
 
 2. As the ellipse widens, the distance ab will decrease. 
 
 The principles of construction involved in the preceding 
 figures are applicable to all rectangular and circular models. 
 An increased number of common objects can now be drawn. 
 A few typical examples bringing in fresh points are now given. 
 
 Fig. 612 shows a box with the lid partly open. The fresh 
 point here is the obtaining of the point a. Hold the pencil 
 vertically and notice the position of point b, which is directly 
 under a. Draw an upright line ab. Compare the height ab 
 with the height of the box, and draw ac. To obtain d, draw a 
 line be vanishing with the length of the box, and from e draw a 
 vertical line ed a little less than ab. Join a with d. 
 
 Fig. 613 shows the lid open at a different angle. To obtain 
 a, find its horizontal distance from, and its vertical distance 
 above, b. 
 
 Fig. 614. To obtain the open cover of the book, produce 
 ab, make ac slightly less, and draw cd. 
 
 Fig. 615. Draw abed. Find the centre by drawing the 
 diagonals, and draw ef vanishing with ab and cd. Obtain the 
 line above ef, showing the opening of the leaves. Notice that 
 the leaves open like the box lid, in a circle of which eb is the 
 
Model Drawing. Standard V 
 
 22$ 
 
 radius. Of course this circle will be represented as an ellipse 
 in the drawing. Draw the top leaves first, and observe that ail 
 
 614 
 
 615 
 
 the openings radiate from the back, and that the long edges of 
 the leaves vanish in the same direction, 
 
 Fig\ 616 shows the cylinder standing on a board. {Always 
 draw the board last.) Having 
 drawn the cylinder after esti- 
 mating the space necessary 
 for the board, notice the 
 distance between at? and the 
 edge of the cylinder. Fix 
 point a with reference to the 
 side of the cylinder, and 
 after noting the inclination 
 draw ab. Find how far b is 
 from the side of the cylinder. 
 Draw ac. Very carefully 
 notice where the back line 
 of the board cuts the cylinder, 
 through it to meet ac. 
 
 Note. A board presents considerable difficulty to young pupils 
 at first. The tendency to make it too wide seems inevitable. This 
 can only be remedied by careful measurement. 
 
 Mark this point, and draw 
 
226 
 
 The Teaching of Drawing 
 
 617 
 
 Draw vertical lines from a, b and c. and set off the thick- 
 ness. If these lines are drawn longer than the required thickness 
 
 as shown, the common error of 
 making these short lines sloping 
 will be avoided. 
 
 Fig. 617 shows the cone with 
 a slate. Proceed as in the pre- 
 vious figure. The width of the 
 slate frame may be obtained by 
 drawing diagonal lines as shown, 
 or as in fig. 591. 
 
 Fig. 618 shows an ordinary 
 jam pot. Draw the rectangle 
 ! abed. Next obtain the bottom 
 
 ellipse. Find the position of 
 the shoulder ef, and draw the ellipse. Divide the space from 
 e to c for the rim and neck. Find the size of the mouth and 
 draw the ellipse. Two similar ellipses on Im and gh will give 
 the neck. In showing the thickness be careful to represent 
 the greatest width at the parts nearest to c and d. 
 
 619 
 
 Fig. 619 shows the same object when lying on its side. 
 After obtaining the inclination of the axis as in fig. 608, draw 
 
Model Drazving. Standard V 
 
 227 
 
 cbde. Obtain the mouth and foot of the jar. The ellipse for 
 the shoulder will fall on the ellipse forming the neck, as shown. 
 The neck will be represented by the inner ellipse. 
 
 Figs. 620-622 show a common jug in three positions. 
 Handles are always difficult to represent well, so that three 
 views are given here. Notice in all that a line through the 
 centre gives the position of both handle and spout. In fig. 620 
 
 the handle is not so difficult 
 620 
 
 the thickness is represented by 
 621 622 
 
 two parallel lines, and the width by a line which gradually runs 
 
 into the thickness. Lines drawn as shown are of considerable 
 
 assistance in obtaining the curve. In fig. 621 the handle is a 
 
 band slightly broadening out where it is 
 
 attached, to the jug. It is in fig. 622 that 
 
 the real difficulty presents itself. Fix the 
 
 position of the spout and draw a line from 
 
 this point through the centre, produce this 
 
 line to b, and draw a vertical line be. The 
 
 handle will fall within these lines. To obtain 
 
 its position on the neck, draw a vertical line 
 
 ad from a. From d draw the curve de, giving 
 
 the position of the handle on the body. Now, 
 
 using these lines as a guide, draw the curve 
 
 The right-hand curve is drawn in a similar 
 
 manner to that on the left, as in the handle shown in fig. 623. 
 
 Join the two curves at the top and complete. All handles of 
 
 this kind should be obtained in this way. 
 
 Q2 
 
228 
 
 The TeacJiing of Drawing 
 
 The drawing of a bucket is shown in fig. 354. Notice the 
 method of obtaining the handle. A bell is shown in fig. 327. 
 The glue pot shown in fig. 356 forms an excellent model, giving 
 double practice in the drawing of handles. 
 
 Fig. 624 shows an ordinary gallon bottle. After obtaining 
 its proportions, * draw the rectangle abed, and the ellipses for 
 the bottom, shoulder, and commencement of the neck. Now 
 
 624 
 
 set off the lines efand gh for the neck and cork. An enlarged 
 drawing of this part is shown with the necessary construction 
 lines. The handle is obtained in a similar manner to that of 
 the jug. 
 
 625 
 
 Fig. 625 shows an ordinary roller. The fresh point to 
 
 notice is the method of drawing the handle. 
 
 After obtaining 
 
Model Drawing. Standard V 
 
 229 
 
 the roller, draw ab vanishing with the length, and join a and b 
 with the ends of the axis. Draw the diagonal dg, and from 
 the centre draw oh vanish- 
 ing with ac. Fix the length c 626 
 and draw Im vanishing 
 with de. 
 
 Fig. 626 shows how to 
 obtain the handle of a 
 common tin saucepan when 
 it is turned either towards 
 or from the pupil. Mark 
 the position of the handle, 
 and draw a line ab through 
 the centre of the top ellipse. 
 Draw bd about the height 
 that the handle stands 
 above the mouth. Draw 
 
 dc vanishing with ab, and produce it towards e. The top of 
 the handle must lie in this line. Mark its position e, and draw 
 the centre line of the handle. The rest of the drawing is 
 easily completed. 
 
 Note. This is a very important principle, and is applicable to 
 many objects. The handle of a hot-water can or of a kettle would 
 need the same lines of construction. 
 
 r -J T -JT; ' 
 
 THE HEXAGONAL PRISM 
 
 This important model is not often set for Standard V, as it 
 is not strictly speaking a purely rectangular model. It is, 
 however, very commonly set for the other standards. If the 
 proper principles of construction are not understood it is by no 
 means easy. The following methods, if followed out carefully, 
 will secure an accurate drawing without much difficulty. 
 
 Axis Vertical. First Lesson. 1. Arrange the prism so that 
 the pupils are opposite one of the rectangular faces. Draw ab, 
 and decide upon its length. Compare the width of the front 
 face with the height and draw cd. Complete the rectangle 
 abed (fig. 627). 
 
2^0 
 
 The Teaching of Draiving 
 
 2. Estimate the distance that ef appears to be from ac, as 
 in fig. 581. Make e/a. little less than ac and draw ae and cf. 
 
 3. Draw the diagonals ec and af. Through draw a line 
 parallel to ac. Make gh=go and /m=/o. (These four 
 distances are always equal in the hexagon.) 
 
 4. Complete the top by drawing ah, he, fm, and mc (fig. 
 628). 
 
 5. Draw hn and mp each a little less than ab, and complete 
 the figure. 
 
 627 628 629 
 
 <--/--> 
 
 --2-H3^ 
 
 Second Lesson. 1. Arrange the prism so that its rectangular 
 faces appear of unequal widths. Draw the vertical edge ab, 
 which is nearest to the pupil. Compare the width of the widest 
 face with ab, and draw cd. (This measurement should be care- 
 fully tested before proceeding further, as the proportions of the 
 other faces depend largely upon this.) Compare the next widest 
 face with ac, and draw ef 
 
 2. Set off the width of the narrower face on the wider so 
 that 1 = 2. On the right of cd set off a little less than the 
 distance marked 3, and draw gh. Then 2 + 3 will be a little 
 greater than 1 + 4. 
 
 3. Test the inclination and draw ac. (This will be almost 
 horizontal^ Draw ae sloping a little more than ac. From e 
 draw eg vanishing very slightly with ac. Join c and g. 
 
Model Drawing. Standard V 
 
 231 
 
 4. Find the centre of eg, and draw al. From e draw em 
 vanishing with al. 
 
 5. From c draw a line through the centre to meet em. 
 Draw gl vanishing with cm. Join m and /. 
 
 6. Complete the prism by drawing bd, bf and dk, vanishing 
 with the corresponding lines on the top. 
 
 Notes. 1. The pupil must bear in mind that the lines of the 
 top vanish very slightly, as they are not very far from each other. 
 
 2. Particular attention should be given to the inclination of ac 
 and ae, as if these lines slope too much the top of the prism will 
 appear distorted. 
 
 3. The pupils' attention should be directed to the fact that there 
 are three sets of parallel lines in the top of the figure. 
 
 4. In fig. 628 the two narrower sides could be made each a 
 little less than half the middle face, and the hexagon finished in a 
 similar manner to fig. 629. 
 
 Axis Horizontal. I. End parallel with picture plane 
 
 t. Draw a vertical line ab to represent the height of the 
 end. As the pupil is directly in front, draw a horizontal line 
 ac for the top side of the 
 end. Compare ac with ab, 
 and draw cd and bd. The 
 width ac should be very care- 
 fully verified in all cases before 
 proceeding any farther, as if 
 that be incorrect the whole of 
 the end will be wrong. 
 
 2. Bisect ab and cd, and 
 draw ef. This is preferable 
 to drawing the diagonals of 
 the rectangle abed, as the 
 pupil has two points through 
 which to draw ef instead of 
 one. 
 
 3. Bisect ef in 0. Set off eg equal to eo zndf/i equal to fo. 
 Complete the end by drawing ag, gb, dh and he. 
 
 Note. These construction lines should be drawn with chalk on 
 the end of the model. 
 
232 
 
 The Teaching of Draivmg 
 
 4. Measure the distance to the back line Im, find the 
 position of the back corners in exactly the same manner as 
 shown in fig. 581, and draw a/ and cm. 
 
 Note Im will, of course, be less than ac. 
 
 5. Draw one vertical line In less than ae. Complete the 
 top half of the back hexagon, and draw gp and hq. 
 
 Nate. The advantage of drawing^ is, that the corners^ and 
 q are then accurately shown. There is a tendency to let the lines 
 gp and pi run into each other instead of showing an angle. 
 
 II. End nearly parallel with the picture plane. 
 
 1. This is similar to the last figure. Draw ab. Find the 
 width between the vertical lines, and draw cd. Test the 
 
 inclination of ac. (Nearly 
 6 3 : level, because the end is 
 
 nearly opposite.) Draw bd, 
 making cd very slightly less 
 than ab. 
 
 2. Bisect ab and cd, 
 and draw ef. Be careful 
 to see that all three lines 
 vanish in the same direc- 
 tion. Find the centre 
 as before, or by drawing 
 the diagonal ad, and set 
 off the distances as in the 
 previous figure. Draw ae, 
 eb, df, and fc. 
 
 3. Test the inclination of ag, bearing in mind that if ac is 
 nearly horizontal then ag will have a considerable slope. 
 The easiest way to find the position of g is to hold a pencil 
 vertically in line w T ith g, and notice its distance right or left 
 of e. 
 
 4. From g draw a vertical line gh, and make it shorter than 
 ab. Draw bh. 
 
 5. From e draw em vanishing with ag, and draw hm and 
 gm. The point ;;/ may also be obtained by drawing the line 
 
Model Drazving. Standard V 
 
 233 
 
 nm from the centre of gh and making it slightly less than the 
 corresponding distance on the front end. 
 
 6. Draw gl vanishing with ac, and cl vanishing with ag. 
 
 Vote. em will be slightly longer than ag, as it is nearer. 
 
 III. End at an angle to the picture plane. 
 
 1 . Draw the vertical lines ab and cd as before. Great care 
 is necessary in deciding upon the width between these lines 
 when the model is in this position. Test the inclination, and 
 draw ac. Make cd a little less than ab, and join b with d. 
 
 2. Bisect ab and cd, and draw ef. This must be carefully 
 scanned to see that ef vanishes with both lines. Find the 
 centre, set off the distances, and complete the end. 
 
 632 
 
 Note. These four distances are, of course, only exactly equa> 
 when the hexagon is quite opposite. Strictly speaking, they 
 gradually diminish from / to e. In a very large drawing it would 
 be more accurate to draw the diagonals ad and be. This would 
 give the first distance slightly larger than the second. 
 
 3. Find the inclination of ag, remembering that if ac be 
 much inclined then ag will be nearly level. Determine the 
 length of ag, and draw a vertical line gh. Make gh less 
 than ab. The difference between them may be tested by 
 measuring. Draw bh. 
 
 4. Look at ag and bh and draw//. Make// slightly longer 
 than ag, and draw Ig and Ih. 
 
 5. Notice ag and draw cm. Make cm less than ag, and draw^w. 
 
234 
 
 The Teaching of Drawing 
 
 THE TRIANGULAR PRISM 
 
 The only point that calls for mention here is the method of 
 obtaining the height of the prism. Draw the rectangular face 
 abed in the usual manner. Find the centre, and draw ^/vanish- 
 
 633 
 
 ing with both ab and cd. At e draw eg and set off the height. 
 Join g with a and c. For the farther end draw//, and make it 
 
 a little less than eg. 
 
 Draw *h and bh. 
 
 PYRAMIDS 
 
 I. Axis vertical. For all pyramids when the axis is vertical 
 the method is the same, viz. : 
 1. Draw the base. 2. Find the 
 centre. 3. Set up the height 
 from the centre. 4. Join the 
 apex with the angles of the base. 
 Fig. 634 shows a square 
 pyramid standing upon its base. 
 Draw the base abed in the usual 
 manner. Obtain the diagonals. 
 From e draw the axis ef, and mark 
 off the height. Join / with a, b 
 and c. 
 
 Fig. 635 shows the same pyramid when one side of the base 
 
Model Drawing. Standard V 
 
 235 
 
 is opposite the pupil. Three of the triangular faces are then 
 visible. 
 
 635 636 
 
 Fig. 636 shows the hexagonal pyramid. Fix point a, the 
 angle nearest the pupil. Draw ab, the widest side and therefore 
 the least inclined. Draw ac y the next widest side. From c draw 
 cd vanishing with ab, and from b draw bd, the narrowest side of 
 the base, to meet cd. Find the centre of cd, and through it 
 draw ae. Look at ae and draw cf. Through o draw bf, and 
 from d draw de vanishing with it. Join e with f. Draw the 
 vertical axis from 0. Set off the height, and join the apex with 
 the angles of the base. 
 
 II. Lying on one of the tri- 
 angular faces. Fig. 637 shows 
 a square pyramid. This is a 
 very difficult position. The 
 simplest plan is to mark point a, 
 and draw the line ab. To get 
 the slope of ab, hold the pencil 
 vertical with b and notice the 
 distance that b is to the right 
 of a. Determine the inclination, 
 draw ad, and complete the base. 
 
 It will not be of much assistance to draw the axis ; the easier 
 plan is to determine the inclination and length of ae, and join b 
 with e. 
 
236 
 
 The Teaching of Draiving 
 
 CYLINDRICAL RING 
 
 I. Axis vertical.- i. Draw ab. Compare cd with ab and 
 draw the ellipse. 
 
 63S 
 
 2. Set off the depth, ae and bf. Draw ef. Make dg a little 
 longer than ae (because it is nearer), and draw the bottom curve. 
 
 3. Set off the width of the ring, ah and bl equal to ae. 
 
 The width at dm will be the 
 same part of ah that cd is 
 of ab. Notice that en will be 
 a little less than d7?i. Draw 
 the inner ellipse. 
 
 4. For the inner bottom 
 curve draw a semi-ellipse on 
 pq. Notice that no will be 
 slightly less than hp. 
 
 II. Axis horizontal. If 
 the ring were level with the 
 eye then the drawing would 
 be similar to fig. 638 turned 
 at right angles ; but if below 
 the eye the axis will be in- 
 clined and ab will not be ver- 
 tical. In the cylinder the 
 inclination of the axis was first 
 obtained, but in this case the axis is too short to test its 
 inclination. It is, therefore, easier to draw the longer dia- 
 
Model Drawing. Standard V 237 
 
 meter of the ellipse first. The only difficulty here is in de- 
 termining the inclination, ab, of this diameter. Hold the pencil 
 in a line with the longer diameter so as to cut the ellipse into 
 two symmetrical portions, and with the other hand hold a 
 pencil vertically with a, as indicated by the dotted line ac. 
 This will assist the eye to estimate the slope. The rest of the 
 drawing is done in exactly the same manner as in the previous 
 figure, and may be easily followed from the construction lines. 
 
 Note. Figs. 627-639 are not included in the Standard V sylla- 
 bus. They are, however, shown here for the sake of completeness. 
 
 VASES 
 
 Three sets are recommended by the Department. 
 
 1. Set of Three Regular Objects of Form in white pottery. 
 
 2. Set of Three Earthenware Vases in terra-cotta. 
 
 3. Set of Five Vases in Majolica ware. 
 
 The first set is the most suitable for schools, as it gives 
 greater variety of shape and simpler lines. 
 
 The general contour should be noted, and the fact pointed 
 out that vases with oval or egg-shaped bodies are generally 
 more effective and beautiful in form than those with either 
 circular or elliptical ones. 
 
 Simple vases in elevation are shown in figs. 214-218, 324, 
 and 332 ; while figs. 381 and 382 show more difficult ones. 
 The method of procedure has already been given on page 99, 
 Standard V, Freehand. Figs. 334, S3^>) an d 338 illustrate the 
 method of drawing the three vases of the first set. Figs. 335 
 and 337 are from the third set. Fig. 330 shows an enlarged 
 drawing of the mouth of fig. 334, and fig. 331 shows the foot 
 of fig. 338. The only additional point needing illustration is 
 the ornamental handle of fig. $^- Tms * s difficult and should 
 be shown on the board, and drawn separately in three positions 
 before drawing it on the vase. If the leaf form to which the 
 ring is attached be examined, it will be found to be of a pen- 
 tagonal shape and divided into five parts. The shape varies a 
 
238 
 
 The Teaching of Drawing 
 
 little on different vases, but the same method of obtaining it 
 should be adhered to. 
 
 Fig. 640 shows the handle when seen on the side of the 
 vase. 
 
 Fig. 641 shows the front view blocked in. Begin with 
 line a?>, and ascertain the proportion which ab bears to the 
 height of the vase. Find the position of c, and draw the base 
 of the pentagon. Mark the width at d and <?, and complete the 
 pentagon. Now draw the ring. Divide the pentagon into five 
 parts as shown. 
 
 640 
 
 641 
 
 642 
 
 643 
 
 644 
 
 Fig. 642 shows the completed sketch. Notice that the 
 points of the leaf are not sharp, but blunt and rounded as 
 pottery would naturally be. 
 
 Figs. 643 and 644 show the most common and also the 
 most difficult view. In fig. 643 the blocking in is shown. The 
 central line follows the curve of the vase, and the pentagon is 
 foreshortened. In fig. 644 notice that the thickness of the leaf 
 is now visible, and that the right-hand side will not be so clearly 
 defined as the left or nearer side. 
 
 Figs. 645-647 show the largest vase from the second set in 
 terra-cotta. It is not recommended for Standard V, as, 
 although of a beautiful shape, it presents too many difficulties 
 
Model Drazving. Standard VI 
 
 239 
 
 for the present stage. It is one of the two vases prescribed by 
 the Department for the examination in what is now known as 
 the Elementary stage of Model Drawing, corresponding to what 
 was formerly second grade Model. The other vase is that 
 shown in figs. 338, 648, and 649. 
 
 The elevation of the vase in fig. 645 is shown in order that 
 the lines to be represented may be clearly seen, as about eight 
 ellipses have to be indicated in the drawing. 
 
 Fig. 646 shows the construction lines. After obtaining the 
 centre line, draw the lines ab, cd, and ef, representing the 
 widths of the mouth, the widest part of body, and the foot, 
 respectively. Now obtain gh, the width of the bottom of the 
 neck, and lm y the width of the top of the foot. Draw the 
 mouth and the curve of the body. The general proportions of 
 these parts should now be carefully examined and the rest of 
 the figure completed, as in fig. 647. Notice how the lines 1 
 and 2 gradually die away before reaching the diameter of the 
 ellipse. 
 
 645 
 
240 
 
 The Teaching of Drawing 
 
 646 
 a^^Ti 1 ^~^>)6 
 
 9^ 
 
 
 
Model Drawing. Standard VI 
 
 241 
 
 Figs. 648 and 649 show two views of the bottle when lying 
 down. These are not intended for Standard V. In fig. 648 
 the axis is nearly parallel to the pupil. First draw the axis ab. 
 To determine the inclination, hold the pencil in a line with ab, 
 and with the other hand hold a pencil in a horizontal position 
 level with a \ the angle between the pencils will give the slope 
 of the axis. Draw cd, ef, and gh at right angles to ab, and 
 sketch the outline as in fig. 338. 
 
 In fig. 649 the contour is lost in the ellipses to a great extent. 
 After obtaining the axis, draw the three ellipses on cd, ef, and gh. 
 The curve of the neck loses itself as shown. The lower part 
 of the body is smaller than the upper part, and the curve of the 
 ellipse (shown by the dotted line) will require a little addition at /. 
 
 e 
 
242 
 
 The Teaching of Drawing 
 
 Syllabus, Standard VI. Draiving from models of regular 
 forms and from easy common objects. _ 
 
 All the models previously shown are suitable for Standard 
 VI. when grouped. The only fresh point is the arrangement 
 of the models. Usually two models are set, but this is not an 
 absolute rule. Very large models should not be used in com- 
 bination with the vases or any small objects, as the vases will 
 be so small when drawn as to make it impossible to show their 
 lines with any degree of accuracy. 
 
 Fig. 650 shows the examples given in the ' Illustrated 
 
 Syllabus.' 
 
 650 
 
 Figs. 627-639 and 645-649 all belong, strictly speaking, to 
 Standard VJ. course. A few groups will now be given, illus- 
 trating difficulties that frequently occur. 
 
 Fig. 651 shows a group of average difficulty, to be drawn 
 with the board. 
 
 1. Begin by comparing the greatest height ab with the 
 greatest width b c, so as to obtain an idea of the proportions 
 of the whole group. 
 
 2. Next draw the hexagonal prism after comparing its height 
 with ab. 
 
 3. Hold the pencil vertically in a line with the axis of the 
 vase, notice where it cuts the prism, and draw de. Hold the 
 pencil level with the foot of the vase, and notice its position, 
 whether above or below the corner / of the prism. Compare 
 the height of the vase with the height of the prism, and com- 
 plete as previously shown. 
 
 4. To draw the board, fix the position of g, its distance 
 below, and its distance left, of e. Find the inclination of gh. 
 Notice how far h is to the right of the prism. Find the inclina- 
 
Model Draiving. Standard VI 
 
 243 
 
 tion of g/ } and determine the position of /. Notice where the 
 back lines of the board cut the other models. Draw vertical 
 lines from /, g, and h, and complete the figure. 
 
 Notes. 1. These earlier groups should be composed of a circular 
 and a right-lined model, and should be placed in easy positions. 
 
 2. They will probably take some time to draw correctly, but it 
 will be found most profitable to endeavour to get the earlier 
 groups well drawn rather than to attempt a larger number of 
 1 drawings. 
 
 652 
 
 653 
 
 3. The board is generally difficult to draw (see fig. 616). Ob- 
 serve that fig. 652 is an incorrect drawing, as if ab were level then 
 the sides should be drawn as in fig. 653. This maybe easily tested 
 
 
244 The Teaching of Drawing 
 
 by the pupil holding the pencil vertically in line with #, as shown 
 by the dotted line, and noticing on which side 67 the pencil c ap- 
 pears to be. 
 
 Fig. 654. First draw the cylinder. Now determine the 
 position of a with regard to b, of c with regard to the edge and 
 length of the cylinder, and draw ac. Test the inclination before 
 
 proceeding further. Obtain the position of d (above and left of 
 a) and draw ad. Find the inclination of ae, and complete 
 the figure. 
 
 Fig. 655. This is a very difficult group to draw, and is 
 shown in two stages. The figures should be blocked in as 
 shown in the top drawing, obtaining all the main lines and 
 proper proportions first. Begin with the centre line of the cup, 
 and draw the ellipse on ab. Now obtain the diameter ef of 
 the saucer j the position for this diameter will be obtained by 
 holding the pencil in a horizontal position level with e and f 
 and noticing where it cuts the sides of the cup. Draw gh for 
 the points of attachment of the handle, and if a. line be drawn 
 from the centre through g the direction of the handle will be 
 indicated. 
 
 For the spoon draw the centre line and block in*as shown. 
 
 In drawing the book, fix the position of / and draw /;;/. 
 
Model Draiving. Standard VI 245 
 
246 
 
 The Teaching of Drazvin^ 
 
 Determine the height of , and complete the end. In drawing 
 the leaves, notice that the horizontal edges will vanish with the 
 length of the book. 
 
 Objects wholly or partly above the eye should also be 
 practised such as a door, window, board and easel, swing 
 slate, &c. 
 
 Fig. 656 shows the construction for the board and easel. 
 Commence with abed, and set up the height as shown. As the 
 top of the easel is narrower than the bottom, the side rails will 
 not come from the points e and/ Hold the pencil level with 
 f, and notice how much e is below/ Draw a line H for the 
 
 6^6 
 
 level of the eye, and remember that all lines below H run up, 
 and those above it run down towards H. Lines like the bottom 
 of the board which are near the level of the eye will be nearly 
 horizontal. The back legs are not so wide apart as the front 
 ones, and are parallel to each other. They will therefore not be 
 drawn to c and d. 
 
Model Draiving. Standard VI 
 
 247 
 
 Fig. 657 shows an ordinary swing slate. The dotted lines 
 show the parts to be drawn first. H marks the level of the 
 eye. 
 
 657 
 
248 The Teaching of Drawing 
 
 I 
 
 CHAPTER XI 
 
 LIGHT AND SHADE. STANDARD VII 
 
 Syllabus. Drawing any common objects and casts of orna- 
 ment in light and shade. 
 
 This is the most difficult part of the syllabus to carry out 
 in ordinary schools, as the difficulties in the way of securing a 
 proper light are very great. The object should be lighted 
 from one window only (with a northern aspect, if possible), as 
 cross lights increase the difficulty to a very great extent by de- 
 stroying the effect of the shadows. The only way to prevent 
 this is to fence off the other lights by means of screens. A box 
 with two of its sides knocked out will frequently answer fairly 
 well for this purpose. 
 
 It is also necessary that the teacher should possess a higher 
 degree of artistic feeling and knowledge than the previous 
 parts of the syllabus necessitate ; practical acquaintance with 
 the subject being absolutely necessary before instruction can 
 be imparted to the pupils. Where these difficulties of teach- 
 ing, lighting, &c, arise, it is much better to take the alternative 
 subject of Geometrical Draiving (h.i.), which is easier and quite 
 as useful to the pupils. (See Chapter VIII. Standard VII.) 
 
 Materials. These are inexpensive and readily procured. 
 They will depend somewhat upon whether the pencil, crayon, 
 or stump is used for the shading. Arguments may be adduced 
 in favour of each, but for producing a good general effect in a 
 short time the stump is preferable. The pupils will need a 
 drawing-board, paper with a rough surface, an F or H pencil 
 for sketching the outline, a piece of indiarubber cut to a sharp 
 point for removing the dark spots, small paper stumps, and 
 prepared stumping-chalk. 
 
Light and Shade. Standard VII 249 
 
 Paper. This must have a rough surface, as smooth paper 
 is perfectly useless. For ordinary practice, French white paper 
 is very suitable, as it is cheap, and has a ridgy surface. Cart- 
 ridge paper will do if it has a good texture. For examination 
 purposes and for finished drawings Whatman's ' Not ' is the 
 best that can be used. 
 
 Stumps. These are made either of leather or paper. The 
 small paper stumps sold at about 3d. per dozen are the most 
 suitable for ordinary purposes. The stump should be held 
 between the thumb and finger, under the hand, and very gently 
 turned round while being used, so that all parts of the chalked 
 end may be brought into use, thus securing an even texture in 
 the shading. 
 
 Stumping-chalk is sold in small bottles by all artists' colour- 
 men. When using it, a small quantity should be rubbed into 
 a piece of wash leather pinned at one corner of the board, and 
 the stump charged by rubbing the point en it. A piece of 
 rough paper, with the bottom corner turned up so as to prevent 
 any of the chalk rolling upon the drawing, will answer just as well. 
 
 When the shading is obtained by using the pencil or crayon, 
 then a BB pencil, or a No. 1 Conte Crayon in wood is the 
 most suitable for the purpose. The Conte Crayon is also use- 
 ful for indicating the edges of the figure, which are sometimes 
 apt to get indistinct and irregular. 
 
 First Lesson. The pupil should begin by practising the 
 laying on of flat even tints of various degrees of darkness. 
 When this has been satisfactorily accomplished, the shading of 
 objects should be at once proceeded with. Copying from 
 shaded drawings is of little use ; the pupil needs practice in 
 drawing from the object, and the training of the eye to dis- 
 tinguish the varied gradations of shade between the highest 
 light of the object and the darkest part of its shadow. 
 
 There are many ways of using the stump, all having the 
 same end in view, namely, the production of an even tint. Some 
 accomplish this by using broad diagonal strokes, others by a 
 zigzag stroke ; probably the easiest for covering a large surface 
 is a rounded zigzag something like the letter S. The method 
 selected must largely depend upon that which the teacher has 
 
250 
 
 The Teaching of Draivim 
 
 found most successful. In all, the steps are the same ; first, 
 the covering of the surface with strokes, giving a general depth 
 of tone, and then securing evenness by filling up the light spaces 
 and removing any dark spots. 
 
 i. Rule a two-inch square. Charge the stump by rubbing 
 it on the chalked leather or paper as previously explained, 
 taking care that no loose chalk is left on the stump, or the 
 stroke will be uneven. Try the stump on a piece of white 
 paper to see that the stroke is of the required degree of dark- 
 ness ; then, holding it as directed, and gently rolling it while 
 working, cover the square as in fig. 658 A. 
 
 In working begin at the left side, work towards the right, 
 and try to avoid crossing over a stroke a second time, as this 
 
 658 
 
 will produce a darker spot which will need removing. For the 
 first practice it is desirable to make the strokes rather large 
 and open, as shown in the bottom part of the square. As the 
 pupil acquires more power the strokes may be made smaller 
 and less open, thus securing an even tint at once. The top 
 part of the square where the strokes are smaller shows a fairly 
 even shade with one process. Be especially careful to use the 
 stump lightly and never scrub the paper. 
 
 2. Fill up the light spaces by gently touching them with 
 the point of the stump as shown in stage B. 
 
 3. Remove any dark spots by gently pressing (not rubbing) 
 the point of the indiarubber on them. Clean the indiarubber 
 after removing each spot by rubbing it on a piece of paper. 
 The tint should then be even as in C. 
 
Light and Shade. 
 
 Standard VII 
 
 251 
 
 659 
 
 Draw another square. Charge the stump more heavily with 
 chalk, and fill up with a darker tint as shown in fig. 659. Finish 
 in exactly the same manner as shown in 
 fig. 658, and the result will be a square 
 of a darker tint than the previous one. 
 
 A third square might be filled up in 
 the same manner with a still darker tint 
 by charging the stump more fully than in 
 the last. 
 
 Notes. 1. Great care should be taken 
 with these first exercises ; speed will come 
 with practice. To put on an even tint 
 
 without much subsequent alteration should be the pupil's aim, as 
 much use of indiarubber or bread is sure to destroy the texture of 
 the shading. 
 
 2. Remember that the three steps indicated in the lesson must 
 always be patiently gone through, though practice and care will 
 gradually decrease the time spent on two and three to a small 
 amount. When occupied with these two stages the student should 
 always sit well away from the work, as the general evenness of 
 the tint can only be seen when the eye is far enough off to take in 
 the whole of the drawing. 
 
 3. A piece of tissue paper should be kept under the hand while 
 working, and the part of the drawing which is not in progress 
 should be covered up. 
 
 Second Lesson. When the power of laying on a flat even 
 tint has been acquired, proceed at once to the shading of a 
 simple rectangular model such as the cube. 
 
 1. Place the model on a sheet of white paper so that the 
 shadow may be more distinctly seen (it may also sometimes 
 be desirable to pin a sheet at the back of the model), and draw 
 the cube very lightly in outline, marking the shadow, and 
 avoiding rubbing out as far as possible (fig. 660). Do not 
 make the drawing too large at first: about three inches is quite 
 long enough for the edge of the cube. 
 
 Note. Use an F or H pencil. Charcoal is frequently used 
 for this purpose, as the lines can be readily dusted out. It is not, 
 however, recommended for beginners, as it requires constant 
 sharpening and is easily broken. 
 
252 The Teaching of Drawing 
 
 2. Direct attention to the fact that some) parts of the cube 
 are lighter than others. The top on which most light falls is 
 the lightest ; one of the vertical faces is darker than the other, 
 and the shadow thrown on the paper is the darkest of all. If 
 the darker vertical face be looked at carefully with half-closed 
 eyes, it will be noticed that this face is not of the same depth 
 of tone, but that the top part is darker than the bottom part. 
 This is due to the light reflected from the white paper upon 
 which the model stands. Remove the white paper, and place 
 the cube upon a black surface, when this difference will not be 
 seen. To illustrate this further, hold a sheet of white paper 
 opposite to the darkest side of the model ; the light reflected 
 from the paper will cause this side to appear much lighter. 
 
 The facts observed may now be summarised as follows : 
 
 (a) The lightest part of the cube is said to be in high light. 
 
 (b) The part of the cube upon which the light does not directly 
 fall is in shade. 
 
 (c) The part of the paper which is deprived of light by the cube 
 is the cast-shadow. 
 
 (d) The parts of the cube made lighter by the paper upon which 
 it stands are in reflected light. 
 
 (e) Place a cylinder on the paper, and in addition to the four 
 preceding points, it will be seen that between the highest light and 
 the shade, there are intermediate tints on the curved surface upon 
 which the light does not fall so directly. This is termed the half- 
 tone. 
 
 3. Begin to shade the darkest part, that is the cast-shadow. 
 Put on an even tint of the same depth as its lightest part 
 (fig. 661). 
 
 4. Shade the darker vertical face with an even tint, as dark 
 as its lightest part. 
 
 5. Shade the lighter side in the same manner. The drawing 
 should now show three degrees of shade, all perfectly even as 
 in fig. 661. 
 
 6. Put in the gradations on the vertical faces (fig. 662). 
 The left-hand face is darker towards the top and /eft, the paper 
 making the bottom part lighter. The right-hand face is 
 darkest at the top and at the left, nearest the light part of the 
 
Light and Shade. Standard VII 
 
 253 
 
254 The Teaching of Drazving 
 
 top and the left-hand face. The pupil will notice that the 
 bottom part of the right-hand face is not the lightest part, as 
 the cast shadow prevents so much light being reflected upon 
 it. 
 
 7. Darken the cast shadow towards the object. 
 
 8. The top of the cube, although the lightest part, is not 
 quite white, and requires a very light tint from an almost clean 
 stump on the part furthest removed. This general principle 
 should be carefully borne in mind : That a light tone if placed 
 beside a dark one appears lighter where it approaches the darker 
 tone, and the dark tone appears darker where it approaches the 
 lighter one. This will be seen to be the case on the cube ; the 
 top appears lighter as it approaches the darker vertical faces, 
 the vertical faces appear darker as they approach the lighter 
 top, and the right-hand face appears darker towards the edge 
 nearest the lighter-toned face, &c. 
 
 Notes. 1. Be very careful not to make the gradations too dark. 
 
 2. As the pupil progresses he will be able to lay on a gradated 
 tint at once, instead of doing it in two stages. 
 
 3. The above steps apply to all models, and the rectangular and 
 hexagonal prisms will present no difficulty to those who have 
 mastered the shading of the cube. 
 
 The Cylinder. This is taken as the type for all circular 
 models, as the same rules are applicable more or less to all 
 similarly shaped objects. 
 
 1. Sketch the cylinder, mark in the cast shadow, and 
 indicate by a light line the part of the cylinder in shade. This 
 line will commence at a, where the shadow is seen to begin 
 
 (fig. 663). 
 
 2. Shade the cast shadow evenly of a depth equal to its 
 lightest part. 
 
 3. Lay on an even tint, from the right-hand side to the line 
 marking the extent of the shade, as dark as its lightest part 
 (fig. 664). 
 
 4. Notice that the darkest part is not at the edge, and 
 gradate the tint already laid on. The highest light is not quite 
 at the left edge. On each side of the. high light put in the half 
 
Light and Shade. Standard VII 
 
 255 
 
 tone on the portions of the cylinder upon which the light falls 
 obliquely. Be careful to gradate these tones so that there is a 
 gradual darkening from the highest light to the darkest shade. 
 5. Darken the cast shadow where necessary, and put a very 
 light tint upon the top, decreasing as it approaches the front 
 
 (% 665). 
 
 The cylinder lying down should be treated similarly ; its 
 
256 The Teaching of Drazving 
 
 vertical end will get lighter as it approaches the dark part of 
 the shade on its length, as in the left-hand face of the cube. 
 
 The cone is treated similarly to the cylinder ; the only fresh 
 point to notice is that the darkest part of the shade is near the 
 apex, as owing to its sloping surface there is less light reflected 
 on this part. The same fact applies to all pyramids when 
 standing on their bases. 
 
 The waterbottle from the three objects of form is shown as 
 an example for vases, as it is the one prescribed for the 
 elementary stage of model drawing, and is in common use. 
 
 1 . Very carefully sketch in the outline ; mark the cast 
 shadow and the line of shade (fig. 666). 
 
 2. Lay on the shade with an even tint as dark as its lightest 
 part. 
 
 3. Put in the cast shadow in a similar manner (fig. 667). 
 
 4. Gradate the shade on the neck as in the cylinder, bearing 
 in mind that the darkest part is not quite at the edge. The 
 darkest part will be at a, as here the shadow from the neck falls 
 upon the shoulder of the vase. The darkest shade on the body 
 is some distance from the edge, owing to the reflected light 
 from the ground. Add the half tones. The lightest part of 
 the body will be at b y as the light falls most directly upon the 
 vase at this part. 
 
 5. Complete the cast shadow. Notice that it falls on the 
 foot with a rather sharp edge ; on the ground its edges should 
 be kept soft. The middle part of this shadow is lighter than 
 the outside, owing to the light reflected from the body of the 
 vase. 
 
 6. Blend the tones carefully, and complete as in fig. 668. 
 When the pupils have shaded several of the models singly, 
 
 they may at once proceed to the shading of a group. The 
 1 Illustrated Syllabus ' shows, as an example, a group of three 
 objects lightly shaded. The pupils should notice the cast- 
 shadow thrown upon the book by the other two objects. Any 
 group of models of about the same degree of difficulty as is 
 usually set for Standard VI will make a suitable group for 
 shading. 
 
 Shading from Casts. The syllabus specifies shading from 
 
Light and Shade. Standard VII 
 
258 
 
 The Teaching of Drawing 
 
 common objects and casts of ornament. In most schools the 
 group of models would probably be taken. Casts of ornament 
 in plaster of Paris may be obtained at a very cheap rate from 
 D. Brucciani & Co., 40 Russell St., Covent Garden, W.C., the 
 agents to the Department. Ten casts of elementary ornament 
 suitable for Standard VII, or for the elementary stage of light 
 and shade, may be obtained for 1/. 
 
Light and Shade. 
 
 Standard VII 
 
 259 
 
 Method of Shading the Cast. Three drawings showing an 
 ordinary cast in three stages of development are given. 
 
 Fig. 669. 1. Place the cast in an upright position against 
 the wall, and about level with the pupil's eye. Begin by 
 drawing the slab upon which the ornament is placed, as this 
 will help the pupil to draw the outline more easily. 
 
 670 
 
260 
 
 The Teaching of Drawing 
 
 2. Draw the middle line and fix the position of the top 
 and bottom of the ornament (a and b). 
 
 3. Find the position of c and draw the line de. In the same 
 manner obtain^. 
 
 4. Draw the curves from these points. 
 
 5. Draw the other big curves after obtaining their position 
 as shown by the construction lines. 
 
Light and Shade. Standard VII 261 
 
 a 
 
 6. Complete the drawing and very lightly indicate the cast 
 shadows. 
 
 Notes. 1. It is not at all necessary that the student should 
 draw all the horizontal lines shown on the figure, as the rubbing 
 out of these lines will spoil the surface of the paper. It will be 
 sufficient in most cases to carry the pencil across and mark the 
 point. 
 
 2. Sketch the cast very lightly, as alterations may then be 
 easily made. 
 
 Fig. 670. t. Very lightly shade the background with an 
 almost clean stump. When there is a large surface to cover, 
 the forefinger, covered with a piece of wash leather very faintly 
 charged with chalk and well rubbed on trial paper, may be 
 used with advantage for this purpose. The portions close to 
 the drawing can be filled up afterwards with the stump. By 
 putting in the background first the student is better able to 
 judge the degree of shade necessary for the various parts of the 
 cast. The light parts will be lighter than the background and 
 will stand out better from it. 
 
 2. Put on the main shades and the cast shadows. Where 
 a shade on a curved portion approaches the lighter part, be 
 careful to let it die away gradually. 
 
 Fig. 671. 1. Gradate the parts in shade by darkening 
 them towards the left, where they approach the high light. 
 Continue the shade over the lighter parts where needed, leaving 
 the highest light white. 
 
 2. Darken the shadow where it approaches the cast. Be 
 careful to keep the edges of the shadow soft, letting them die 
 away somewhat gradually into the surface of the slab. 
 
262 The Teaching of Drawing 
 
 CHAPTER XII 
 
 THE ELEMENTARY DRAWING CERTIFICATE 
 
 As all teachers of boys' schools are required to teach drawing 
 it is very necessary that they should qualify themselves by 
 obtaining the certificate. This certificate covers the work 
 required from the standards, and the Education Code, 1893, 
 art. 60, states that ' No teachers, passing the second year *s exam- 
 ination after December, 1896, will be recognised as certificated 
 teachers unless, or until, they have obtained the First or Second 
 Class Elementary Drawing Certificate? This applies to all 
 teachers, both male and female. 
 
 Those teachers who may be partially qualified and wish to 
 obtain their certificate should procure information from the 
 Science and Art Department as to what subjects they must 
 take to complete it. 
 
 The requirements at present for the First Class Certificate 
 are a First Class in : (a) the Elementary Stage of Freehand 
 Drawing {subject 2b) ; (b) the Elementary Stage of Model 
 Drawing (subject $a) ; (c) the Elementary Stage of Shading from 
 Casts {subject $b) ; and (d) a pass in the Elementary Stage of 
 Practical Plane and Solid Geometry. 
 
 For the Second Class Certificate :(<*) a pass in the Ele- 
 mentary Stage of Practical Plane and Solid Geometry ; (b) a 
 second class in the Elementary Stage of Model Drawing ; (c) 
 a second class in the Elementary Stage of Freehand Drawing. 
 
 'Pupil teachers may, after August 31, 1893, be examined 
 at their schools in the Elementary Stage of Freehand, of 
 Model, of Shading from Casts, and of Perspective. Teachers 
 wishing to be examined in Geometrical Drawing must sit for 
 examination in that subject at the May examinations of Science 
 
The Elementary Draiving Certificate 263 
 
 and Art schools and classes, and the examination in Geometrical 
 Drawing at elementary schools will cease.' 
 
 A few hints and directions are given with regard to each 
 subject. If the method of working explained in the previous 
 chapters be thoroughly understood and well practised, the 
 teacher should not experience any great difficulty in doing the 
 work required. 
 
 Elementary Stage Freehand. The instructions for ex- 
 amination are : That the leading lines of the whole figure 
 must be sketched in, and that the drawing should fairly fill the 
 paper supplied (J imperial sheet, i5^in. by n^in.). When 
 this is done, carry the drawing to completion, as far as possible 
 in clear outline. 
 
 The object is clearly to ascertain whether the proper 
 method of drawing a copy is understood. Figs. 377, 378, 379, 
 380, show the leading lines of the figures they accompany and 
 are suitable for preliminary practice. Two recent examination 
 tests are also given, from which the student may see the 
 character of the copies set and the proper method of drawing 
 them. 
 
 Figs. 672 and 674 show the copies as set, slightly reduced 
 in size. 
 
 Fig. 673 shows the construction and leading lines of fig. 
 672. The left side is carried a little further towards completion 
 than the right. 
 
 Fig. 675 shows the construction and leading lines of fig. 
 674. The student will have no difficulty in following after 
 studying the figure. In both copies begin with the spiral 
 curves and the circles containing the flower, leaving the detail 
 until last. The copies would require enlarging to abDut 2\ 
 times the given size. 
 
 Elementary Stage Model. Practise the methods of draw- 
 ing the models and vases given in Chapter X., and especially 
 notice the remarks concerning the arrangement of the group in 
 fig. 651. 
 
 It is usual to give three models in the group for examina- 
 tion, which are frequently required to be drawn with the board 
 upon which they may be placed. 
 
264 
 
 The Teaching of Drawing 
 
 672 
 
The Elementary Drawing Certificate 265 
 
 673 
 
266 
 
 The Teaching of Drawing 
 674 
 
 The examination is now confined to groups composed from 
 the following models and vases prescribed by the Science and 
 Art Department, and which are all dealt with in Chapter X. 
 The cube, square prism, square pyramid, triangular prism, hexa- 
 gonal prism, cylinder, cylindrical ring, and cone, together with 
 the bottle from the three objects of form (figs. 338, 648, and 649) 
 and the large terra cotta vase (figs. 645-64 7 ). 
 
 Practise groups of these models, paying special attention to 
 the method of drawing ; as, if the group be correctly drawn, even 
 though not finished, the student would undoubtedly get 
 through. To secure a first-class the group should be correctly 
 drawn and completed in the hour allowed. 
 
 Elementary Stage of Shading from Casts. The student 
 is required to make a drawing in chalk, from a cast in lour 
 relief, in three hours. The cast shown in figs. 669-671 is 
 suitable for the purpose and is one in common use. The 
 
The Elementary Drawing Certificate 
 675 
 
 267 
 
 Illustrated Syllabus also shows two casts such as are set for 
 this stage. 
 
 Read over the directions given in Chapter XL, and then 
 draw a variety of casts, as success largely depends upon the 
 amount of practice bestowed upon the subject. At the same 
 time the student will find that more useful knowledge of shading 
 will be obtained by well finishing two or three casts, than by 
 making rough drawings of a large number. 
 
 Elementary Stage of Practical Plane and Solid Geo- 
 metry. The course indicated for Standards VI. and VII. forms 
 a good introduction. The student who thoroughly understands 
 the principles there dealt with will be able to take up the Ele- 
 mentary Stage without much difficulty. ' Practical Plane and 
 Solid Geometry,' by I. H. Morris (Longmans & Co., two shillings 
 and sixpence), amply covers the requirements. 
 
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 UNIVERSITY OF CALIFORNIA LIBRARY