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 -
 
 FREE-HAND DRAWING 
 
 LIGHT AND SHADE 
 
 AND 
 
 FREE-HAND PERSPECTIVE 
 
 Art Students and Teacbers 
 
 BY 
 
 ANSON K. CROSS 
 
 INSTRUCTOR is THE MASSACHUSETTS NORMAL ART SCHOOL AND IN THK SCHOOL 
 OF DRAWING AND PAINTING, MCSKUM OF FINE ARTS, BOSTON 
 
 ILLUSTRATED BY 32 PLATES 
 
 BOSTON 
 
 PUBLISHED BY THE AUTHOR 
 1892
 
 COPYRIGHT, 1892, 
 i:\ ANSON K. CROSS. 
 
 ALL KK.IITS KKMCKVED. 
 
 TYPOGRAPHY BY J. S. CrSIIlNr, ,<t Co., FinsTON.
 
 Plate I. 
 
 FIG. i. 
 
 THE 
 DRAWING
 
 TO 
 
 MY FRIEND AND FIRST TEACHER 
 L\obrrt ll\. Fonnol} 
 
 I INSCRIBE THIS BOOK 
 
 IN RECOGNITION 
 
 OF HIS EFFORTS TO ADVANCE 
 
 SERIOUS AND CONSCIENTIOUS 
 
 STUDY OF NATURE
 
 PREFACE. 
 
 THE notes on Model Drawing, forming the body of this 
 book, were prepared for the use of the students of the Mas- 
 sachusetts Normal Art School. They were printed with- 
 out illustrations, as explanations of the drawings given in 
 the course of lectures on this subject, and will be of 
 little assistance to those not taking the lectures. Having 
 been requested for the book by persons not students of 
 the school, and realizing that drawing is often poorly 
 taught, especially in our public schools, and being unable 
 to recommend a book which treats the subject simply 
 and presents artistic methods of work, I concluded to 
 rewrite the notes, adapting them to general use, and 
 meeting, as far as possible, the demand for a text-book 
 on the principles of free-hand drawing. 
 
 The book is intended especially for teachers, and at 
 first glance the artist may think it considers more theory 
 than is necessary. No one can be more strongly con- 
 vinced than I, of the folly of teaching and depending 
 upon theory alone. I believe that theory is of use only
 
 v i PREl-ACE. 
 
 to the artist who can draw without it. To such a per- 
 son and to the teacher, theory may be of great assist- 
 ance. The artist who should depend upon theory 
 instead of upon his eyes, would certainly be very unwise, 
 and would probably produce unsatisfactory work. If his 
 work consisted simply in drawing from Nature, and from 
 subjects before him exactly as they are to be repre- 
 sented, he would have little need of theory, and could 
 safely depend upon his eyes ; but the artist often lias 
 to design and draw without a subject before him, and 
 for this work he must depend upon his knowledge. If 
 this has been arranged under a few simple rules which 
 he has discovered while drawing from Nature, he will 
 draw with more freedom and far greater accuracy than 
 when without these helps. 
 
 If his mind is so constructed that he cannot discover 
 and apply the few rules necessary for this work, it is 
 quite likely that his time will be more profitably spent 
 in some other direction ; for the rules of perspective 
 which the artist requires are so simple as to be easily 
 given in a few sentences. From the standpoint of the 
 artist, then, there may be more theory than is needed, 
 but the teacher of much experience will not find this 
 true. 
 
 Every teacher has found the bright, thoughtful student 
 who has asked questions of which the teacher has never 
 thought. Nearly all the points considered in these notes
 
 PREFACE. vii 
 
 have been suggested by such questions, which have been 
 referred to me. It is impossible to furnish answers to 
 all the questions which the teacher is likely to be asked, 
 but the main points can be covered, and these under- 
 stood, other questions depending upon them can be 
 readily met. 
 
 Though intended for the teacher and student, the 
 subject-matter is to a greater or less extent interesting to 
 the artist, the illustrator, and others who may not have 
 the knowledge of Projection and Scientific Perspective 
 necessary to follow some of the problems considered. 
 The problems requiring this knowledge are more impor- 
 tant to the teacher than to the artist, and it is hoped 
 that the average art student may find the simpler prob- 
 lems suited to his capacity and his needs, aiul that those 
 not interested in the scientific discussions will study the 
 parts intended for them. 
 
 The teacher may feel inclined to criticise the way in 
 which the free-hand part of the subject is presented. He 
 may desire a rule as to which line to draw first, which 
 second, etc. He may not wish to cultivate his feeling to 
 such an extent as to cast aside conventional methods of 
 working. He may upon consideration acknowledge the 
 methods advised to be more artistic, but he may say 
 that they are harder to teach. There is no question but 
 that artistic feeling and correct taste are difficult to 
 obtain, but surely this is no reason why we should not
 
 viii PR El- ACE. 
 
 cultivate the small amount of taste which the students 
 may possess, no reason for choosing conventional and 
 mechanical methods which must destroy artistic feeling. 
 
 An artistic method is difficult to teach to students who 
 have been taught an inartistic one, and the change will 
 involve a struggle on the part of both pupil and teacher ; 
 but 1 do not admit that it is more difficult to start right 
 than to start wrong, and the objections of those who 
 have to change old methods will last only as long as 
 they refuse to change. I believe that the easiest and the 
 best time to train the eye to see is in the beginning, 
 when the mind has not been so developed as to perform 
 nearly all the duties of the eye. If there were any way 
 by which less knowledge of the things seen could be 
 awakened, it would be unnecessary for the student to 
 spend many years of severe labor to enable himself to 
 see, and not to reason the appearance of Nature ; but 
 until the training of the mind to accept the story of the 
 eye is made as complete as, and begins with, the training 
 of the mind concerning facts, the art student will in 
 truth find that " Art is long." 
 
 There is no good reason for postponing this training 
 until the student decides to make Art his profession, and 
 when it is realized that the teacher in charge of art edu- 
 cation in the public schools has a most important posi- 
 tion, the first step in advance will have been made. 
 Ability to talk well and intelligently of general matters,
 
 PREFACE. ix 
 
 and even of art as presented by various writers, does not 
 constitute this special fitness ; neither does the ability to 
 draw pretty things upon the blackboard, nor to explain 
 the course as arranged in a set of text- books ; and even 
 the faculty of planning and carrying out a course so as 
 to produce an interesting exhibition of drawings, fancy 
 work, manual training, etc., is not enough. All these 
 things are important, but of greater importance is per- 
 sonal artistic feeling and practical ability in art, involving 
 more study than most who are teaching in the public 
 schools have been able to give. Without this training, 
 which alone can enable one to justly realize the end of 
 his teaching and thus to work from the first for this end, 
 the instruction given must be unnecessary, mechanical, 
 illogical, and harmful. 
 
 I do not wish to disparage the valuable results which 
 have been accomplished, nor to criticise the teachers 
 who have worked so faithfully in this field. I wish sim- 
 ply to encourage those now in the work to look for its 
 artistic qualities as much as possible, and to advise those 
 intending to take up the study to obtain good art training, 
 and not to accept as a good reason for proceeding in a 
 certain way the fact that all authorities of the past have 
 done thus. The influence of the honest impressionist 
 is being felt. We are beginning to use our own eyes 
 instead of those of other people, who in like manner have 
 depended upon others, and the time is at hand when in
 
 PREFACE. 
 
 spite of the present ridicule of" those who have never 
 learned to see, the honest student of appearances will be 
 appreciated, and those who ridicule will be forced to 
 study or to step into the background.
 
 CHAPTER I. 
 TRAINING OF THE ART STUDENT. 
 
 MUCH has been said and written concerning this sub- 
 ject, but there seems to be no more unanimity of opinion 
 than in the past. I should hesitate to say anything upon 
 this point, if the subject of art instruction could be con- 
 sidered in part ; but this is impossible. The influence of 
 the higher art instruction is felt through all the earliest 
 attempts in this direction, and the matter of art instruc- 
 tion in the public schools is in its present chaotic con- 
 dition largely through the contradictory teachings of 
 many advanced art schools. 
 
 I am aware that my opinions are very different from 
 those of some who have established reputations as writers 
 and teachers, but I also know that others will agree with 
 me. The variety of opinions upon this subject is due to 
 the different individualities and to the lines of training 
 pursued. The average person changes faith in religion, 
 Art, or any subject long considered very rarely. Preju- 
 dice and unquestioning faith in the doctrines in which
 
 2 FREE-HAND DRAWING. 
 
 we have been educated prevent even consideration of 
 the opinions of other people. 
 
 The ability to think and act independently is possessed 
 by the few who lead. Thus it is that we recognize in the 
 work of an artist the technique of the teacher withwhom 
 he has studied, and find him frequently unable to see 
 merit except in his favorite school ; and some are unable 
 to separate the result from the way by which it was pro- 
 duced, the method being of greater importance than the 
 result. 
 
 The tendency in this direction increases as the ability 
 decreases, and is strongest among those who direct art 
 instruction in the public schools. This is the result of 
 teachers, who have given great attention to the best 
 methods of teaching the ordinary branches, attempting 
 to teach art when they know nothing of it, and naturally 
 arises from the necessity which exists in most places for 
 the regular teachers giving the lessons in drawing. I 
 will consider this work by itself, but I wish now to 
 express the impossibility of formulating systematized 
 schemes arbitrarily fixing details of art work, and rules 
 by which it is to be judged as good or bad. 
 
 I have known of teachers who have told their students 
 that all methods but a certain way of working or using a 
 medium were out of date, and that drawings made in 
 these ways were necessarily bad. I have seen the 
 attempt to produce work in accordance with some such
 
 TRAINING OF THE ART STUDENT. 3 
 
 plan result in atrociously bad drawings, which nevertheless 
 were to be admired because done according to the latest 
 and only approved method. Some,, for instance, now say 
 that a charcoal drawing must be made entirely with the 
 point, of the charcoal, and that if the drawing shows any 
 blending, it is not good. Such a statement results only 
 from the ignorance which looks at the paper and char- 
 coal instead of for the effect or the impression the draw- 
 ing is intended to convey. 
 
 The problem for the art student to master is drawing, 
 it is drawing whether he uses the pencil in an outline 
 sketch, the charcoal in a shaded sketch, or the brush 
 and color. Though new colors may be discovered, the 
 problem is practically what it has been for hundreds of 
 years, during which time almost all ways and means of 
 producing a drawing have been tried and used success- 
 fully by those who have practised art. The strong artists 
 of the past did not confine themselves to one medium or 
 to one way of using it. They worked with pencil, crayon, 
 pen and ink, chalk, water color, oil, and other mediums, 
 apparently often using that which was handiest. Their 
 aim was not the way of using the medium, but jhe ex- 
 pression of an idea, and this must be the only end worthy , 
 ofjhe best effort of the artist. 
 
 Too much importance is laid on technique and the way 
 the story is told. It is even said that in looking at a 
 picture, we should first see how it is painted, as if the
 
 4 FREE-HAND DRAIVIXG. 
 
 kind of canvas, the thickness or thinness of the paint, and 
 how it is applied, concerns the public. As well might we 
 say that we must analyze the peach to decide whether or 
 no we like its flavor ; or formulate a theory of color to 
 decide if the color of its skin is agreeable ; or analyze 
 the sentences of an orator before we can permit ourselves 
 to be moved by his eloquence. The question of tech- 
 nique should be accorded the importance which it 
 deserves, and it deserves very little. If a picture tells its 
 story well, and is pleasing in color and sentiment, it must 
 be good whether painted with much labor or quickly. 
 whether the paint is thick or thin, rough or smooth^ 
 When the public realizes that it is not methods but results 
 which constitute art, a great advance will have been 
 made. 
 
 The question of how the picture is painted should con- 
 cern only the artist and the advanced student, for they 
 are interested in its practical construction as a builder is 
 interested in that of the houses which he sees. 
 
 To the student, a study of the ways in which other 
 painters have secured results serves as a guide and cor- 
 rective. But it is important to observe that strong painters 
 work in many different ways, and pictures even by tin- 
 same artist are entirely different in their handling. Study 
 of the technique of others \yill soon convince the student_ 
 that there is morethan one way to paint. 
 
 The artist should understand all the details of his work
 
 TRAIXIXG OF THE ART STUD EXT. 5 
 
 as fully as the workman in any of the industrial arts un- 
 derstands the use of his tools, but to produce the best 
 work he must express his own personality. 
 
 Undoubtedly the first requisite for the student is to be 
 able to represent Nature truly, and this is a point beyond 
 which very few can expect to pass ; for the poetic tem- 
 perament is rare, and without it the artist can simply 
 study Nature. If possessed of this temperament, he must 
 still be able to represent Nature as she appears, in order 
 to exercise his higher faculties in the painting of com- 
 positions and imaginative subjects. The ability to repre- 
 sent Nature truthfully is the first step for the student, and 
 he should be satisfied to study her seriously until he has 
 attained a high degree of perfection. It is so often said 
 that the aim of art should be not reproduction but ideali- 
 zation, that the student is likely to be deceived, and to 
 attempt to produce the ideal before he can truthfully 
 represent Nature. It cannot be contradicted that the 
 higher is possible only through the lower, and the student 
 must be satisfied to study until he can give easily and 
 truthfully form, color, and values, in short, effects. To 
 produce a great work of art the mind must be given 
 entirely to the result. This cannot be done if the atten- 
 tion is frequently diverted by drawing, light, and shade, 
 and color. Through these the painter should express 
 himself, as unconscious of means as the orator through 
 words.
 
 6 FREE-HAND DRAWING. 
 
 It is not meant that the final aim of the student should 
 
 be the power of photographically delineating Nature, but 
 
 that careful study of drawing, values and color should be 
 
 considered necessary to the advanced and more valuable 
 
 work where the artist is free to express his feeling. 
 
 ff Reproduction is impossible. We cannot " paint " even 
 
 // the simplest object. We can only paint what may create 
 
 ,/ a more or less truthful impression of it. Many of Nature's 
 
 ff effects are far beyond the possibilities of the palette, and 
 
 /f art must be acknowledged to be not reproduction. The 
 
 ^ artist is thus justified in using whatever means may best 
 
 H answer his purpose of creating an impression of the ideas 
 
 /, Nature creates in him, and in his highest work it is a 
 
 1 1 question not only of what he sees, but of what he feels. 
 
 The common sfeps in the work of the art student are 
 
 i st. Drawing in outline from Nature and sometimes 
 from flat copy. 
 
 2d. Light and shade in charcoal from casts, the antique 
 and still life. 
 
 3d. Study from life in charcoal. 
 
 4th. Color study from still life, life and Nature. 
 
 There is no question but that the color sense is the most 
 difficult to cultivate, and is very rare at the present time. 
 The deficiency in color perception is probably due to 
 lack of training in this direction. If the education of the 
 color sense were begun earlier, undoubtedly much good
 
 TRAIXIXG OF THE ART STUDEXT. 7 
 
 would result, and it may be true, as some have suggested, 
 that if the first instruction were in the use of color, far 
 greater progress would be made. 
 
 The great difficulty is that before art instruction is 
 given, the students have obtained a very practical knowl- 
 edge of both the actual form and its absolute color. The 
 knowledge of the form prevents the acceptance of its 
 appearance, and the mind is trained to accept the image 
 of the eye only after long-continued efforts. The form 
 is absolute, and if the efforts are continued, almost any 
 one can learn to draw fairly well. The color of the 
 object is absolute, and the mind knows this color as well 
 as the absolute form ; but the color appears to change 
 in a much greater degree than the form. The form 
 appears to change according to certain fixed and simple 
 laws, but the color changes according to no laws that can 
 be given ; for the same local color may appear an infinite 
 number of different colors according to light and sur- 
 roundings, and it is far more difficult to prove that a yellow 
 appears blue or green or some color not yellow to a 
 student who cannot see it, than it is to prove that a hori- 
 zontal line below the eye appears to incline upward as it 
 retreats. 
 
 The tendency of the student who knows theories of 
 anatomy, or perspective, or color is too frequently to work 
 by theory instead of by observation, and it is a question 
 if in many cases he would not be better off without a care-
 
 S FREF.-HAXD DRAWIXG. 
 
 fully arranged theory for all conditions. Certainly this is 
 so unless he can be made to realize that theory should 
 come last and careful study of Nature first. 
 
 Though color is so difficult to realize, it is more impor- 
 tant to the artist than any other quality. We see color first. 
 \\'e may not realize the appearance of the color, but we 
 recognize the mass by the color, which is familiar to us 
 through previous observation. Form may be almost 
 obliterated by distance or other conditions, but the color 
 is seen, and through it we know the object. The masses 
 of light and shade are second in importance ; if these are 
 correct, the effect of Nature is given even if the drawing 
 of detail is faulty. This reverses the order in which these 
 factors are often arranged, and according to which draw- 
 ings are criticised. 
 
 Most instruction in drawing has for its end form. It 
 may be that it is of no use to look for color, as some 
 claim, that the student himself will acquire the color 
 sense ; but this certainly is not true of values (the rela- 
 tions of the masses of light and dark) which are more 
 necessary to the effect of a picture than absolute form. 
 That students do not appreciate the masses, or the effect 
 of Nature, is proven by the numbers of pictures which 
 are so cut up by exaggerated detail that the effect can- 
 not be realized at a proper distance. This criticism, 
 more frequently than any other, may be made of the pic- 
 tures in our exhibitions. The fault is due in part to the
 
 7'fiAAYAVG OF THE ART STUDENT. 9 
 
 search for form to the exclusion of other qualities, and it 
 seems that the latter which are of so great importance 
 should receive more attention, even if the elaboration of 
 outline and detail at present attained, is not secured. 
 
 The training of the art student should be more liberal. 
 Instead of continually working in one medium, as char- 
 coal or crayon, and upon drawings of the same size, he 
 should change the medium or its treatment, and the size 
 of the drawing ; and instead of always working for form, 
 it is most important that he look for effect at least part of 
 the time. 
 
 1 )ra\ving an object or a figure by itself without refer- 
 ence to its surroundings is very good practice in drawing, 
 but this practice alone cannot prepare the student to 
 paint a picture, in which there must be atmosphere, more 
 or less of distance, and in which the proper relations of 
 the parts to each other must be kept. Moreover, this 
 work does not tend to give the student an idea of the 
 simplicity of the masses. It is practice largely in draw- 
 ing. If instead of representing the figure by dark upon 
 a white surface, the effect of the figure against the back- 
 ground is studied and the background is represented of 
 its proper value, the conventional character of the drawing 
 at once disappears. The result is a picture instead of a 
 drawing. The student is painting with charcoal instead 
 of with color, and is becoming familiar with the problems 
 he must meet in his later work.
 
 10 FREE-HAXD DR A IV IXC,. 
 
 When he is not likely to have a long course of study, I 
 should advise that drawing and values be considered in 
 this way in most if not all of his work. If the drawing is 
 from life, very little time is required to indicate the back- 
 ground of its proper value ; and in drawing from still life 
 there is no excuse for not making a study of effects. 
 This way is of much more value than that which permits 
 the student in beginning to think of only one thing at a 
 time. When he has formed this habit, it is almost impos- 
 sible to break away so as to consider the parts with refer- 
 ence to the whole, and he can certainly never look at 
 Nature as he should until he is able to see the masses 
 and effects. The masses are of the greatest importance, 
 and when our students start by observing them, one of 
 the chief difficulties now in their way when they leave the 
 schools will be removed. 
 
 The advanced student may sometimes study with ad- 
 vantage form or local values^ without a background. If 
 his first study has enabled him to see relative values, he 
 may not need farther study in this direction as much as 
 special study, for instance of the figure. In the public 
 schools, evening drawing schools, industrial schools, and 
 all elementary and preparatory schools, values shouLl be 
 considered as important as form, and all work should 
 represent the object and its background. 
 
 Another fact which does much to continue bad meth- 
 ods of work is that many art students, even in advanced
 
 TRAINING OF THE ART STUDENT. 11 
 
 schools, are either advised or permitted to work from the 
 part to the whole. Thus in a figure we find them paint- 
 ing the first day the head, the second, the shoulders, and 
 so on, getting on the last day to the feet or possibly not 
 as far as this, the canvas being covered part by part. By 
 such work it is not possible to obtain a harmonious whole. 
 In the first place, it is impossible to determine the effect 
 until the entire canvas is covered ; second, the light and 
 color are constantly changing, the effect being warm the 
 first day, cool the second, and so on. Such a way of 
 working does not consider the effect, and it is a wonder 
 that students trained thus produce as good work as they 
 do. 
 
 The endeavor of the artist should be to produce a 
 pleasing effect of color, light and shade, and true values, 
 in short, a satisfactory result. Why should not the train- 
 ing of the student look to these points? If it is to do 
 this, the student must try to express the effect as quickly 
 as possible, so that he may be able to change and bring 
 all the detail into its proper relations. All parts of the 
 drawing should be begun at once, and should be carried 
 along together. It is of little importance how the student 
 works, so long as he has as his aim the quickest possible 
 suggestion of the whole effect. He may draw with char- 
 coal or with the brush, or he may make no preliminary 
 drawing, as some recommend, but he must get the can- 
 vas covered and the masses placed in a short space of
 
 12 FREE-HAND DRAU'IXG. 
 
 time, and in doing this he is working upon the most 
 important part of the drawing all the time, until the effect 
 is fairly obtained. 
 
 First Study. 
 
 How shall the student who is commencing the study 
 of art best spend his time ? What shall he draw and 
 what mediums shall he use? As has been stated, no one 
 method should be permanently adopted to the exclusion 
 of all others. There is value in all, and in his later work 
 he may find it necessary to use many different means of 
 expression. If we accept as well founded the practice of 
 the schools, we shall postpone color, and begin with the 
 pencil or charcoal, making outline or shaded drawings 
 from casts or from geometric objects. In some cases, 
 students begin by copying from the flat. Some benefit 
 may be derived from this work, but it cannot be recom- 
 mended. 
 
 The simplest drawing made from Nature is of more 
 value than the most elaborate copy. 
 
 Copying of outlines cannot assist one to see the pro- 
 portions for original drawings. Copying in other medi- 
 ums can only assist in the matter of technique, and this 
 should not concern the student at first. His problem is 
 drawing, and the medium which allows him to think of 
 the drawing, and does not require thought about its
 
 TKAJ.V/.VG OF THE ART STUDENT. 13 
 
 handling, is the best for him to use until he can draw 
 fairly well. The pencil or charcoal in outline work, and 
 charcoal in light jind shade, are means which enable him_ 
 to give his entire thought to the drawing, and they should^ 
 be used until form has been mastered. 
 
 He may work from the cast or from geometric objects. 
 The geometric solids can be obtained in complete sets, 
 exactly made and embodying all the type forms. 1 My 
 experience has led me to believe that study from these 
 objects for a few weeks will give greater ability in draw- 
 ing than a similar amount of time spent in any other way. 
 The lines of a cast or a figure are very fine, and it is 
 more difficult to see them correctly than those of the geo- 
 metric forms, in which foreshortening and convergence 
 are illustrated in the simplest way. An untrained eye 
 can see the errors of drawing much more easily in a cube 
 or plinth than in the more difficult cast. Moreover, the 
 means for testing the appearance of the geometric forms 
 are so simple that a child can apply them, and discover 
 the errors of his drawing ; and when several objects are 
 arranged together, every point is seen in relation to so 
 many other points that this relation cannot be neglected. 
 Thus the drawing involves so many problems that the 
 training it gives is most valuable. 
 
 This work will also give a practical knowledge of per- 
 
 1 They may be obtained of art dealers, also a set of vase forms, 
 copied from the ancient Greek.
 
 14 FREE-HAND DRAWIXG. 
 
 spective, which will be of great value to the student in 
 all his later work. These subjects seem best for many 
 reasons, but the strongest one is that the use of the 
 thread to cover the various edges and continue them to 
 intersect the opposite edges of the group (see page 74), 
 provides a test so simple that all can apply it, and so 
 sure that it discovers at once all serious errors in the 
 drawing. It makes the student his own teacher, and if 
 he carries on the drawing properly, uses first his eyes, 
 then tests and changes without erasing but by drawing 
 new lines, he will quickly attain ability which will enable 
 him to draw with freedom from any subject. 
 
 Frequently the student is first required to draw in 
 outline. Sometimes this may be necessary ; but as cor- 
 rect values are second in importance to color, and out- 
 lines are of least importance, it seems that when possible 
 he should combine the study of form and _values in a 
 light and shade drawing. If at first the attention is to 
 be given to one medium for any length of time, charcoal 
 in light and shade is preferable to outline work, but the 
 best way is an alternation of light and shade with outline, 
 as explained on page 22. 
 
 Light and Shade. 
 
 In order for the drawing to be a complete study of 
 values, the subject must be represented with its back- 
 ground. It is not meant that when a group is seen
 
 TRAINING OF THE ART STUDENT. 15 
 
 against other objects, all of these must be carefully 
 drawn, but that the general value of the background as 
 compared with the group should be given. It is well at 
 first to place the objects so that they are seen against 
 simple backgrounds, as a sheet of gray paper or any 
 flat colored material. The group should have a strong 
 light coming preferably from the left and from above. 
 When drawing from the models, which are white, some 
 dark object should always be placed in the group. If 
 this is not done, the student will make the shades too 
 strong, for by contrast with the lights the shades seem 
 very dark when the objects are strongly lighted. 
 The drawing may be made as follows : 
 The size and position of the drawing should first be 
 determined by suggesting with light and rapid strokes the 
 general effect of the mass of the group. This amounts 
 to drawing the rough outline of the group seen as one 
 object, as shown by Figs. 5 and 8. This drawing, as all^ /* /ty " 
 should be made by the eye unaided by tests or measure- ' 
 ments_ (page 35). When made, it may be tested by 
 measuring the apparent width and height of the group 
 with the pencil, as explained on page 68. Within these 
 lines the inner lines and the masjes of light and dark 
 should next be suggested^ the drawing and the light and^ 
 shade progressing at the same time. The tendency is 
 to draw the outlines and then put in the shade, but it is 
 better to allow the light and shade to help in the draw-
 
 16 FKEE-HA\ 7 D DRAU'IXG. 
 
 ing, for the masses of light and dark are more easily seen 
 than the edges, which are often almost invisible in the 
 light or lost in the shade. Then the cast shadows are 
 very important, and of these the outline drawing takes 
 no account. There is no preconceived idea concerning 
 the shapes of the cast shadows, and thus the mind is in 
 a condition to accept without prejudice the image of the 
 eye, and the student will find that the shade and shadow 
 together form masses of dark, which are more easily seen 
 and placed than any other features. These masses being 
 indicated of one value, it is easy to strengthen the darker 
 part and thus bring out the separation or edge, whose 
 direction is often placed much more truly by referring it 
 to the shadow, than it would be by drawing first the out- 
 lines and then the shadows. 
 
 The masses of dark should be lightly indicated at first, 
 in order that they may be moved about until they arc 
 rightly placed. Whatever lines may be drawn as repre- 
 sentations of edges should be very lightly sketched, for 
 the same reason. It is much better to change by draw_-_ 
 ing a new line slightly stronger than the first, and to tlms_ 
 continue until the correct position is secured, than to_ 
 draw a line and erase as soon as it is found incorrect^ 
 Although the student may not see the importance of 
 working in this way, too much stress cannot be placed 
 on the value of the training obtained by bringing _the_ 
 drawing into place without erasing.
 
 TRAINING OF THE ART STUDENT. 17 
 
 Figure i gives the appearance of the sketch when the /z. _J__ 
 drawing is found to be correct. The charcoal may now 
 be removed from the lights by chamois skin, cloth, 
 bread, or any kind of eraser, and the background may 
 be carried as far as is necessary This gives the second 
 stage of the drawing, Fig. 2. For some time it will be 
 well not to attempt more than the jvaluesjof the back- 
 ground, the light (represented by a light tint of char- 
 coal), the shade, and the cast shadow, as in Fig. 2. 
 
 The shades and cast shadows together^ form dark 
 masses which are opposed to the masses of light made 
 by the surfaces which receive the direct rays of light ; 
 and the drawing, Fig. 2, must not be regarded as simply 
 a stage, but as expressing a most important fact which is 
 to be kept in mind in all the later work. 
 
 Many students have great difficulty in seeing the 
 variety of light and shade in Nature, and nearly all make 
 very serious errors. A common trouble is the failure to 
 realize the difference between the shades and shadows 
 on different colored objects. Thus the shade side of a 
 white cube is made as dark as that of a red or blue box, 
 and unimportant detail in the mass of either the light or 
 the shade is made so strong as to entirely destroy all the 
 effect, the grays in the light being as strong as the shade, 
 and the reflected lights as strong as the high lights. 
 Such errors will be made by all until the ability to look 
 at the whole and not at a part is secured.
 
 18 FREE-HAXD DRAll'IXG. 
 
 The effect can be realized only when the entire group 
 is seen at a glance, and to do this the vision must be 
 blurred until all parts are seen equally and necessarily 
 indistinctly. This effect may be obtained with the ryes 
 in focus for a shorter or longer distance than that of 
 the group, and is the same as that given by looking 
 through a lens of twelve or fifteen inches focus. Open- 
 ing the eyes is better than nearly closing them, for this 
 cuts off most of the light and loses the color. In light 
 and shade this is a matter of not much consequence, but 
 it is better to study in light and shade so as not to be 
 obliged to change for advanced work. 
 
 The struggle comes in seeing for the first time. A 
 lens of twelve inches focus has been of great assistance 
 to many. By its aid they have been enabled to see the 
 masses and to realize their errors when no amount of 
 explanation or assertion on the part of the teacher has 
 been of the least value. Some recommend the reducing 
 glass or a Claude Lorraine mirror, but the blur glass is 
 the only means that I have been able to use with any 
 degree of success. After the student has once appre- 
 ciated the masses, and has seen how unimportant is the 
 detail in these masses, he will need no artificial help. A 
 little practice will enable him to see the entire group 
 without special effort ; in fact, to see naturally the group 
 as a whole, and it must not be forgotten that this is the 
 only way to see effects.
 
 TRAINING Of THE ART STUDENT. 19 
 
 When a number of drawings which give simply the 
 masses of light and dark, as Fig. 2, have been made, the /* - / 
 student should try to get all the values, being careful that 
 the grays and detail in the lights, and the reflected lights 
 in the shade, are not made too prominent. He should 
 understand that the first drawings made express the most 
 important truth, that with strong light there is always the 
 contrast of well defined masses of light and dark. The 
 tendency is to look upon the drawing, Fig. 2, as simply a 
 stage, and to study the detail, which can always be found 
 upon close examination, so carefully as to lose all general 
 effect. There is always a tendency to exaggerate the 
 slight differences, which appear greater than they really 
 are, and the student must struggle to keep the drawing 
 simple. Frequent comparison from a distance, of the 
 Jrau'ing with the group is necessary, the drawing being 
 placed beside the group. If the two are thus compared, 
 the effect being realized by use of the blur glass if the 
 student has not yet learned to use his eyes, it is thought 
 that if he works earnestly, he will in a short time be able 
 to produce fairly truthful representations of the effect. 
 
 Figure 3 represents the group already studied with all ' f 7/ 
 the gradations. It will be noticed that there is always 
 some point in the group that is lighter than any other, as 
 the high light on a white vase or sphere. These points 
 should be carefully considered, and it is evident that the 
 rest of the masses of light must be slightly gray. There
 
 20 FKEE-HAXD DRAH'IXG. 
 
 is also in every group some spot that appears darker 
 than any other. All the other darks must be compared 
 with this, and to be sure of truth with each other, as 
 must also the grays in the light. 
 
 The tendency is to make the drawing too black. This 
 may be avoided by comparing the darks in the group 
 with a large piece of charcoal held in front of them, and 
 shaded by the hand so as to appear black. This makes 
 the darks of the group seem quite gray. 
 
 There is another point of great difficulty, and this is in 
 regard to the colored objects ; for, as already explained, 
 colors do not appear their real colors.. The student who 
 sees a colored object in front of a cast which is grayish 
 white immediately thinks of the actual color of the 
 object in comparison with the actual color of the cast. 
 The color may be darker than the cast. This being so, 
 it is frequently nearly impossible for him to realize that 
 the color, even if quite dark, may be so lightened by 
 direct light, as to appear even lighter than the gray of 
 the cast without a shadow upon it. 
 
 The statement is often made that the surface receiving 
 the most direct rays of light appears lightest. This is 
 not true even for objects of the same color. The high- 
 est lights are the surfaces that reflect the light most 
 directly to the eyes, not those that receive the most 
 direct rays of light. 
 
 The difficulty increases if the colored objects have
 
 TXALVJXG OF THE ART STUDENT. 21 
 
 smooth or polished surfaces, and frequently very dark 
 colors may appear much lighter than the light objects 
 of the group, through their reflecting more light to the 
 eye than the lighter objects. The only safe rule for the 
 student is not to work by theory, or to think how he 
 ought to see the colors, but to look for the actual impres- 
 sion, remembering that this is very likely to contradict 
 what he thinks. After having frequently made his 
 drawing exactly opposite from what it should be, the 
 student should have no difficulty in transferring his 
 dependence upon his ideas to his eyes. When this 
 step has been taken, Nature is before him as an open 
 book, to be studied when he wishes, and it is no longer a 
 question of seeing, but of the best way to do what he feels. 
 A point which must be carefully guarded against in all 
 work is the hardness that comes from definite lines, and 
 sharp separations between the different parts. The e^e 
 sees _but_a point at any one time. This point is seen 
 clearly, all ojjier points indistinctly, so that the effect _of 
 Nature cannot be given by a drawing in which all the 
 edges and separations are brought out by hard lines. In 
 Nature there are no lines. We see objects through con- 
 trasts of color and light and shade, and we do not see 
 sharp definitions between the different colors. Even the 
 straight edges of the models are not seen as sharp lines, 
 the atmosphere and the action of the eye causing them 
 to blur and soften.
 
 22 FKZE-HAND DRAWING. 
 
 The drawing must be definite without being hard. 
 Frequently the outlines^are_ errtij^Jost, This occurs in 
 the shadows or in the mass of the light, and particularly 
 is it true of detail in casts. Generally the outlines dis- 
 appear for a short distance only. The student, knowing 
 the form, is verj^p^josuj)pjyth^misjing^rjia^t, and draw 
 what he does not see, and thus his drawing becomes hard 
 and cut up. If he will study the effect and draw only 
 what he sees, avoiding sharp edges and hard separations, 
 he cannot fail to make a gooddrawing. 
 
 I have described the way in which the student should 
 work to produce the finished light and shade drawing, 
 but do not advise him to spend all his time in this 
 work, for I think great benefit will result from the study 
 of outline simply. It is better from the start for him to 
 give part of this time to pencil outline. I say pencil in 
 preference to charcoal, because erasures should not be 
 made until the correct outline is secured. If charcoal 
 is used, it is impossible to make many changes with- 
 out erasing. With a medium pencil the lines may be 
 given many different positions, the last line being slightly 
 strengthened each time, and the correct result obtained 
 without erasing a line. The training thus given is very 
 valuable. I would have drawings made in this way from 
 the models, until groups of five or six of the most diffi- 
 cult ones can be correctly drawn in an hour or two. In 
 finishing the drawings, the lines should be accented as 
 explained on page 44.
 
 TRAINING OF THE ART STUDENT. 23 
 
 In connection with this work the student will find that 
 the making of quick sketches in a note-book, with a soft 
 pencil, will greatly assist to freedom and accuracy. These 
 sketches may be made complete studies of light and 
 shade and values ; and if one is made each day, beginning 
 with simple objects, he will soon be able to draw freely 
 and well a group of several objects. 
 
 I have said little about tests. He who intends to 
 study art as a profession, or even as an accomplishment, 
 should be able to depend upon his eyes, and should use 
 few tests. The following tests are sufficient : The pencil 
 for measuring proportions, and held in front of lines 
 to give their angles, or held horizontal or vertical for 
 comparisons, and in beginning, the use of the thread, and 
 later, the passing of the pencil point over the lines or the 
 drawing in the air. If he cannot succeed with these, his 
 time will be better spent in other work. Under the head- 
 ing of tests, in the latter part of this book, are given several 
 means for assisting the pupil to apply the tests correctly, 
 but these are intended for public school teachers who 
 have to teach those without special ability, and though 
 such aids may be necessary in these cases, they should 
 not be required by the art student. 
 
 Use of Materials. 
 
 At first, the matter of technique and handling is of no 
 importance to the student, whose only aim should be to
 
 24 FREE-HAND DRAWING. 
 
 obtain good drawing and corrgct values. By this we do 
 not mean that it is of no importance how the student 
 works, for he may work 'in bad ways and with unworthy 
 ends in view. We mean that, having as a result the pro- 
 duction of drawings true in effect, in as direct a manner 
 as possible, he is not likely to waste time over a way of 
 handling which does not tend to this result, for the earnest 
 and honest student is thinking of the effect rather than 
 the execution of the drawing. It is interesting to see 
 clever handling and brilliant execution, and they are to 
 be desired, but the student should not try for them. 
 Cleverness and style will come of themselves in time. If 
 the student tries for these, he may .secure them, but prob- 
 ably at the expense of the substantial qualities which 
 make a strong picture. He should be satisfied to study 
 Nature and work earnestly until a true representation of 
 her is obtained. This drawing is much more valuable, 
 even though the labor spent upon it is evident, than the 
 most clever study which is untrue. Honest study gives 
 the knowledge which in time enables one -to express 
 directly, and thus with an interesting handling. 
 
 Not only does this honest study of Nature and appear- 
 ances produce the most valuable results, but from the 
 start it is most interesting to the student who, each time 
 that he discovers a new fact, experiences the pleasure of 
 an investigator in a new field, and with each new idea, 
 he presses on with renewed. vigor.
 
 TRAINING OF 7^ HE ART STUDENT. 
 
 25 
 
 That this study is interesting to all, even the youngest, 
 is shown by Viollet Le Due, in his most valuable work, 
 " Learning to Draw." His illustration of little Jean's 
 drawing of the cat strikes the keynote of the present 
 tendency in art ; and Jean's replies to his questions may 
 be studied with great profit by 
 many teachers. Especially when 
 in answer to the question, " Do 
 they teach you to draw at school ? " 
 he replies, " No, sir ; they teach us 
 to make only rounds and squares." 
 
 A stick of soft charcoal should 
 be used for all except the careful 
 drawing of the finishing touches. 
 In the first stage the side of the 
 charcoal may be placed upon the 
 paper, and even tints be produced 
 by a regular motion and uniform 
 pressure, each movement making 
 a wide tint, and only a few seconds being required to 
 cover the background or any other large surface. In the 
 later work for the careful drawing, it will be necessary to 
 use a stick of hard charcoal sharpened to a chisel-shaped 
 point. 
 
 Some teachers insist that the drawing shall be made 
 entirely by the use of the point of the charcoal, and 
 allow no softening or blending even by the finger, and 
 
 LITTLE JEAN'S DRAWING.
 
 26 FREE-IIAXD DRAWING. 
 
 even beginners in the public schools are obliged to render 
 light and shade by a hatching of lines as in a lithograph. 
 Adherence to any such rules will cause much loss of time ; 
 for sometimes one way is quickest, and sometimes another, 
 liut to make a light and shade drawing by means of lines 
 is the most difficult and slowest way imaginable, and the 
 student is advised to defer all ways of handling which are 
 difficult and slow, to the time when he may pursue these 
 methods for training simply in their handling, and not as 
 mediums for the study of light and shade. He should 
 work for effects until he can render them truly, and 
 should not allow himself to be trammelled by arbitrary 
 rules or difficult ways of working. He should aim to get 
 good drawing and values in the shortest time, and all 
 means which accomplish this should be legitimate. 
 
 Some teachers advise the use of the stump, the char- 
 coal being rubbed by it to an even tint. The objection 
 to " stumping " is that the pupils seem to think that 
 smoothness is a virtue, and all that is necessary is to move 
 the stump about vigorously, and in some way or other the 
 stump will make the drawing. Such use of the stump not 
 only quickly spoils the paper, but tends to create the 
 idea that the drawing cannot be made directly. The 
 stump may be used with advantage, to place the charcoal 
 in parts too small for the finger, and for lifting the lights, 
 but the tendency to use improperly is so strong that no 
 rubbing with the stump should be allowed.
 
 TRAINING OF THE ART STUDENT. 27 
 
 In order to get atmosphere, it will frequently be neces- 
 sary to fill in the grain of the paper by moving the char- 
 coal about until the depressions of the paper have received 
 a tint. This may be done by very lightly passing the 
 finger over the paper. When the grain of the paper has 
 been filled in this way, the drawing should be finished, as 
 directly as possible, with the point of the charcoal, a tint 
 of the proper strength being placed by careful drawing 
 just where it is wanted. If a small part has been made 
 too dark, it may be lightened by touching with the finger 
 or stump ; a large part, by blowing off the charcoal. The 
 lights may be drawn with an eraser. Faber's eraser 
 made in pencil form is good for this work, and the fine 
 lines of light may be taken out with the hard eraser 
 called "Nigrivorine," which should be cut to a thin edge 
 wide enough to be strong. Bread rolled into the form of 
 a pencil is the best eraser. It will quickly remove almost 
 all the charcoal from a large surface without injury to the 
 texture of the paper. 
 
 \Yhcn the drawing is finished, it must be sprayed with 
 fixatif. This should be applied with great care. If 
 drops are allowed to form on the paper, they will float the 
 charcoal and spoil the drawing. If too much is applied, 
 the drawing will shine and lose its life. It should be 
 applied a little at a time and allowed to dry between the 
 applications. It is well to avoid too much surface char- 
 coal, on account of the difficulty of fixing the drawing
 
 28 FREE-HAND DRAWING. 
 
 without floating it over the paper and thus spoiling the 
 drawing. 
 
 The darkest parts will require more fixatif than the 
 light parts. It can be placed upon these parts by cover- 
 ing the drawing with a paper in which a hole is made of 
 the size of the place needing fixatif. 1 
 
 Having described the ways in which the student may 
 study to obtain facility in drawing, I wish to say that he 
 who can draw and render values in charcoal is ready to 
 work in any medium, and after the first experiments 
 necessary to a new medium, he will do so with success if 
 he understands that whatever the medium, the problem is 
 the same, and is simply and always drawing and values 
 and color. 
 
 There are too many who paint by receipt, but there 
 should be no such thing as a rule or a way of doing, as 
 many seem to think, when they ask how to represent 
 trees, or grass, or drapery, etc. To all who would lie 
 serious, the problem is simply observation ; and since 
 Nature is always different, there can be no receipts for 
 representing her infinite variety. 
 
 Some students seem to think that they are commenc- 
 ing a new subject when taking up a new medium. This 
 
 1 Fixatif may be made by dissolving white shellac in pure alcohol. 
 The alcohol should stand, after the gum has been dissolved. long enough 
 for the impurities to settle at the bottom. The upper part will then l>e 
 of a clear amber color. It may be turned into another bottle, and it too 
 strong, diluted so that a drop will evaporate, leaving just a trace of gum.
 
 TRAINING OF THE ART STUD EXT. 29 
 
 is not so, for the subject is always the same, and the 
 treatment should be the same in striving first for the 
 masses and the effect. 
 
 The most frequent error of all is the attempt to finish a 
 part before the effect is indicated. Much time is spent 
 in carefully drawing and finishing a part, only to find when 
 the rest is in place that it is out of drawing or incorrect 
 in values. The drawing should begin and progress all 
 at once and equally until the desired effect of the masses 
 is attained, when the detail may be studied. The more 
 quickly the white paper or the canvas is covered, the 
 better, and until the values and masses are nearly cor- 
 rect nothing else should be considered. 
 
 There are so many drawings and paintings which are 
 merely conventional pretty things, that the student may 
 have difficulty in realizing that they are not true, and that 
 his work should be serious and honest. It is hoped that 
 soon a higher standard may be placed before the art stu- 
 dent, that he may understand that not all h 
 
 in the drawing, but that values and cojor are equally_and 
 even more important tjian^absolute form, and that he 
 may acquire the power to represent Nature easily and 
 truthfully.
 
 CHAPTER II. 
 OUTLINE DRAWING. 
 
 IT is often said that there are no outlines in Nature. 
 In a way this is true, but it cannot be understood to 
 mean that form is unnecessary or that it may be slighted. 
 The student cannot learn to paint or to make pictures 
 in any medium, without drawing the forms of the objects. 
 The defining of the lights and shades and the various 
 bits of color which are seen in Nature is necessary to 
 give solidity and character to a picture, and it is useless 
 to think that anything can be accomplished with color or 
 light and shade if approximate representations of form 
 cannot be made. 
 
 Every object has definite form and size, and though 
 it may not be outlined, it has boundaries. Although the 
 representation of objects in outline only, is at best a 
 conventional and imperfect means of expression, so far 
 often as even form is concerned, the student can lie 
 taught to observe effects, and may often succeed in con- 
 veying a fair impression of the character of the object, 
 and of varieties of surface and texture. He will find 
 that the study of appearances and their representation, 
 3
 
 OUTLINE DRAWING. 31 
 
 as fully as possible, even in so simple a way as outline 
 drawing, will in great measure prepare the way for work 
 in light and shade and color. The whole question is 
 simply one of seeing, and the student should not trouble 
 himself over technique, as his only aim should be a true 
 representation of Nature. 
 
 The most important points in free-hand drawing are 
 freedom, directness, and accuracy. It is difficult to give 
 directions which will produce these results, as individu- 
 ality will prevent all from working in a uniform way, and 
 handling and technique are of little importance. Since 
 the production of truthful drawings is the end desired, it 
 is of no consequence that such drawings are produced 
 by different persons in different ways, but it may be well 
 to give a few general directions. 
 
 It is most important that the pencil should be held 
 lightly, and the first lines of the drawing suggested freely 
 and rapidly. The paper should be not less than eleven 
 by fifteen inches, and the drawings should be large, as 
 small drawings will produce a mechanical way of work- 
 ing. A long pencil will assist to freedom of motion. It 
 may be held as a stick of charcoal between the thumb 
 and first two fingers, and as far as possible from the 
 point. 
 
 The paper should be fastened upon the board with 
 its edges parallel to those of the board. If the edge of 
 the paper is not straight, a horizontal line may be drawn
 
 32 //.'// HAND I*K.\ \\'ING. 
 
 near its lower edge, so th.ii dhe< li.m-, ma\ ].< referred 
 
 to tin', hue. i; ( -i..ic attempting ti. draw any object. the 
 
 student should ae<|inre the Iteedoin ol motion \vliidi is 
 necessary to ;:>od woik. b\ diawin:; lines in :ill direc 
 tions. ^Curved lines may be produced by 
 
 _ 
 pencil from the wrist, dhow, or BhoilWer;Iand_jti 
 
 ly a motion of the entire arm. These inovements 
 
 should lie |ii;ulised unlil lines (.in In- diawn instantlv 
 
 the |u|iei in .m\ din-etion. This frc-e motion is 
 
 most important for all sketohin: . l'ia_in fun hm^ or 
 
 accenting .1 dr.iwing, whose |>ro|><rtions h.ive lu-en 
 thus -.keldied, more |ii(->snre will be re<|iiii cd. and the 
 I'eiu il m.i\ lie held more linnlv :md ne.irer the point. 
 
 The lirsl snlije. Is in. iv lie the -eometrie solids, or :mv 
 common ol.jeets. I will e\|l.im the wav in which 
 Ihe-.e in. iv be studied, lyv in.ikini; a sket< h ol a l>o\ with 
 OVei thiown luck. (See l''i;;. ,|.) k / jU 4~~ 
 
 I ii-.l, ne.ulv ( lo-.e the eves and try to see the box, not 
 
 ..lid. but as a silhouette, the outline of the mass ol 
 
 the box against the lueki;ronnd hem:; what should lirst be 
 
 ( aieliillv studied. A little piaetiee with the e\ es neailv 
 
 < lo-.ed will enable one to see the mass in this wav. ( 1 '; 
 
 In order to leah/e the directions wliieh the ., 
 appear to ha\e. lines max be diawn in the air. bv nun - 
 in:; tlu- pen. al point so thai it appeal-- to eo\er the > 
 \\hen this is done, care should be taken not to move the 
 pen. il awa\ lioin the eyCS, that is. in the a. In al diree
 
 OUTI.IXK DRAWING. 33 
 
 tion of the edges, but to keep the pencil point where it 
 would be if it were held upon a pane of glass plared 
 directly in front of the student. This test is the mo^t 
 valuable of all, because it is the simplest and easiest to 
 apply. It is really the same as the use of the thread, 
 explained on page 74, and nearly all other means of 
 testing will at last be discarded in favor of this first and 
 simplest. 
 
 After careful study of the mass, its outline may be 
 lightly sketched, no measurements of proportion having 
 bern made. 1 The aim is to train the eye to see cor- 
 rectly. In order to do this, the student must depend 
 upon his eye, and put down its first impression, rather 
 than the results of mechanical tests of proportions. He 
 must first draw, and then test by measuring. 
 
 When the^ outline of the mass has been sketched^ the 
 inner lines may be drawn, and the result carefully studied 
 to see that it agrees with the appearance. When it is jis 
 near as can be seen, the drawing may be tested by meas- 
 uring the proportions as explained on page 68. If_the 
 sketch doesnpt agree with these tests, it must be 
 changed. All changes should be made, not by erasing, 
 but by drawing new lines, and the drawing should be^ 
 carried on in this way, untiTthe correct lines are foumi._ 
 
 The first lines must be very light. As changes are 
 made, the strength may be increased to distinguish them, 
 until the correct line is secured. The drawing having 
 
 1 These lines are approximate, and little time should be given them. See 
 page 15.
 
 34 FREE-HAND DRAWING. 
 
 been changed to agree with the measurements of the 
 whole height and width, and tested by moving the pencil 
 point to cover the edges, it will be well to test, by means 
 of vertical and horizontal lines, taken through the differ- 
 ent angles of the box. Thus, drop the pencil point verti- 
 cally from point i, and see where it cuts the lower edge, 
 and carry the point horizontally from point 2, and note 
 its intersection with the front edge. The pencil may now 
 be made to continue the apparent directions of the 
 edges A, B, C, etc., until the points where the continued 
 lines appear to intersect the opposite outlines are noted. 
 These tests may also be applied by the pencil used as a 
 straight edge and held horizontal and vertical, and to 
 appear to coincide with lines. These tests, if carefully 
 made, will produce a drawing which is practically true, 
 and should be depended upon. The first measurements 
 of height and width should be very carefully taken. 
 Distances which are nearly equal, as EF and FG, may 
 also be compared, but as a rule, few measurements of 
 proportion should be made, as short distances, or short 
 with long distances, cannot be compared with sufficient 
 accuracy to be of any value. (Fig. 6.) 
 
 The thread may be used instead of the pencil for tests, 
 as explained on page 74. The thread appears a fine 
 line, whose intersections with the edges may be easily 
 placed, so that until the eye can be depended upon the 
 thread is preferable to the pencil.
 
 OUTLINE DRAWING. 35 
 
 It is most important that all changes be maclq not by 
 erasing, but by drawing new lines. Erasing and keeping 
 but one line from first to last will surely produce a hard 
 and inaccurate drawing ; and although it may finally__be_ 
 made to agree with all the tests, it will still be la 
 
 .snjrit.. It is difficult at first for most students to draw 
 lightly enough to secure the correct lines without too 
 great heaviness, but it is better, rather than to erase, to 
 throw the drawing away and start anew until the result 
 can be secured without having lines so black that they 
 cannot be easily erased. 
 
 The reason for working in this way is that we wish the 
 student to depend, as far as possible, on his eyes. If he 
 erases and has one line from the start, unnecessary time is 
 given to the drawing, and he will hesitate to erase his lines. 
 If light lines are drawn and not erased, but others drawn 
 as soon as there is doubt about the first being rightly 
 placed, the student is much more free to change as each 
 suggestion occurs, and toward the last he has his choice of 
 the various lines already drawn and can experiment freely. 
 
 This is by far the quickest and most accurate way, and 
 prepares for rapid and truthful sketching. It is difficult 
 at first for the student who has been taught the mechani- 
 cal way of drawing one line at a time, but he will not 
 have to draw very long in this way before he will be 
 able to produce truthful sketches without drawing many 
 unnecessary lines.
 
 36 FREE-HAKD DRAWING. 
 
 There is not much choice of pencils for this part of 
 the work, but it is well to use always as soft a one as the 
 nature of the work will permit. As no pressure should 
 be used, the lead making at first as light a line as can be 
 seen, and as all lines except the correct ones must be 
 erased, there is no reason why the student who has diffi- 
 culty in using a soft pencil should not use a hard one 
 until the drawing is ready to accent. 
 
 When the correct outline has been found, it is neces- 
 sary to finish the drawing. The paper must first be 
 cleaned, all the lines except the last being erased. The 
 easiest way to reserve these lines is to make them 
 stronger than the others so that they will show faintly, 
 when the eraser has been passed over the paper, remov- 
 ing all but an indication of the result. 
 
 The drawing may now be accented with a soft pencil. 
 The pencil may be held more firmly, and the lines drawn 
 of their proper strength by one touch, the attempt being 
 not to produce a fine even line in imitation of a ruled 
 one, but rather a line of medium strength which will con- 
 vey the idea of straight edges. For the present it is 
 better for the lines to be made of uniform strength, with 
 no attempt at gradation, or the frequent conventional 
 accenting of the nearer edges by heavier lines. This 
 point will be considered later, but we wish now to advise 
 the student, if he is already familiar with it, to forget it 
 as quickly as possible, and to finish in lines of one 
 strength or as explained on page 44.
 
 OUTLINE DRAWING. 37 
 
 The student should draw from various objects in dif- 
 ferent positions, until he is able to see them very nearly 
 correctly at first. The time required for this will depend 
 wholly upon the pupil and the care with which directions 
 are followed. 
 
 Groups. 
 
 After the practice from single objects, several should 
 be arranged in a group. The student will probably 
 attempt to draw the objects one at a time, taking first the 
 prism A, Fig. 7, next the vase B, then the cylinder C, 
 and last the frame D. The objection to this way of pro- 
 ceeding is that as the objects are drawn one at a time, 
 until the last is completed, the proportion of the whole 
 group that is, its greatest height in comparison with its 
 greatest width cannot be seen. Indeed, this is often not 
 even considered, the student taking it for granted that 
 since he measured and tested each object as it was 
 drawn, the single objects are correct, and therefore the 
 group. But from what has been said it will be seen that 
 each object is likely to be a little out of proportion ; 
 indeed, we may say is sure to be so. This being the case, 
 the errors are multiplied ; and if the height and width are 
 compared, the proportion is found to be far from correct. 
 It is a principle generally acknowledged that in all teach- 
 ing the whole should be presented before its parts, and it 
 cannot be contradicted that adding one object to another
 
 38 1-KEE-JLL\D DRAWING. 
 
 until finally the patchwork is complete is an uneduca- 
 tional way of proceeding. Practically it is also most 
 unsatisfactory, as with each object the difficulties in- 
 crease, and at last it becomes impossible to place the 
 drawings where they belong. The only logical way is to 
 draw the group all at once, first considering it as a mass 
 and blocking in its proportions by lines passing from the 
 principal points, Fig. 8. When these lines have been 
 drawn and considered, they may be tested by measuring 
 the whole height and width, and the directions tested 
 by use of the thread or pencil as explained. 
 
 A good plan is, as soon as the proportions have been 
 determined, to draw horizontal and vertical lines forming 
 a rectangle enclosing the drawing, and to be careful that 
 the drawing is kept within these lines. The proportions 
 of the whole group being thus determined as nearly as 
 measurements can determine, the objects may now be 
 sketched by eye, the most important lines being drawn 
 first. These are the lines whose positions and directions 
 are most easily seen. They are the longest lines, lines of 
 one object which are nearly continuations of those of 
 some other object, and lines which are brought out dis- 
 tinctly by shade or shadow. It is evident that in this 
 way the drawings of the different objects are proceeding 
 at the same time, and the shorter and less prominent 
 lines being drawn last, the group may be said to be drawn 
 all at once, or as if a single object having many parts.
 
 OUTLINE DRAWIXG. 39 
 
 While drawing, the student must think of the tests, 
 applied by the thread, of horizontal and vertical lines, 
 and of continued lines ; and drawing in the air by passing 
 the pencil point to hide the edges to be represented, will 
 help greatly. The object should be studied in this way 
 and changed as often as found incorrect, until the eye 
 can do no more. It is now time to apply systematically 
 the tests explained by the drawing of the box. 
 
 The first test is to compare the height and width of 
 each object of the group, and also to compare these 
 dimensions with those of the whole group. This test is 
 the most important, and should be very carefully taken. 
 Slight inaccuracy can hardly be avoided, but these dimen- 
 sions are the longest measurements, and can be compared 
 more accurately than any others, especially in the case of 
 those which are nearly equal, and the best that can be 
 done is to make the drawing agree wkh these measure- 
 ments. By this time the student should be able to meas- 
 ure as accurately as these drawings require. 
 
 These tests will generally change the drawing through- 
 out. The changes should be made, not by erasing, but 
 by adding lines, and without other measurements until 
 the eye can see no more to be done. The thread may- 
 then be used, first for the tests of horizontal and vertical 
 lines, second for the continuing of all the edges, and third 
 for covering points in the group opposite one another, 
 that the intersections of these diagonal lines with the
 
 40 FREE-IIAXD DRAWING. 
 
 edges may be noted. The thread used thus will discover 
 every discrepancy except the slight deviations which 
 only the accurate eye can detect. After the training 
 which is given by these drawings made entirely by eye 
 before any tests are applied, this accuracy will soon be 
 secured. 
 
 When the correct lines have been found, the others 
 are to be erased, as explained on page 36, and the draw- 
 ing is to be accented. But now the student will do well 
 to think of effect, and to see if more interest and expres- 
 sion cannot be given to the drawing than is given by uni- 
 form lines. The student has perhaps been taught that 
 the nearest objects are seen most strongly, and that the 
 strength diminishes with the distance. This of course is 
 true in a general way. It is the effect of aerial perspec- 
 tive, or the changing of color by intervening atmosphere. 
 Thus of a row of Hght objects the nearest will appear the 
 lightest and brightest, and of a number of dark objects 
 the nearest will appear the darkest. The light object in 
 the distance appears darker, 1 and the dark one lighter, 
 and in a sketch representing considerable distance this 
 principle will be of assistance. But it must be stated so 
 as not to convey the idea that there can be nothing in 
 the distance as strong or stronger than the unimportant 
 features of the foreground, for we do not see objects 
 more or less distinctly according to their distance ; in fact, 
 
 1 Very light objects may change but little.
 
 OUTLINE DR. I \\~L\G. M 
 
 distance has practically nothing to do with it. We tiistin- 
 gitish objects as masses of color, lighter or darker than tlie 
 L-olo_rs^ against which they arc seen. This being so, it is 
 evident that a light object in the background, as a white 
 house seen against dark foliage, must be much more 
 prominent than a near object, seen against another of the 
 same color. 
 
 In general, when there is little or no contrast of color, 
 objects are difficult to see without regard to their distance. 
 Place a square of white cardboard in front of a larger 
 square of the same, the latter coming in front of the 
 blackboard. The smaller can be seen very faintly. In 
 comparison with the distinctness with which the larger is 
 seen against the blackboard, the smaller is practically 
 invisible. This experiment proves that we distinguish 
 objects through contrasts of color, and we have to con- 
 sider what can be done in outline simply, to render the 
 effect of Nature. Can no more be done than to repre- 
 sent the form by lines of uniform strength ? 
 
 The opinion seems to be general that more can be 
 done. We find that instruction is often given to repre- 
 sent the nearer edges by strong lines, the farther ones by 
 light lines ; in fact, to proportion the strength of the line 
 to the distance of the part it represents. Apply this 
 rule to the representation of the two pieces of cardboard, 
 and the nearer is accented by heavy lines, the farther by 
 light lines. This is a direct contradiction of what we see,
 
 42 FREE-HAND DRA\VL\C,. 
 
 for the outline of the nearer is barely visible, while the 
 farther is distinct against the blackboard. 
 
 In color we certainly should not think of representing 
 the nearer as darker than the farther, or in any other 
 way than as it appears, and the same is true of light and 
 shade. Why should we not do the same when possible, 
 with outline ? No reason to the contrary can be given, 
 for the difference in clearness with which the various 
 lines are seen is the result, not of distance, but of con- 
 trasts of color, and light and shade. Of course we shall 
 expect to find the strongest lines among the nearest ones, 
 but farther than this we cannot go, and if we adopt the 
 conventional accenting recommended by text-books, we 
 are working by rule and not by observation, and the result 
 will be the production of hard, mechanical drawings. 
 
 Character appears in outlines. An object, as a cast, 
 having a smooth, hard surface shows these qualities in 
 its outlines, which will be represented by smooth lines. 
 A cube with smooth faces has sharp, straight edges, which 
 will be represented by straight lines. A box made of 
 rough boards has broken edges, whose character may be 
 given by drawing the irregular outline in which one sur- 
 face breaks into the other. A drawing from the figure 
 can express the variations in the appearance of the cut- 
 lines, parts of which are sharp, other parts blurred by 
 light or a growth of hair. 
 
 Light affects the appearance of the outlines strongly,
 
 OUTIJXR DRAU'lXG. 43 
 
 in some places making them distinct, in other places 
 indistinct. An even line for everything disregards all 
 these variations of effect ; so also does any conventional 
 variation of strength. If the student is allowed to disre- 
 gard effects in outline work, he will have great difficulty 
 in seeing them in later work. There is no more labor 
 involved in representing effects than in disregarding 
 them, for one line is as easy to make as another, observa- 
 tion only being required. The student who can see can 
 perform, and as long as any differences can be found 
 between his drawing and Nature, he can learn to correct 
 the errors. 
 
 The conventional accenting taught in the public schools 
 produces the most mechanical, hard, and unnatural 
 sketches when the student works from Nature, indoors or 
 out. Undirected he would never produce such childish 
 and ridiculous effects, but after his instruction in drawing 
 from the object, where he has learned that lines must be 
 represented with a degree of strength corresponding to 
 their distance, he naturally does not think of observing 
 and drawing what he sees, but simply mechanically 
 grades the strength of line as he has been taught. He 
 makes the heaviest lines of the drawing where there 
 
 should be the faintest indications of lines, and often 
 
 
 
 where no lines at all would be better than faint lines. 
 
 It is almost impossible to get a student from the pub- 
 lic schools to make sketches in which the unimportant
 
 44 FREE-HAXD DRAWING. 
 
 detail, which is no part of the effect, is not brought out 
 with heavy black lines. This is not surprising, for he 
 sees this detail and it is near him, therefore according to 
 his instruction it must be strongly accented. 
 
 In outline, as in other mediums, we should do the best 
 we can to express what is before us. The effect of the 
 subject should be considered as well as its form. There 
 is no reason why the student should not be taught to 
 observe the effect, and if once started rightly he will 
 advance rapidly and will make drawings which, since 
 they are representations of Nature, will have variety of 
 effect, will be true, and artistic. 
 
 No rule can be given other than to study and represent 
 simply what is seen, as far as possible, as it appears. In 
 outline, without any light and shade, it is impossible to 
 always accent the lines just as they appear. For instance, 
 some edges of the object may be so lost in the shade as 
 to be wholly invisible, but without them the drawing 
 might be incomplete and unsatisfactory. A correct 
 impression of the facts must be conveyed. No important 
 line can be omitted even if not seen, but otherwise the 
 lines should be represented as they appear. 
 
 In drawings of the geometric solids, where there are 
 few lines in nature, it will sometimes be impossible to 
 accent the lines as they appear, for some of the most 
 important ones may be invisible, or seen so faintly that 
 to represent them as they appear would make the draw-
 
 OUTLINE DR A \VL\G. 45 
 
 ing give a false impression. Frequently when the objects 
 are strongly lighted their outlines on the light side of the 
 group intersect one another, so that the outline of the 
 mass is composed of parts of those of several objects. 
 This outline is very prominent, while the edges inside 
 the outline are almost lost in the mass of light. It is 
 evident that in this case we cannot accent as we see. 
 We must accent as we feel the group, and when accent- 
 ing as the lines are seen is unsatisfactory, we must use 
 our judgment and make the accenting express the facts 
 in a satisfactory manner. 
 
 When drawing from furniture or from any subject hav- 
 ing many lines, the effect will generally be satisfactory 
 when the lines are accented as they are seen. Here 
 there are so many lines and so many changes in direction 
 that the parts which are not seen will rarely be missed, 
 and the student can represent more nearly what he sees. 
 But it must be understood that it is wholly a matter of 
 feeling for which no rule can be given. 
 
 At first most students will have difficulty in seeing any 
 difference in the way in which the various edges appear. 
 This is due to the fact that but a single point can be 
 clearly seen at any one time. The eye glances rapidly 
 over the whole of an object, carefully observing all its 
 parts. We are unconscious of this motion. All parts of 
 the object are seen distinctly, and the variety of effect is 
 not realized. All the parts will continue to give the
 
 46 FREE-HAND DRAW IXC,. 
 
 impression of equal strength until the ability to see the 
 whole of an object at once has been acquired, as explained 
 on page 18. It is not possible otherwise to see simply, 
 to realize effects and masses, and the student must prac- 
 tise until he can thus see before he thinks of success in 
 any medium, for all demand equally a study of the com- 
 parative strength of detail. 
 
 Although no rule for accenting can be given, the effect 
 is found to conform to the principle that any detail which 
 comes in cither the mass of the light or that of Hie shade 
 if unimportant. Thus an edge defining a light surface 
 against another surface also light is not prominent, and 
 an edge separating a surface in the shade from another 
 shade surface is seen faintly. The important features 
 are those which come between the light and the shade.

 
 CHAPTER III. 
 INTERIORS AND GENERAL WORK. 
 
 ALL drawing, whatever the subject, should be carried 
 on in the same way, first by blocking in the mass of the 
 whole, then the masses of the various parts, the detail 
 coming last but always being carefully studied. 
 
 In drawing from objects having curved lines, the stu- 
 dent should be careful not to be content with the gen- 
 eral effect of the line, but to give the variations from the 
 regular curves found in many objects. Thus in a cast, 
 lines which at first glance seem of uniform curvature will 
 be found to be composed of many short, flat curves. 
 Character will be given only by a study of these flat 
 curves, but the search for straight lines must not lead to 
 the drawing of straight lines where none can be seen, as 
 in an ellipse. 
 
 After the models, common objects as boxes, furniture, 
 etc., may be drawn. These may be arranged in groups 
 and an idea of pleasing composition be given. This 
 work leads directly to the drawing of interiors. No 
 principles other than those explained are involved. In 
 this work, as in all, the aim should be to represent as 
 
 47
 
 48 FREE-HAND DRAIVIXG. 
 
 nearly as possible the actual appearance of everything. 
 We obtain the dimensions of this appearance on a plane 
 which is perpendicular to the direction in which we see 
 the object. Carrying out this principle and extending 
 the subject, we find that the surface which gives the 
 appearance is that of a sphere, which cannot be devel- 
 oped. This, then, is the reason why we cannot always 
 draw just what we see, and it is impossible to make a 
 sketch which shall include an extended range of vision, 
 and give the exact appearance of each part, and a correct 
 impression of the whole (pages 92, 93). 
 
 The space which can be included in a model drawing. 
 and which may be represented on a plane without notice- 
 able distortion, should not include an angle at the eye of 
 over twenty-eight degrees. If this is much exceeded 
 the questions of the curvature of parallel lines for both 
 horizontal and vertical distances will arise, but as most 
 drawings require a larger angle the question must be con- 
 sidered. 
 
 The mind, knowing lines to be straight, will hesitate to 
 accept their representation by curved lines, or knowing 
 them to be vertical, will not readily accept their repre- 
 sentation by inclined lines. The drawing should give 
 the impression of Nature, as far as possible, even when 
 the eye is not at the proper distance. The impression 
 of vertical lines is given by vertical lines, and of straight 
 lines by straight lines. For this reason, it seems best
 
 1XTERIORS AXD GENERAL WORK. 49 
 
 that the student should represent what he sees, as nearly 
 as possible, but in accordance with the perspective prin- 
 ciple that straight lines shall be represented by straight 
 lines. This will cause him to represent horizontal lines 
 which extend on both sides by parallel horizontal lines, 
 and to substitute for the curved lines found in objects at 
 angles with the picture, straight lines extending to two 
 vanishing-points. This will change the drawing very 
 little, as shown on plate 28. 
 
 When the subject is extended or comes very near the 
 draughtsman, causing visual angles of from forty-five to 
 one hundred degrees either horizontally or vertically, it 
 is evident that the difference between the appearance 
 and any drawing made on one plane will be very marked, 
 and so.me parts of the drawing must be quite different 
 from the actual visual angles formed in the eye. This 
 may prevent the drawing from being truthfully blocked 
 in as a whole at first. It can, however, and must in the 
 beginning be placed as a whole approximately. The 
 central part or the most important portion can then be 
 drawn as it appears. The proportions of the outer parts 
 ran be referred to the central, and the distortion, which 
 is inevitable somewhere in an extended subject, be re- 
 duced to the smallest degree by making the perspective 
 of these outer and less important parts agree with that of 
 the central and important mass. 
 
 The different parts of an extended subject cannot be
 
 50 FREE-HAND DRAWLVG. 
 
 measured or compared by the ordinary use of the pencil, 
 for its distance from the eye changes with every new posi- 
 tion. If it is desired to compare the visual proportions, 
 the pencil must be held at one distance from the eye by 
 means of a thread attached to it and held at the brow by 
 the left hand. 
 
 When it becomes necessary to make a perspective 
 drawing throughout, as sometimes happens when three 
 walls of a room are to be shown, the proportions of this 
 drawing may be very exactly found by holding the pencil 
 in a plane parallel to the end of the room. 
 
 This drawing should be avoided when possible on 
 account of the serious distortion of its outer parts, and it 
 will also be well to avoid representing one side of a 
 room which extends far on both sides of the spectator. 
 If one wall is to.be represented, it is better to draw from 
 one end of the room than from the centre, as the lines 
 will vanish and the distortion be less marked. When two 
 walls are represented, the lines of both must vanish. 
 When three are shown, the middle one must have no van- 
 ishing. Figure 9 shows that if its lines vanish, the whole 
 of the left wall will be outside of both vanishing points 
 of the drawing, and thus very unpleasantly distorted. A 
 drawing should never extent beyond ///< vanishing points 
 of its lines. 
 
 A very slight distance may be represented to the left of 
 the left point in Fig. 9, when the drawing represents a
 
 LVTEKIOKS AXD GEXEKAL IVOKK. 51 
 
 court or any interior where the part at the left is a very 
 unimportant portion of the drawing, but it is generally 
 safer to end the drawing at the vanishing point. 
 
 Distortion such as that in P'ig. 9, is seen in photographs 
 taken with a lens of wide angle, and photographs, the 
 most common perspective drawings, exert a strong influ- 
 ence to perpetuate the serious distortions in the drawings 
 of our illustrators and artists. 
 
 In drawings of street scenes, etc., the lines are long and 
 broken, and their apparent curvature may not be noticed 
 if each part is drawn as it appears. In such subjects one 
 does not know the conditions. The lines may be curved 
 in Nature. Hence there is not the instant contradiction 
 between the appearance of the drawing and the knowl- 
 edge concerning the facts of the things represented. If 
 the artist chooses sometimes to represent straight lines by 
 curved lines, he has Nature as authority and the example 
 of noted predecessors, and no one would wish to say that 
 his drawing is not good or that it would be improved by 
 plane perspective. 
 
 In interiors and in street scenes, there is not only the 
 question of horizontal foreshortening to be considered, 
 but also that of vertical foreshortening. Whether or no 
 this foreshortening shall be given is a question which can 
 ' be answered only as it arises, and decided according to 
 the conditions of the subject and the aim of the drawing. 
 It is a question of the less important giving way to the
 
 52 FKKE-IIAXD DR. Ill' IXC,. 
 
 more important, and is for the artist rather than the stu- 
 dent, who should, until he has attained by long practice 
 ability to judge proportions correctly, never be permitted 
 to draw other than those he sees. 
 
 The unnumbered plates following are from students' 
 drawings from Nature. Such work should be the aim of 
 drawing in the public schools, whose pupils, taught to 
 observe and to do what they see, may make a great 
 advance-in this direction. 
 
 The sketches are by students of the perspective cl 
 at the School of Drawing anil Painting of the Museum of 
 Fine Arts, and at the Normal Art School. They illustrate 
 the beginning and the end of a course in model drawing, 
 which is the only perspective necessary to the artist.
 
 CHAPTER IV. 
 DRAWING IN THE PUBLIC SCHOOLS. 
 
 THE value of a course in drawing when the subject is 
 properly presented can hardly be overestimated, but it 
 must be confessed that much of the instruction given is 
 such that its benefit is a matter of doubt. 
 
 At the beginning of his art education, the pupil should 
 be taught to see correctly. When this has been accom- 
 plished, and he is able to represent truly what is before 
 him as it appears, and not as he thinks he sees it, then 
 he is in a position to advance, and his personality may be 
 cultivated. But as the first point to be gained is ability 
 to see truly, it follows that we should from the very start 
 demand truth, truth of outline, truth of light and shade, 
 and truth of color. 
 
 In beginning, I wish to say that drawing in the public 
 schools can never accomplish results of any value until 
 the pupils can observe for themselves ; in other words, 
 until they can draw from objects instead of from draw- 
 ings. This is impossible in many places now because the 
 teachers have not materials. The schools must have 
 models and all necessary materials, or the work will be 
 
 53
 
 54 FREE-1IAXD DRA\\'L\<J. 
 
 simply the copying of drawings in the books, or if these 
 are not used, the copying of theory drawings on the 
 board. In the elementary grades the instruction can be 
 given well enough in the classroom, but the advanced 
 grades should have provided for them a room arranged 
 for the purpose. Drawing cannot be taught without 
 materials any more than manual training can be taught 
 without tools, and a part of the necessary materials can 
 be used in one no more than in the other. 
 
 No committee would expect a boy to use a gouge to do 
 the work of a chisel, or to learn to use his tools without 
 wood, or that a class should get along with tools for one 
 student ; yet the committee or superintendent often ex- 
 pects drawing to be taught without materials, or with ma- 
 terials for part of the class. 
 
 In most public schools attention is now given to draw- 
 ing. In cities this instruction is generally in charge of a 
 special teacher, but this special teacher can do little more 
 than to direct the regular teachers. The subject is com- 
 paratively new, these teachers have had perhaps no regu- 
 lar instruction in drawing, and few have had the liking 
 for the subject necessary to interest them in the work, or 
 to cause them to obtain the knowledge they are expected 
 to impart, and with all the stress of work upon them, it is 
 surprising that they have accomplished as much as has 
 been done in some places. In many cases the special 
 teachers have had but little training, and frequently this
 
 IN THE PUBLIC SCHOOLS. 55 
 
 has been simply in the direction of understanding the 
 course of work laid out in drawing-books, or of studying 
 the '' best methods " instead of acquiring some practical 
 ability in drawing. This has been the inevitable result 
 of the rapid growth of the subject, and years must pass 
 before it will be understood in all its bearings, and before 
 there will be special instructors who have had the training 
 requisite to success. 
 
 The aim of drawing in the public schools should be 
 educational, and not specialistic. The pupils cannot all 
 be artists or designers, or engineers, but all will be bene- 
 fited by a logical course in drawing, and if they have it, 
 discover special talent, which may be developed in the 
 higher schools. The instruction in free-hand drawing can 
 be practical and give to all right ideas, and to almost all 
 ability to sketch from Nature with a degree of freedom 
 and truth. The public school instruction can be such 
 that the student who wishes to study art upon leaving 
 school may do so with a good foundation and nothing to 
 unlearn 
 
 The instruction in pictorial drawing is now the weak- 
 est part of the work in the public schools. It is so be- 
 cause it is neglected, or because bad methods are used. 
 At the present time instruction in drawing in many places 
 is largely instruction in manual training and kindergarten 
 work. Without doubt this i.s valuable, but not as draw- 
 ing, and it should not take the place of drawing. Draw-
 
 56 FREE-HAND DRAWIXG. 
 
 ing should have an hour by itself. Cutting paper, whit- 
 tling paper-knives, sewing pen-wipers, etc., can never give 
 the least ability in drawing ; neither can this work, as 
 many carry it on, give any knowledge of working draw- 
 ings. The making of objects can be of great assistance, 
 anil should naturally go with the study of working draw- 
 ings, but the objects should be made from the drawings 
 which must show all the construction. 
 
 I do not see how the making of objects can be done in 
 school without special time being given to it, and the 
 subject of drawing proper not suffer ; and it seems that 
 as the result in many places of the present agitation in 
 favor of manual training, this subject takes the place of 
 drawing. Many drawing teachers are unconsciously 
 effecting this by placing in their course paper-cutting 
 and the making of objects that have no connection with 
 either the free-hand or the instrumental drawing. 
 
 In many cities drawing-books are used. These books 
 contain examples of historic ornament and design which 
 are to be copied, and also drawings of models and com- 
 mon objects, some of which are to be copied, and others 
 are given as illustrations of possible appearances. 
 
 In many places most if not all of the work in object 
 drawing is thus copying, and so little of actual drawing 
 from the objects is done, that with the objects before 
 them students are found copying the drawing of the 
 student in front, and the drawings of a whole row are
 
 DKAU'LVG L\~ THE PL' BUG SCHOOLS. 57 
 
 alike ; or copying the drawing made upon the board to 
 illustrate the principles. We have even known of cases 
 where the pupil has turned to some text-book, as a geom- 
 etry, in which he has tried to find the appearance of the 
 object before him. Such are the results which come 
 from copying drawings. 
 
 It is easier for the teacher to allow the pupil to copy, 
 but such work is of no value, and the copies, even if 
 neatly done, deserve only censure. The few teachers 
 who have had the courage to dispense with copies deserve 
 praise for showing that drawing can be taught from the 
 objects, and their example should result in a general 
 change from books to Nature. In many places it is pos- 
 sible that nothing could be done in drawing were it not 
 for the books. Rightly used, they may be of assistance, 
 but the pictorial drawing should be by itself in a blank 
 book, and each drawing should be made from the object. 
 
 The change from copying to drawing from the object 
 will require hard work from both pupil and teacher, and 
 at first the drawings will be very unsatisfactory in them- 
 selves ; but after a short time, when the pupils have been 
 started rightly in the lower grades, they will draw readily 
 and with greater freedom, and will be able to draw from 
 Nature, which they never are under the present systems 
 that allow them to copy from a book or the board. 
 
 We have advised that art students draw with charcoal 
 and in light and shade at once. Charcoal is not suited
 
 58 l-'KEE-HAXD DRAWING. 
 
 to public school work, at least not in the lower grades, 
 where it becomes a question of outline in pencil. 
 
 At present it is the aim of most courses in drawing to 
 give a thorough knowledge of the actual form before 
 attempting to represent its appearance. The knowledge 
 of the facts is of course of some assistance to the person 
 who is to represent them. A glance at the object and it 
 is recognized, and the mind supplies the information 
 which it might take the eye some time to discover. But 
 this knowledge is more apt to do harm than good, for 
 the pupil uses it instead of his eyes. For this reason, I 
 should advisv. that the continued and thorough study of 
 facts, now followed by most teachers, be postponed until 
 the pupils have had some practice in representing the 
 facts, or at least that the study of the appearance begin 
 with the study of the facts. 
 
 The facts can be taught perfectly in a very short time, 
 but to attain perfection in their representation is a prob- 
 lem requiring much more study and long continued effort, 
 and for this reason it should be given earlier and more 
 serious attention. 
 
 The study of appearances in the lower grades may 
 begin with plane figures cut from cardboard or paper, as 
 the square, circle, triangle, hexagon, etc. These may be 
 placed horizontal upon the desk and their appearances 
 studied. This involves the use of the pencil in measur- 
 ing, and it must also be held horizontal to assist the pupil
 
 DRAWING LY THE PUBLIC SCHOOLS. 59 
 
 to see the angles of the lines. In beginning, this work 
 may be made easy by placing the card in the centre of 
 the desk, when the lines of the desk serve for horizontal 
 comparison. 
 
 The cards may be of such dimensions that the draw- 
 ings can be made the size of the cards. The measure- 
 ment of height will then be obtained by placing the lower 
 end of the pencil at the nearest point or side of the card, 
 and the thumb-nail to cover tUe farther angle or edge of 
 the card. This gives the exact height of the drawing. 
 It is thought that this use of the pencil in determining 
 proportions will be readily understood. The pencil 
 should of course be about vertical, but to be exact it 
 should tip back slightly. 
 
 When the card has its nearest edge parallel to the 
 desk line, the width of the drawing will be the length of 
 this edge. If the edge is not parallel to the desk, its 
 length will be measured on the pencil by placing the 
 pencil parallel to the edge of the desk and touching the 
 nearest end of the line, whose apparent length will be to 
 the point just under the farther end, or to where a verti- 
 cal pencil covering the farther point will meet the hori- 
 zontal pencil. This way of measuring will give very good 
 results, but before measuring any except the nearest edge, 
 the drawing should be made by the eye alone. 
 
 It will be well to draw the cards at different levels. 
 This may be done by placing them on boxes or books.
 
 60 FREE-HAND DRAWING, 
 
 By holding them horizontal and on the level of the eye, 
 the pupil will see that they all appear horizontal lines, 
 and that their forms are seen only when they are above 
 or below this level. 
 
 I should not attempt to teach much perspective theory. 
 Until the pupils are older, practice alone is what they 
 need. They can see that the apparent heights of the 
 figures decrease as the planes are brought toward the 
 level of the eye, at which all appear lines. They can 
 also discover that parallel retreating edges appear to 
 converge. This may be seen by placing two pencils 
 together, and then separating them until each appears 
 to coincide with an edge. The pencils must of course 
 be held at right angles to the direction in which the 
 object is seen. 
 
 The cards may be held in a vertical position by a small 
 block of wood, to which they may be fastened by a tack. 
 In this position the height will be the greatest dimension, 
 but the proportions will be obtained as before. The 
 positions of the cards being changed for each lesson, in 
 a short time the pupils will learn to use their eyes and 
 will draw the cards fairly well. 
 
 Both horizontal and vertical positions of the cards may 
 be studied in the same lesson by folding a rectangular 
 card so that a right angle is formed, one part being hori- 
 zontal and the other vertical, and held at right angles by 
 being tacked to a small piece of wood. Other forms 
 may be studied in the same way.
 
 DRAW IX G IN THE PUBLIC SCHOOLS. 61 
 
 When able to draw the cards from the position directly 
 in front, the next step is to draw them when at the right 
 or left. To do this, each pupil may draw from a card 
 placed near the corner of his desk or on the desk at his 
 side. This is much more difficult than to draw from the 
 card placed on the centre of his own desk. The ten- 
 dency will be to think of the line of the desk as appear- 
 ing horizontal, when in this case it appears to vanish. 
 For this work the pupil must learn to hold the pencil 
 horizontal, and at right angles to the direction in which 
 he sees the card. As this position of the card involves, 
 beside this difficult test, the comparison of height ami 
 width on the pencil, it may be found necessary to post- 
 pone the work until the pupil has had practice in draw- 
 ing from objects placed in front of him. It will be well 
 to advance the work as rapidly as possible. The teacher 
 should have little trouble in showing that the work is nec- 
 essary and the beginning of pictorial drawing, and if 
 properly presented, the pupils will be interested. The 
 more the drawing seems in itself a picture and not a dia- 
 gram, the more interested will they be. 
 
 A simple preparation for the subject of model drawing 
 from the solid blocks may be given by drawing from two 
 planes, so placed as to represent the bases or ends of the 
 various prisms. Thus two squares may be fastened by a 
 tack through their centres to a small cylinder of wood, 
 which represents the axis of the prism. The prism thus
 
 62 FREE-HAXD DR A \VI.\C. 
 
 represented may be placed vertical or horizontal. As all 
 the edges of each card are seen, this practice will help 
 the pupil when he draws from a solid, in which all the 
 edges are not seen. 
 
 A better arrangement is a skeleton frame in which the 
 edges are represented by wires, or in which wires con- 
 nect the bases of the object, which are sheets of tin. 
 Drawing from these objects will be interesting and prac- 
 tical. 
 
 After this work the solids may be studied in whatever 
 order seems best. If the pupil has learned to use his 
 eyes, there is little choice as to the order, and by the 
 time he is ready for the high school he should be able 
 to draw the common forms quickly and truthfully, not 
 only singly, but in groups. 
 
 The best and cheapest way to teach model drawing is 
 by the use of a slate of glass on which the drawing is 
 made with a pencil prepared for the purpose, and erased 
 when finished. If drawings are made in this way, they 
 ran be instantly tested by holding the slate in front of 
 the object so that the lines upon the slate appear to 
 cover the edges of the object, the drawing being of such 
 size that the slate may be held in the hand to apply the 
 test. If the objects are large, they should be placed far 
 enough away to have the drawing upon the slate come of 
 the right size. The easiest way is to have the pupils 
 draw from small objects on their own desks. When the
 
 DRAWING IN THE PUBLIC SCHOOLS. 63 
 
 drawing is to be tested, the slate can rest upon the desk 
 or be steadied by the hand. 
 
 As an objection to the use of this slate, it could be said 
 that some might trace the appearance without previous 
 drawing, but this would not in itself be harmful, for it 
 would simply decrease the value derived from the lesson 
 by drawing first by the eye alone. 
 
 When the drawing on this transparent slate has been 
 carried as far as the pupil can see, he may instantly test 
 it by holding it in front of the object. If correct, the 
 lines of the drawing will appear to cover the edges of the 
 object ; if not correct, the inaccuracies can be noted and 
 a second attempt made. 
 
 The cost of the glass will be equalled in a short time 
 by that of the paper saved by its use. I am confident 
 that the slate used in this manner will in a short time 
 give the average pupil of even the lower grades more 
 ability in drawing than he now obtains by his entire 
 public school training. This method will make drawing 
 easier and more interesting, and will enable all the teach- 
 ers, without special exertion, to make drawing of some 
 value. 
 
 The drawing lesson will certainly be easier for the 
 teacher than now, for the drawings will test themselves, 
 and teachers who cannot draw may obtain good results. 
 I do not mean that teachers can get along without being 
 able to draw, for drawings on paper must be made and
 
 64 FREE-HAXD DRAWING. 
 
 corrected, but I think the glass will be of very great value, 
 especially when teachers are not thoroughly prepared. 
 
 It is thought that this use of the slate will prove inter- 
 esting to the pupils, but if it is found that they do not 
 apply themselves to the work, thinking that a slate is too 
 childish, it may be used at first as in the later work, in 
 connection with the use of paper. The drawing may be 
 made by eye alone, first on the slate or on the paper, as 
 is preferred. In whatever way the work is carried on, 
 the use of the slate gives an easy and sure test of the 
 accuracy of the proportions, and for this purpose the 
 slate may be used to great advantage through the work 
 of all the grades and the high school. 
 
 An improvement on the simple frame is the attachment 
 at each side of wires fitting in the frame so as to be drawn 
 out to any length, the desk having two holes made to 
 receive the wires. By means of these wires the slate 
 with the drawing may be held perfectly steady, thus 
 allowing the exact comparison of the drawing with the 
 object. Of course the eye must be held in one place for 
 this comparison. 
 
 By means of this skite, any teacher can quickly obtain 
 all the practice necessary to make up for lack of training 
 in drawing, and if the slate is properly used, the drawing 
 always being made by eye before holding the glass slate 
 in front of the object, it will be of great assistance to all 
 who wish to learn to draw.
 
 DRAWING IX THE PUBLIC SCHOOLS. 65 
 
 When the pupil can draw the simple objects, there is no 
 reason why the light and shade may not be represented 
 by pencil tints put on with the side of the pencil ; in the 
 advanced grades charcoal can be used. 
 
 The high school work should include furniture draw- 
 ing, and corners of the room, with more difficult groups of 
 models. A graduate of this school should certainly have 
 the ability to sketch indoors and out, with truth so far as 
 proportion is concerned. It is hoped that the importance 
 of this subject may be realized, and that, if necessary, 
 some of the less important work may give way that this 
 may improve. 
 
 Much help will be obtained from examples of good 
 drawings by advanced students and illustrators. With 
 very small outlay each teacher can procure from maga- 
 zines and papers reproductions of pencil, pen and ink, 
 and shaded drawings by the best artists. If these repro- 
 ductions are placed where they can be seen all the time, 
 they will interest the pupils, and give them an idea of 
 expression such as they can never obtain from the mechan- 
 ical cuts of most drawing-books. Care should be taken 
 to secure some drawings simple in character, which may 
 serve to interest the pupil in his own elementary work. 
 
 These drawings should not be copied, for if copying is 
 begun, it is almost certain to be done to excess, and as 
 has been said, the elementary work of the public schools 
 cannot properly consider technique. It is hoped that
 
 66 FREE-HAND DRAWING. 
 
 soon the teachers who are now talking about methods, 
 etc., may give their attention to the simple study of 
 Nature, and the making of truthful drawings. 
 
 Some have attempted to state theories of color and 
 aesthetics, which the student may study to improve his 
 taste. The value of this theory may be illustrated by 
 referring to the numerous statements of perspective prin- 
 ciples which have been drilled into the students of many 
 schools, who are at the present time making the fearful 
 and wonderful productions labelled " from the object." 
 
 The most practical solution of this problem has been 
 given by an artist, who in one of the schools of Salem, 
 Mass., has just arranged pictures by good artists, photo- 
 graphs, casts, and other reproductions of the best art 
 work. The influence of good examples of this nature 
 cannot fail to cultivate the taste and raise the artistic 
 standard of the people. The time given to theories of 
 the beautiful will be much better spent in the study of 
 Nature involved in the simplest drawing.
 
 CHAPTER V. 
 TESTS. 
 
 Paragraphs marked (T.) are for the use of teachers only. 
 
 IN beginning, the student should understand that his 
 drawings are of no value in themselves, but are of use only 
 as they train the eye to see correctly. The eye can be 
 taught, or rather the mind can be made to accept the 
 image of the eye, only by depending upon it, and if the 
 student begins by measuring and testing he will never be 
 able to draw otherwise. This is undesirable for many 
 reasons, the most important being that no measurements 
 can be applied which will take the place of correct per- 
 ception, or begin to equal the trained eye. It is thus 
 important that the student, from the beginning, depend 
 entirely for his first drawing upon his eyes. 
 
 The best possible training for all young or old is the 
 use of the glass, explained on page 62. Any one who 
 wishes to train his eyes to correct seeing can do so most 
 quickly by drawing with the special pencil upon this slate 
 by eye alone, his impressions of the form, and then testing 
 the drawing by holding it in front of the object. 
 
 The readiest way of determining the apparent propor- 
 tions of an object is by the use of a pencil or any straight, 
 
 67
 
 68 FREE-HAND DRAWING. 
 
 slender rod held at arm's length, and to appear to cover 
 the lines to be compared. Thus the end of the pencil 
 may be held so as to appear to cover the top of an 
 object, whose apparent height may be measured on the 
 pencil by means of the thumb-nail placed so as to appear 
 to cover the bottom of the object. If the pencil is now 
 turned into a horizontal position, the apparent height of 
 the object may be compared with its apparent width. If 
 the measurement covering the height is one-half the dis- 
 tance on the pencil which covers the width, the group 
 appears twice as wide as high. In this way the apparent 
 proportions of any object or group may be found. 
 
 It is important that this use of the pencil shall deter- 
 mine simply the proportion of the drawing and not its 
 actual size. The measurements on the pencil must not 
 be transferred to the paper, for the eye and hand are in 
 different positions when the various measurements arc- 
 taken, and if they are transferred to the paper the draw- 
 ing resulting will be incorrect in proportion. 
 
 The slightest change in distance of the pencil from the 
 eye when proportions are compared will occasion inac- 
 curacy. The only way to be at all correct is to hold the 
 pencil as far from the eye as possible, the arm being per- 
 fectly straight and the pencil being turned by twisting the 
 entire arm. 
 
 The pencil must be at right angles to the direction in 
 which the object is seen. Nearly all students think the
 
 TESTS. 69 
 
 pencil should be parallel to the side of the room, or the 
 bench upon which the object rests. This, however, is 
 wholly false, for the position of the object with reference 
 to its surroundings is of no consequence, and must not 
 be considered when the actual appearance of the object 
 is desired. If a cube is to be represented, the student 
 must look at it, and the plane which gives its real appear- 
 ance is perpendicular to the direction in which he looks, 
 and when measuring, the pencil must always be held in 
 this position. When thus held, its ends are the same 
 distance from the eye. 
 
 A good plan is to find some position in the fingers in 
 which the pencil is perpendicular to the arm, which /- /// 
 when outstretched, brings the pencil into practically the 
 correct position, Fig. 10. 
 
 (T.) In the public schools when the subject is begun, 
 some may find that a pin pushed into the pencil at right 
 angles to it will help to place the pencil. When the pencil 
 is held so that only the head of the pin is seen, the pen- 
 cil is perpendicular to the direction in which the pupil 
 looks. A better device may be made by bending a piece 
 of soft wire (a hair-pin) about a large knitting-needle as 
 shown in Fig. 12. One end of the wire projects at right 
 angles to the needle, and the other extends back and 
 projects a short distance perpendicular to the first end. 
 The longer end serves as a sight to place the needle cor- 
 rectly. The wire should press the needle enough to
 
 7U 1-KEE-JI.lXD DR. \}l'L\\;. 
 
 keep in place upon it. It may be moved by the finger 
 or thumb, and the measurement taken by sighting over 
 the short end. This slide will assist greatly, and as it is 
 important that measurements should be correct, it is 
 advised that every student who cannot hold the pencil 
 properly be provided with this measuring-needle and 
 slide. It will also assist when one measurement is not an 
 easily determined part of the other. See page 23. 
 
 (T.) The smaller measurement should always be com- 
 pared with the larger. If the former is one-half or one- 
 third of the latter, this is easily determined, but if the first 
 is three-fifths or four-ninths of the second, the proportion 
 is not so easy to determine, and if the two measurements 
 can be taken in such a way that they may be compared 
 at leisure^ the proportion may be more surely determined. 
 This may be done by taking the smaller by the sliding 
 wire and the larger by the thumb. 
 
 If the back end of the pencil is used to measure by, 
 the pencil will be held correctly when the end appears a 
 straight line, thus producing the same result as the pin 
 projecting from the pencil. 
 
 The distance of the needle or pencil from the eye 
 when proportions are compared must be the same. The 
 distance is so apt to vary that unless each comparison is 
 made several times with the same result, there is little 
 chance of the measurements being correct. It is useless 
 to think that tests not carefully taken are worth the time
 
 TESTS. 71 
 
 given them. It is much better to take the one proportion 
 of height and width carefully, than to spend the time 
 necessary to do this on half a dozen measurements which 
 are sure to contradict, and do more harm than good. 
 
 It is impossible to compare accurately a short distance 
 with a long. If the height is equal to or nearly one-half 
 or one-third the width, care will so determine it, but with 
 every new position of the hand in moving a short dis- 
 tance over a long inaccuracy arises, and it is well to 
 avoid such comparisons. 
 
 The inaccuracy is produced by inability to hold the 
 pencil at exactly the right place, and also by the change 
 in the distance of the pencil which every movement 
 away from the first position occasions. 
 
 This movement may be realized by tying a thread to 
 the pencil and measuring its distance from the eye by 
 holding the thread with the left hand against the brow. 
 If the arm is dropped for the measurement of a near 
 object and the thread is tight, it will loosen when the arm 
 is raised, and in the same way it will change for horizon- 
 tal movement. The only way in which exact measure- 
 ments of an extended subject can be taken is by the use 
 of such a measuring-thread for the pencil ; but we wish 
 to simplify the subject as much as possible, and if reason- 
 able care is exercised the variation in the distance of the 
 pencil may be made so slight as to be unimportant in 
 the drawing of small objects.
 
 72 FREE-HAXD DKAll'IXG. 
 
 \Yhen possible, all comparisons should be made by 
 swinging the pencil from a vertical into a horizontal posi- 
 tion, by motion of the whole arm from the shoulder, and 
 avoiding change in distance by revolving the pencil 
 about one end of the first measurement. Thus if the 
 height and width of a table are to be compared, instead 
 of measuring the width along the top and dropping the 
 hand to compare the width with the height, or measuring 
 the height and then lifting the hand to compare with the 
 width, make the comparison by taking the width along 
 the top, and swinging the pencil down about the thumb ; 
 or by taking the width at the bottom and swinging the 
 pencil up about the thumb, as in Fig. 13. Measuring in 
 this way will assist greatly to correct results. 
 
 (T.) A short distance may of course be compared with 
 a long, with a degree of accuracy varying with the student ; 
 but such measurements are not recommended and are 
 unnecessary, as other tests will give better results. 
 Another way by which distances may be compared is by 
 marking upon the edge of a ruler or piece of cardboard 
 with a pencil. The distances may be compared at 
 leisure. 
 
 The above are the direct tests for proportion, and if 
 carefully taken, should give the correct mass of the draw- 
 ing, but for smaller proportions and directions of lines 
 other tests are better. 
 
 The lines with which it is natural to compare directions
 
 TESTS. 7J 
 
 are vertical and horizontal lines. A horizontal line 
 
 whose ends are equi-distant from the eye appears hori- 
 zontal and is represented by a horizontal line. A verti- 
 cal line appears vertical and is always represented by a 
 vertical line. If a ruler is held horizontal, with its ends 
 equally distant from the eye, it illustrates the appearance 
 represented by a horizontal line in the drawing. By 
 looking over the ruler thus held, the apparent directions 
 of lines of the object may be compared with the horizon- 
 tal. 
 
 A thread with a weight attached serves as a plumb- 
 line. By holding it in front of the object its lines may 
 be compared with the vertical. The thread is often bet- 
 ter than the ruler or pencil for the horizontal line, as it 
 hides none of the object. Care must always be taken to 
 hold the thread perpendicular to the line of sight. This 
 position is easiest obtained by directly facing the group, 
 extending the arms equally, and holding about two feet 
 of the thread, whose ends are then equally distant from 
 the eye. 
 
 More care must be exercised to have the thread hori- 
 zontal. This position can be obtained only by seeing 
 nothing^ but the thread until it is levelled, when the stu- 
 dent may look behind it. If the student sees the group 
 bjfjre the thread is level, its lines will probably make the 
 thread seem horizontal when it is not. If there are hori- 
 zontal lines in the subject which are parallel to the pic-
 
 74 1-KEE-UAXD DKA\VL\(J. 
 
 tn re (' not foreshortened "), they will appear horizontal 
 and will place the thread correctly ; but if the horizontal 
 lines of the subject are not thus situated, they will not 
 appear horizontal, and so will cause the thread to be out 
 of level. 
 
 It may seem that unnecessary space has been given to 
 these directions, but it has been found almost impossible 
 to make many students understand the matter, and hold 
 the thread correctly, even after repeated explanations 
 and illustrations. Some, after months of study, are 
 found holding the thread or pencil at an angle of from 
 ten to thirty degrees away from the correct position, and 
 it is thought that no explanation can be too careful. 
 The problem is so simple that any student who wishes to 
 succeed should have no difficulty. He may be sure 
 that he will never learn to draw until he is able to dis- 
 cover his mistakes, and as the use of the thread is a 
 most important test, it should be correctly applied. 
 
 Any object, as the cube, Fig. 14, having been drawn, 
 it may be tested by the thread as follows: Hold the 
 thread horizontal to cover point 5, and note its apparent 
 intersections with the edges 1-6 and 6-7. Hold the 
 thread vertical in front of point 3, anil see where it 
 intersects 5-6. Hold it in front of 6-7, and notice its 
 intersection with 2-3. Hold the thread to cover i and 
 5, also 2 and 4, and compare the directions with a hori- 
 zontal line. Continue the edge 2-7 to intersect 5-6, and
 
 TESTS. 
 
 75 
 
 4- 7 to intersect 21. Cover any opposite points as i 
 and 3, 3 and 6, 4 and r, etc., and notice where the 
 
 ta,vui ,1,11. -I.-.- t^ ;*- * i-- edges between. 
 
 ply a more exact method 
 wing lines in the air, the 
 
 1 the eye is trained, the 
 ipler, is all that is needed. 
 
 2 use of the thread pref- 
 which can be made to 
 object, and its intersec- 
 much more readily than 
 
 1 or rule, which hides con- 
 se tests with the thread 
 > discover every error of 
 
 (T.) A last test may be applied by holding two pencils 
 together at right angles to the direction in which the 
 object is seen, and separating them until one covers 2-3 
 and the other covers 5-6. If great care is taken, the 
 directions of these lines with reference to each other may 
 be seen, and the drawing tested by continuing these lines 
 in the drawing. 
 
 (T.) One way of measuring the apparent angle between 
 lines is by folding a piece of paper and holding it so that 
 each part appears to coincide with one of the two lines. 
 This way is easiest applied 'by the use of a hinged rule 
 or straight edge of two parts. I cannot recommend
 
 74 FKEE-UAXD DK.l \VL\U. 
 
 tare ('' not foreshortened "), they will appear horizontal 
 and will place the thread correctly ; but if the horizontal 
 lines of the subject are not thus situated, they will not 
 appear horizontal, and so will ca- 
 of level. 
 
 It may seem that unnecessary i 
 these directions, but it has been f 
 to make many students understan 
 the thread correctly, even after 
 and illustrations. Some, after 
 found holding the thread or penci 
 ten to thirty degrees away from th 
 it is thought that no explanatioi 
 The problem is so simple that any 
 succeed should have no difficult) 
 
 that he will never learn to draw i .^ uui<_- 10 ins- 
 cover his mistakes, and as the use of the thread is a 
 most important test, it should be correctly applied. 
 
 Any object, as the cube, Fig. 14, having been drawn, 
 it may be tested by the thread as follows: Hold the 
 thread horizontal to cover point 5. and note its apparent 
 intersections with the edges 1-6 and 6-7. Hold the 
 thread vertical in front of point 3, and see where it 
 intersects 5-6. Hold it in front of 6-7, and notice its 
 intersection with 2-3. Hold the thread to cover i and 
 5, also 2 and 4, and compare the directions with a hori- 
 zontal line. Continue the edge 2-7 to intersect 5-6, and
 
 TESTS. 75 
 
 4-7 to intersect 21. Cover any opposite points as i 
 and 3, 3 and 6, 4 and r, etc., and notice where the 
 thread appears to intersect the edges between. 
 
 This use of the thread is simply a more exact method 
 of discovering angles than drawing lines in the air, the 
 first method explained. When the eye is trained, the 
 first, which is of course the simpler, is all that is needed. 
 1 5ut most students will find the use of the thread pref- 
 erable, as it gives a fine line which can be made to 
 exactly cover the edges of the object, and its intersec- 
 tion with the edges can be seen much more readily than 
 that of a line formed by a pencil or rule, which hides con- 
 siderable of the object. If these tests with the thread 
 are applied, they cannot fail to discover every error of 
 importance. 
 
 (T.) A last test may be applied by holding two pencils 
 together at right angles to the direction in which the 
 object is seen, and separating them until one covers 2-3 
 and the other covers 5-6. If great care is taken, the 
 directions of these lines with reference to each other may 
 be seen, and the drawing tested by continuing these lines 
 in the drawing. 
 
 (T.) One way of measuring the apparent angle between 
 lines is by folding a piece of paper and holding it so that 
 each part appears to coincide with one of the two lines. 
 This way is easiest applied 'by the use of a hinged rule 
 or straight edge of two parts. I cannot recommend
 
 76 FREE-llAXD DRAM'IXC,. 
 
 this test, for there are t\vo straight edges to be held at 
 right angles to the direction in which the student looks, 
 and it is so difficult to do this that I do not know of 
 many students who have succeeded. Those who can hold 
 the rules correctly, may depend upon their eyes and gi-t 
 the drawing better without many mechanical tests than 
 with them. 
 
 (T.) Another way of testing the direction of a long 
 line is to hold a straight edge upon the line of the draw- 
 ing, and then lift the board and straight edge into the 
 position of the picture plane, when the straight edge 
 appears to coincide with the line if its direction in the 
 drawing is correct. 
 
 I have dwelt thus carefully upon each test in the 
 hope that the student may reali/e their importance, for 
 he will learn to draw correctly only through his own 
 efforts, gaining with each discovery of error. He can 
 never become a draughtsman as long as he depends upon 
 a teacher for corrections. Let him carry his drawing so 
 far that a thorough application of the tests explained 
 will show no error, then as it is simply a question of 
 exactness to be determined by the eye, if the trained eye 
 of the teacher discovers mistakes so slight that the stu- 
 dent cannot rightly be expertt-d to determine them, these 
 may be pointed out. As the chief benefit results from 
 what the student himself sees and does, he will be much 
 better off without* a teacher than with one who does his 
 work for him.
 
 TESTS. 77 
 
 As stated on page 23, the art student should use few- 
 texts and should not require the mechanical aids to test- 
 ing which have been explained. They may sometimes 
 be required by teachers in the public schools, when 
 students have no capacity for the work, but even then 
 they will not be necessary if the glass is used to train 
 the eye to see proportions, or as a means for testing. In 
 all work, the student should aim to use few aids and to 
 throw these aside as soon as possible. 
 
 There are many who say that measurements and tests 
 are mechanical, and that to learn to draw the student 
 should draw by eye simply. It is true that measurements 
 and tests, as unfortunately too many students are taught 
 to use them, cannot fail to produce hard and mechanical 
 drawings and retard progress. Still it seems better for 
 the student, when he can see no farther, to be shown by 
 tests where his eyes have failed, rather than to carry draw- 
 ings only as far as he can by eye, and then put them away 
 and begin others which can be carried but little if any 
 further. Therefore the student is advised to apply the 
 tests explained after he has carried his drawings as far as 
 he can see, and not to put any drawings away which the 
 tests show to be untruthful. It is believed that this* train- 
 ing will most quickly produce ability to draw truthfully at 
 sight.
 
 CHAPTER VI. 
 PERSPECTIVE PRINCIPLES. 
 
 (See Preface, page vii.) 
 
 " OUR whole past, and especially the ideas and emo- 
 tions of the present moment, determine how we perceive 
 any object." 
 
 This being true, the student must work long and 
 earnestly before he can separate facts from appearances, 
 as the knowledge of the actual form prevents the mind 
 from accepting its appearance. The impression con- 
 veyed to the mind of one not trained to accept the image 
 of the eye, is the result of a combination of what tin- r\v 
 sees with what is by far the greatest factor, what the mind 
 knows concerning the actual conditions of the object. 
 The student must struggle continually not only against 
 this influence of his mind, but also against the effect 
 which one line exerts to change the apparent directions 
 of others. This effect is sometimes so strong that even 
 the practised eye of the artist is deceived, and we may 
 safely say that the most perfect eye, with the longest 
 training, is liable to be deceived. A knowledge of the 
 perspective principles governing the appearance of form 
 78
 
 PERSPECTIVE PRINCIPLES. 79 
 
 is thus helpful to the draughtsman who would be truthful, 
 and there is no reason why there should not be truth and 
 artistic rendering at the same time. 
 
 The Plane of the Drawing. 
 
 The mind through the sense of sight perceives form, 
 the rays of light from any object entering the eye, being 
 focused on the retina, and forming an image of the object, 
 as in the camera, except that in the latter the image is 
 formed on a plane surface, while that in the eye is formed 
 on a spherical surface. As but a single point can be seen 
 clearly at any time, the image of the eye is practically 
 the same as that of the camera. 
 
 The artist's problem is to make his drawing so that it 
 shall create the same ideas of form, size, and position as 
 the objects which it represents. It is evident that this 
 must occur when the drawing produces the same image 
 in the eye as the objects. To do this the drawing must 
 be similar to the image. 
 
 The rays from any object to the eye form a conical 
 body. If this cone of rays is intersected by any plane, the 
 intersection is a picture of the object, which if the object 
 is taken away, will still create its image in the eye. If 
 this plane of the picture is at right angles to the cone, the 
 section (the picture) will be a true picture of the object, 
 that is, be similar to the image of the eye. 
 
 it .
 
 80 FRF.E-If.lXD DRA 
 
 Figure 15 represents a circle A, placed vertical and in 
 front of the eye. The cone formed by the visual rays is 
 represented by lines b-b, and a vertical plane cutting 
 through the cone of rays, by line P. If the student will 
 hold any cone horizontal, it will perfectly illustrate the 
 figure, the base of the cone representing the circle A, and 
 the apex representing the eye. With the cone the 
 student will at once see that a vertical plane between 
 the eye and the base intersects the cone in a circle. This 
 circle is the picture of the base A. 
 
 Figure 16. If now the plane of the picture is inclined 
 to the axis of the cone, its intersection with the cone is 
 still a picture of the circle, but in shape it differs from 
 that in Fig. 15, which is a circle. The oblique intersec- 
 tion is an ellipse, but it is important to notice that it docs 
 not appear such to the eye at the apex of the cone. It 
 appears a circle exactly covering the base of the cone. 
 It makes no difference how the plane of the picture is 
 placed, or what the proportions of the resulting ellipse, 
 it must always appear to the eye a circle, in fact, the 
 circle of the base. When the eye is removed from the 
 apex of the cone, the ellipse appears an ellipse, and is not a 
 true picture of the circle. The circle of Fig. 15 and the 
 ellipse of Fig. 16 are pictures of the circle A, and create 
 in the eye, when it is at the apex, a circular image of the 
 circle, but the former only is similar to the object A. 
 When looking at pictures we naturally hold them in
 
 This must be at right angles u> me >mv.v t,^,. ........ 
 
 the object is seen. The plane cannot be perpendicular 
 to all the rays, but should be so to the central one. 
 
 A " tme " picture of any object may be obtained by 
 drawing upon a sheet of glass with a brush and color, or 
 a special pencil, or on a wire screen with chalk. The 
 gl iss or screen should be placed at right angles to a line 
 from the centre of the object to the eye, the eye and 
 screen held in one position, and lines drawn to cover all 
 the edges which are seen. It is desired that every stu- 
 dent make drawings in this way, a small pane of glass and 
 a special pencil being the best materials. The drawings 
 should be made with the glass at right angles to the rays. 
 also when it is held obliquely. The drawings may be
 
 6*JL 
 
 
 tion is an ellipse, but it is important to notice that it does 
 not appear such to the eye at the apex of the cone. It 
 appears a circle exactly covering the base of the cone. 
 It makes no difference how the plane of the picture is 
 placed, or what the proportions of the resulting ellipse, 
 it must always appear to the eye a circle, in fact, the 
 circle of the base. When the eye is removed from the 
 apex of the cone, the ellipse appears an ellipse, and is not a 
 true picture of the circle. The circle of Fig. 15 and the 
 ellipse of Fig. 16 are pictures of the circle A, and create 
 in the eye, when it is at the apex, a circular image of the 
 circle, but the former only is similar to the object \. 
 When looking at pictures we naturally hold them in
 
 PERSPECTIVE PRIXCIPLES. 81 
 
 front of us, at right angles to our line of vision, as in the 
 position of the plane P of Fig. 15. If plane P of Fig. 16 
 is thus held, the ellipse upon it appears an ellipse, and 
 cannot create the idea of a circle. We see that the first 
 picture is preferable to the second, for it is a circle, and 
 wherever the eye is placed creates a circle in the eye. 
 (It is of course understood that it is always looked at 
 perpendicularly.) 
 
 We will distinguish the first picture from that given by 
 any other position of the picture plane, by calling it a 
 y meaning that it is similar to the image 
 
 created in the eye by the object. There can be but one 
 position of the picture plane which gives a ''true" picture. 
 This must be at right angles to the direction in which 
 the object is seen. The plane cannot be perpendicular 
 to all the rays, but should be so to the central one. 
 
 A ' true " picture of any object may be obtained by 
 drawing upon a sheet of glass with a brush and color, or 
 a special pencil, or on a wire screen with chalk. The 
 gl iss or screen should be placed at right angles to a line 
 from the centre of the object to the eye, the eye and 
 screen held in one position, and lines drawn to cover all 
 the edges which are seen. It is desired that every stu- 
 dent make drawings in this way, a small pane of glass and 
 a special pencil being the best materials. The drawings 
 should be made with the glass at right angles to the rays. 
 also when it is held obliquely. The drawings may be
 
 82 
 
 compared, and the student realize that the glass must 
 be perpendicular to the direction in which he looks for 
 the drawing to give the real appearance of the object. 
 
 It appears that a drawing on any plane or surface 
 creates the correct impression, only when the eye is in 
 the position which it had when the drawing was made. 
 All drawings, then, are best seen from some one point or 
 distance. The trained eye will select this distance. As, 
 however, drawings and pictures will be viewed by un- 
 trained eyes, and as the proper point may not always be 
 accessible, it is important that all should be avoided 
 which causes marked distortion, when the picture is not 
 seen from the proper point. If the picture is a "true" 
 picture, the distortion produced when it is viewed from 
 too long or short a distance, appears not in the shape of 
 its parts, but only in the relative sizes of the objects 
 represented. Thus the distortion of a " true " picture is 
 always less than that of a drawing on a plane oblique to 
 the visual rays, and the " true " picture is by far the best 
 drawing that can be made for general use. It is called 
 a Model 1 Drawing. 
 
 Before beginning the problems, we will choose a term 
 which shall mean the position in which any line appears 
 its real length, and any plane its real shape. This 
 occurs when the line or the plane is perpendicular to the 
 direction in which it is seen, that is, is parallel to the 
 picture plane. The words " parallel to the picture plane "
 
 PERSPECTIVE PKIXCIPLES. S3 
 
 might cause confusion, from the fact that in perspective 
 the picture plane is gene-rally vertical, and takes in a 
 wide field of view, while in Model Drawing the plane is 
 perpendicular to the direction in which one looks, and is 
 thus continually changing. We wish a term which shall 
 mean the position in which any line appears its real 
 length and any plane its real shape, and will select the 
 words not foreshortened. Any line is "' not foreshort- 
 ened " when its ends are equally distant from the eye, 
 ami any plane when its angles are equally distant. 
 
 We must also decide upon a term which shall mean 
 the appearance of the facts instead of the facts. We 
 select perspective!)'. " Perspectircfy " parallel thus means 
 the appearance of parallel lines, which is that of conver- 
 gence. " Perspectively " parallel lines are lines which 
 converge towards a point, and " perspectively " equal 
 distances on any line are unequal, the space representing 
 the nearest of the equal distances being the longest, as in 
 Fig. 24. x f>?0 
 
 The apparent angle at which parallel lines seem to 
 converge, that is, the angle between the lines represent- 
 ing parallel lines, we may speak of as large or small, and 
 say that lines converge or vanish quickly or slowly. 
 They vanish quickly when the vanishing-point is near the 
 drawing, and slowly when it is far from the drawing. 
 
 The angle which any line appears to make with a 
 horizontal line that appears horizontal, we will call the
 
 f 
 
 I 
 
 7te.tr 
 
 S4 
 
 FREE-IIAXD DRA \\~IXC. 
 
 angle of inclination. Thus all horizontal lines whose ends 
 are not cilia-distant, appear to incline at smaller or 
 greater " angles of inclination," according to the angle: 
 which the lines make with the picture plane. Lines not 
 level appear inclined at " angles of inclination " which 
 increase with the angles of the lines with the picture 
 plane and the ground. The " nn^ks of inclination " i>f 
 horizontal lines increase or dec rease u>itli the ilistancc <>/ 
 the ranisliing-point, that is, with the angle of convergence. 
 In all the problems explained, the picture plane is 
 supposed to touch the object at its nearest point, and 
 the drawing is the largest possible to be made on a phme 
 in front of the object. 
 
 Stiuty i]f Principles. 
 
 Figure i 7. Place a large cube a few feet distant from 
 the eye, so that its centre is on the level of the eye, 
 four of its edges vertical, and one face visible, with its 
 angles equally distant from the eye. This face is " not 
 foreshortened," and appears its real shape. 
 
 Figure 18. Turn the cube so that its left side appears 
 very narrow. It will be noticed that the upper end of 
 the farther vertical edge B appears below the upper end 
 of the front edge A, and that the lower end of the 
 farther edge appears above the lower end of the front 
 edge. The farther edge thus appears shorter than the
 
 PERSrr.CTl 1 7s L'KfXCrPLES. 
 
 85 
 
 front edge. It is also seen that the horizontal edges D 
 and K, which connect the ends of these verticals, appear 
 to converge. If these lines of the drawing are con- 
 tinued, they will meet. The continued lines must be the 
 representations of continuations of the edges, and we see 
 that parallel retreating lines in Nature appear to con- 
 verge to a point called their vanishing-point. V,r. 
 
 \Ve now find that the right edge C is farther from the 
 eye, and thus appears shorter than the central edge A, 
 and the horizontal edges F and G appear to converge, as 
 the horizontal edges of the left face. The edge C is 
 much nearer the eye than B, and appears longer. It is 
 really but little farther from the eye than A, and the con- 
 vergence of F and G is very slight. As the eye is 
 opposite the centre of the cube, the apparent distances 
 that the upper ends of B and C are below that .of A 
 must be the same as the apparent distances of the lower 
 ends of B and C above that of A; and the "angles of 
 inclination" of the upper edges D and G must be the 
 same as those of the lower edges E and F. Since these 
 edges appear equally inclined, they will appear to vanish 
 on the level qf .the centre of the cube, that is, of the eye. 
 
 If now the eye is lifted, the "angles of inclination" 
 at the top decrease, and those at the bottom increase. 
 When the eye comes to the level of the top of the cube, 
 the upper angles disappear, and the whole top is seen as 
 a horizontal line. 
 
 /6
 
 86 
 
 J-KEE-IIAXD DKA \VL\(J. 
 
 From this study of the cube, we see, 
 
 i st. That of two parallel and equal lines which do not 
 vanish, the nearer appears the longer. The relative 
 lengths appear to decrease as the distances increase. 
 See Fig. 19, in which 1] being twice the distance of A 
 from the eye, appears one-half as long as A. 
 
 2d. That parallel, retreating lines appear to converge 
 towards a point, called their vanishing-point. (All lines 
 whose ends are unequally distant from the eye are 
 retreating lines.) 
 
 3(1. That horizontal, retreating lines appear to de- 
 scend or vanish downward when the lines are above the 
 level of the eye, and to ascend or vanish upward when 
 they are below the level of the eye. This is evident from 
 the fact that the eye must be dropped to look from the 
 nearer to the farther end of the line above the eye, and 
 be raised to look from the nearer end of the line below 
 the eye to its farther end. 
 
 4th. That parallel, retreating horizontal lines appear 
 to vanish at the level of the eye. 
 
 5th. That a horizontal hne at the level of the eye 
 appears horizontal, and a horizontal plane at this level 
 is seen edgewise, and appears a horizontal line. 
 
 We will now draw upon the wall of any room lines 
 which' have the apparent directions of the horizontal 
 
 lines A, B, C and I), at floor and ceiling, which are per- 
 - . A 
 
 pendicular to the wall. We find that the lines on the
 
 he eye. Par- 
 oint infinitely 
 e transparent, 
 
 continue on 
 to converge. 
 
 the continu- 
 se Unes, (the 
 
 point in the 
 This point 
 
 I lines is in a 
 
 To draw the lines on the side of a room, two students 
 must work together, one observing, the other drawing the 
 lines with a straight edge. But the students may work 
 individually by drawing a sketch of any room, the direc- 
 tions of the perpendiculars to the end being determined 
 by holding the thread or a ruler to cover the lines. This 
 experiment proves that to see tJic vanishing-point of a sys- 
 tem of parallel lines, u<e must look in their direction. 
 
 All parallel lines which hare one end nearer the eye 
 than the other appear to converge, and the convergence is 
 in the direction of their farther ends. According to this 
 statement, the vertical edges of a cube above or below the 
 eye appear to converge, but they are not so represented. In
 
 86 
 
 1'KEL-U 
 
 From this study of th 
 
 i St. That of t\vo para 
 vanish, the nearer appt 
 lengths appear to decn 
 See Fig. 19, in which B 
 from the eye, appears OIK 
 
 2d. That parallel, retr 
 towards a point, called th 
 whose ends are unequa 
 retreating lines.) 
 
 3d. That horizontal, n 
 scend or vanish downward 
 level of the eye, and to a 
 they are below the level of 
 
 the fact that the eye must ._ .^^^ uom the 
 
 nearer to the farther end of the line above the eye, and 
 be raised to look from the nearer end of the line below 
 the eye to its farther end. 
 
 4th. That parallel, retreating horizontal lines appear 
 to vanish at the level of the eye. 
 
 5th. That a horizontal Hue at the level of the eye 
 appears horizontal, and a horizontal plane at this level 
 is seen edgewise, and appears a horizontal line. 
 
 We will now draw upon the wall of any room lines 
 which' have the apparent directions of the horizontal 
 
 lines A, B, C and D. at floor and ceiling, which are per- 
 A 
 
 pendicular to the wall. We find that the lines on the
 
 -; CTIl'E / Yv'/.VC 'fPLES. 
 
 S7 
 
 wall intersect at a point directly opposite the eye. Par- 
 allel lines in Nature appear to meet at a point infinitely 
 distant. Suppose the end of the room to be transparent, 
 and the lines perpendicular to the end to continue on 
 the other side. Retreating, they appear to converge. 
 The lines drawn on the end are pictures of the continu- 
 ing lines. The point on the wall where these hues, (the 
 pictures,) meet must be the picture of the point in the 
 infinite distance where the actual lines meet. This jKnnt 
 is in a perpendicular to the end of the room passing 
 through the eye ; that is, it is in a line through the eye 
 parallel to the lines. Hence we see that, 
 
 The vanishing-point of any set of parallel lines is in a 
 parallel to them, passing through the eye. 
 
 To draw the lines on the side of a room, two students 
 must work together, one observing, the other drawing the 
 lines with a straight edge. But the students may work 
 individually by drawing a sketch of any room, the direc- 
 tions of the perpendiculars to the end being determined 
 by holding the thread or a ruler to cover the lines. This 
 experiment proves that to see the vanishing-point of a sys- 
 tem of parallel lines, we must look in their direction. 
 
 All parallel lines which have one end nearer the eye 
 than the other appear to converge, and the convergence is 
 in the direction of their farther ends. According to this 
 statement, the vertical edges of a cube above or below the 
 eye appear to converge, but they are not so represented. In
 
 S8 
 
 FREE-II. LVD DA\lll'LYu. 
 
 
 a model drawing vertical lines are represented by verti- 
 cal lines (see page 96). 
 
 Figure 21. Place a cube so that its top and front laces 
 are seen, and so its right side appears a vertical line. The 
 edges A, A, A have their left ends a little farther from 
 the eye than their right ends ; but the distance is so 
 short that the convergence is very slight, and the edges 
 appear practically horizontal. Line B of the drawing is 
 longer than C, and yet the edge C is nearer the eye than 
 B. This proves inexact the statement frequently made 
 that "of two parallel and equal lines, the nearer appears 
 the longer." /$0 
 
 Figure 22 is a top view, representing the eye, a hori- 
 zontal square, and a vertical picture plane. It shows that 
 of two parallel and equal lines, AB and CD, unequally 
 distant from the eye, the nearer, AB, appears the shorter 
 when the lines are at a greater angle than 45 with the 
 picture plane. When at a less angle than 45, as Bl) 
 and AC, the nearer, BD, appears the longer. This state- 
 ment is only exact for lines whose angles are noticeably 
 larger or smaller than 45. 
 
 The figure also shows that of two equal lines, AB and 
 BH, perpendicular to each other and having one end 
 common, the one which makes the greater angle with the 
 picture appears the shorter ; or conversely, the one nearest 
 parallel appears the longer. It, shows, too, that if one 
 line of a right angle vanishes toward the left, tlie other 
 must vanish towar,/ /he right.
 
 PEKSPE C TI VE PRINCIPLES. 
 
 S'J 
 
 If one side of the right angle is " not foreshortened," 
 the other side extends directly away from the spectator, 
 and vanishes at a point above the side " not fore- 
 shortened," on the level of the eye. 
 
 Figure 23 shows that two equal, horizontal lines, per- 
 pendicular to each other, at equal angles with the picture, 
 appear equal in length. When below or above the level 
 of the eye they are at equal " angles of inclination." 
 
 In Figs. 22 and 23, the visual rays intersect the pic- 
 ture plane, and give the positions upon the picture plane 
 of the vertical lines which contain the ends of the lines 
 representing the sides of the square, which are thus
 
 S8 
 
 1-RKE-IIAXn DRA \l~L\\i. 
 
 
 a model drawing vertical lines are represented by verti- 
 cal lines (see page 96). 
 
 Figure 21. Place a cube so that its top and front tares 
 are seen, and so its right side appears a vertical line. The 
 edges A, A, A have their left ends a little farther from 
 the eye than their right ends ; but the distance is so 
 short that the convergence is very slight, and the edges 
 appear practically horizontal. Line B of the drawing is 
 longer than C, and yet the edge C is nearer the eye than 
 B. This proves inexact the statement frequently made 
 that " of two parallel and equal lines, the nearer appears 
 the longer t ' ' J)Q 
 
 zor 
 
 of 
 
 dis 
 
 wli 
 
 pk 
 
 an< 
 
 me 
 
 lar 
 
 a 
 
 BI 
 
 CO 
 
 pic 
 
 pa 
 if/, 
 
 in
 
 PERSPECTIVE PRINCIPLES. 89 
 
 If one side of the right angle is " not foreshortened," 
 the other side extends directly away from the spectator, 
 and vanishes at a point above the side "not fore- 
 shortened," on the level of the eye. 
 
 Figure 23 shows that two equal, horizontal lines, per- 
 pendicular to each other, at equal angles with the picture, 
 appear equal in length. When below or above the level 
 of the eye they are at equal ' angles of inclination." 
 
 In Figs. 22 and 23, the visual rays intersect the pic- 
 ture plane, and give the positions upon the picture plane 
 of the vertical lines which contain the ends of the lines 
 representing the sides of the square, which are thus 
 longer than the distances seen in the plan. 
 
 The apparent length and angle of any retreating line 
 depends upon its angle with the picture, the level of the 
 line, (referred to the eye), and the distance of the eye 
 from the line. 
 
 The greater the angle of any line with the picture, the 
 more it is foreshortened, and the greater the " angle of 
 inclination." 
 
 As the eye is lifted, the " angles of inclination " of the 
 lines AI5 and CD, Figs. 22 and 23, increase. Placing 
 the eye nearer the lines produces the same effect, but 
 the ' angles of inclination " must always be much less 
 than the real angles which the lines make with the pic- 
 ture plane. The ''angle of inclination " decreases as 
 the eye approaches the level of the line, and also as the 
 distance of the eye increases.
 
 90 FREE-HAND 1)RA\\'L\<J. 
 
 The statement often made that "of parallel and equal 
 lines the more distant appears the shorter," has prob- 
 ably accomplished as much harm as good, for it is only 
 true of lines "not foreshortened," and of vertical lines 
 within the limits of ordinary drawings. It is not neces- 
 sary to think of this point in the case of horizontal lines, 
 for therq are other tests upon which it is always better to 
 depend. 
 
 Figure 24. AB represents a horizontal line lying upon 
 the ground, and i, 2, 3, etc., equi-distant points in the line. 
 The lines from these points to the eye represent the 
 visual rays by which the points are seen. These rays, 
 intersecting the picture plane, show that ike equal dis- 
 tances appear unequal, tJie nearest appearing the longest, 
 and the farthest the shortest, the apparent length decreas- 
 ing as the distance increases. This is always true of the 
 appearance of equal lengths on retreating lines. 
 
 There are three sets of parallel lines in the cubc\_ 
 AM*" They all appear to vanish unless they are "not fore- 
 
 I shortened," and are so represented except when they are 
 
 vertical, or are situated as in Figs. 21 and 25. 
 
 They vanish in the directions of their farther ends, 
 and these are points of the invisible faces of the object. 
 
 If both ends of an edge are points of an invisible side 
 of the object, the edge must be considered as " not 
 foreshortened," even when the eye is not opposite its 
 centre.
 
 X) 
 
 13 
 
 <r*ty *^ ~*^ /-s^U 
 
 ^r^Ui^ CS*^*-^_
 
 f if VAT tort 
 
 / 
 
 2-, 
 
 Figure 24. AB represents a horizontal line lying upon 
 the ground, and i, 2, 3, etc., equi-distant points in the line. 
 The lines from these points to the eye represent the 
 visual rays by which the points are seen. These rays, 
 intersecting the picture plane, show that the equal dis- 
 tances appear unequal, the nearest appearing the longest, 
 and tlie farthest the shortest, the apparent length decreas- 
 ing as the distance increases. This is always true of the 
 appearance of equal lengths on retreating lines. 
 
 There are three sets of parallel lines in the cube^ 
 They all appear to vanish unless they are " not fore- 
 shortened," and are so represented except when they are 
 vertical, or are situated as in Figs. 21 and 25. 
 
 They vanish in the directions of their farther ends, 
 and these are points of the invisible faces of the object. 
 
 If both ends of an edge are points of an invisible side 
 of the object, the edge must be considered as " not 
 foreshortened," even when the eye is not opposite its 
 centre.
 
 jb<*ue^i 
 
 e c .
 
 C4\
 
 PERSPECTIVE PKIXCIPLES. 91 
 
 If the eye is opposite one end, as in Fig. 21, and the 
 edges are short, they will be best represented by parallel, 
 horizontal lines. 
 
 If the edges are long and the eye is opposite or near 
 an end, as in Fig. 25, it may sometimes be better to 
 distort the nearer and smaller part of the drawing in 
 favor of the larger part, by representing the lines as they 
 appear. This will happen in an interior when the prism 
 is at the side of the picture so that the distortion of the 
 nearer end is not very noticeable. 
 
 In any drawing representing simply the prism, it will 
 generally be better to give the effect of a right prism, 
 and avoid the distortion of the nearer part by making 
 the lines horizontal. /// general, parallel horizontal lines 
 K>/i if /i extend on both sides of the spectator should be 
 represented 1>\ parallel horizontal lines. The student 
 should not be allowed any other way, but should treat 
 all edges as " not foreshortened," when neither end face 
 of the object is visible. 
 
 In Nature there is no effect like that given by parallel 
 perspective. The difficulties which have just been con- 
 sidered are easiest settled by avoiding the question when 
 possible, by moving so that an end appears and two van- 
 ishing-points can be used, the drawing being between 
 them. If one vanishing-point is in the drawing, as in 
 Fig. 9, the drawing must be distorted, for when one line 
 of a right angle vanishes toward the left, we expect to see
 
 92 FREE-HAND DRAWING. 
 
 the other vanish toward the right. When the question 
 cannot be avoided in this way, and parallel straight lines 
 extend on both sides of the spectator, they should be 
 represented by parallel straight lines, and in the case of 
 horizontal lines, by horizontal lines. 
 
 Parallel straight lines in Nature appear curved. This 
 is shown by the shadows of clouds at sunset, which some- 
 times may be seen extending across the sky, converging 
 in the west toward the sun, and in the east toward a 
 point opposite the sun. Any straight lines which the 
 mind does not know to be straight will, if long, produce 
 the impression of curved lines. This is best shown by 
 the rays of the electric search-light. 
 
 In many drawings from Nature by our leading illus- 
 trators, the curvature resulting from drawing tin* differ- 
 ent parts of long lines as they appear, is very noticeable. 
 
 Although the student may have difficulty in seeing the 
 effect of curvature, even in long lines, he may very easily 
 prove that curvature will result if he draws the parts, 
 even of short lines, as he sees them. This may be done 
 by drawing from three boxes or prisms, placed a short 
 distance apart and in a straight line, the central box 
 being directly opposite him, so that only two faces arc- 
 seen. 
 
 Figure 26 represents the appearance of the left-hand 
 box, both sets of whose horizontal edges appear to van- 
 ish, for two sides of the box are seen.
 
 PERSPECTIVE PRIXCIPLES. 93 
 
 Figure 27 represents the central of the three objects. 
 Only one set of its horizontal edges vanishes, for since 
 but one side is seen, the other set is " not foreshortened." 
 
 Figure 28 represents the right-hand box, whose ap- 
 pearance must be similar to that of the box at the left. 
 
 The vertical edges of the objects at the sides are 
 farther from the eye than those of the central one, and 
 thus appear a little shorter than the edges of the latter, 
 and if the long lines of the drawings are continued, they 
 will form curved lines. 
 
 Figures 26, 27, and 28 are each correct representa- 
 tions of the appearance of a single box ; but if they are 
 looked at all at once as a single picture, the impression 
 of the objects being placed in a curve is produced. 
 No one would think of making this drawing as a repre- 
 sentation of three objects placed in a straight line. The 
 drawing below, Fig. 29, would be made by all, but this 
 drawing does not represent correctly the appearance of 
 the boxes at either side, and it appears that to give the 
 correct general impression, drawings sometimes cannot 
 be exact in detail. 
 
 There are some who think that the study of this ques- 
 tion is unnecessary, that without theory all would natu- 
 rally make the drawing, Fig. 29, as a representation of the 
 three boxes. This is probably true ; but the knowledge 
 that we see as we cannot always represent is very neces- 
 sary, as is proved by the many illustrations from the pens
 
 94 FREE-HAND DKAll'lXG. 
 
 of those who fail to apply to a large subject the reason- 
 ing which gives Fig. 29, and thus produce drawings 
 which are flagrant violations of the simplest rule of per- 
 spective, and this is frequently the result of the attempt to 
 draw by eye the appearance of the parts of a large sub- 
 ject (see page 49). 
 
 Straight lines appear curved, but their representation 
 by curved lines is generally unsatisfactory, and the stu- 
 dent should never be allowed to represent straight In- 
 curved lines. As shown on plate 28, straight lines may 
 be substituted for the curved lines, changing the drawing 
 very little when there are two vanishing-points. 
 
 The influence of diagram perspective, and particularly 
 the appearances of parallel perspective, are so powerful, 
 that many illustrators do not realize that they do not see 
 parallel perspectives in Nature, and that there must be 
 two vanishing-points for the horizontal lines of any rec- 
 tangular object, when two of its sides are seen. It is not 
 necessary to advise the student not to make as one draw- 
 ing the Figs. 26, 27, and 28, or not to represent the end 
 of a room as curved; yet the draughtsman who would 
 never think of making the latter mistake in the case of a 
 single unbroken surface, will frequently do it when the 
 surface is broken or when there are many short lines in 
 different planes. 
 
 Diagram perspective has created many false ideas, and 
 is responsible for much bad drawing, and yet the per-
 
 PERSPECTIVE PRINCIPLES. 95 
 
 spective principle that straight, parallel lines have the 
 same vanishing-point is absolutely necessary to the illus- 
 trator. 1 
 
 Application of Principles to Drawings of the Cube. 
 A cube with edges of four feet. Scale ]/% in. = I ft. 
 
 Figure 30. The cube with four edges vertical, its 
 lower face on the level of the eye, and one surface visi- 
 ble with its lower edge AB " not foreshortened." 
 
 The lower face appears a horizontal line. The upper 
 edge CD of the front face is farther from the eye than 
 AB, but unless the eye is very near the object, the face 
 will be foreshortened so little as to appear practically its 
 real shape. 
 
 Figure 31. A cube with its top/our feet below the cube 
 of Fig. 30. 
 
 The receding horizontal edges vanish at point C, the 
 centre of edge AB, because this edge is on the level of 
 the eye, and a line from its centre to the eye is parallel 
 to the edges. The front face is below the eye, and will 
 be foreshortened, as shown by Fig. 32, so that its appar- 
 ent height is less than its width. The edge EF is farther 
 
 1 Illustrators and artists, even the most noted, have made "parallel 
 perspective " drawings from the earliest periods. The influence of the 
 many strong painters who have used one vanishing-point when there 
 was no reason for not drawing what was seen, and making use of two 
 vanishing-points, probnbly accounts in large part for the frequent errors 
 of the illustrators of the present time.
 
 96 FREE-11AXD DRAIVIXC. 
 
 from the eye, and appears shorter than the edge GH. 
 It appears the length of 1-2. (This distance may be 
 found by means of a plan of the cube, the picture plane, 
 and the eye.) Connecting i-G and 2-H, the vertical 
 edges are represented by inclined lines. This is not satis- 
 factory. The model drawing must represent vertical edges 
 by vertical lines. If verticals are drawn from G and H, 
 the front face will seem too wide ; if from i and 2, it will 
 seem too narrow. The proper effect will be given by 
 verticals between these lines, or by verticals from G and 
 H, the line 1-2 being dropped a little. 
 
 The model drawing is not the exact drawing upon the 
 inclined plane, but this drawing corrected by substituting 
 vertical for inclined lines. 
 
 Figure 33. The cube with its vertical faces at 45 to 
 the picture plane, the top being on the level of the eye. 
 
 The top is seen as a horizontal line. The sides, since 
 at equal angles with the picture, appear of equal width, 
 and the edges A and B vanish upward at equal angles 
 which depend upon the distance of the eye. When hori- 
 zontal lines are at angles of 45 with a vertical picture 
 plane, the distance of their vanishing-points from the 
 centre of the picture, (that is, line E,) is the same as the 
 distance of the eye from the picture plane. 
 
 The entire width of the appearance is the perspective of 
 the diagonal 1-2 of the base of the cube, which is " not 
 foreshortened." This line is behind the picture plane, 
 
 Gcft
 
 (V 
 
 Figure 34. The cube, with its lower face on the le\-ei 
 of the eye, and its vertical faces extending to the left at 
 30, and to the right at 60. 
 
 The left face is nearest parallel to the picture plane, 
 and thus appears wider than the right face. The edges 
 A and 1! vanish downward at angles which depend on 
 the distance of the eye from the object, but the angle of 
 A must always be less than that of B. For equal dis- 
 tances of the eye, the width of the appearance must be 
 less.when the faces are seen unequally, than when they 
 are seen equally. The apparent width decreases as the 
 cube is turned toward the position in which only one 
 side is seen. 
 
 Figure 35. The cube with its vertical faces vanishing 
 equally, its top being four feet below the level of the eye. 
 * Here the sides appear of equal width, and the " angles
 
 verticals between these lines, ui u^ . 
 H, the line 1-2 being dropped a little. 
 
 The model drawing is not the exact drawing upon the 
 inclined plane, but this drawing corrected by substituting 
 vertical for inclined lines. 
 
 Figure 33. The cube with its vertical faces at 45 to 
 the picture plane, the top being on the level of the eye. 
 
 The top is seen as a horizontal line. The sides, since 
 at equal angles with the picture, appear of equal width, 
 and the edges A and B vanish upward at equal angles 
 which depend upon the distance of the eye. When hori- 
 zontal lines are at angles of 45 with a vertical picture 
 plane, the distance of their vanishing-points from the 
 centre of the picture, (that is, line E,) is the same as the 
 distance of the eye from the picture plane. 
 
 The entire width of the appearance is the perspective of 
 the diagonal 1-2 of the base of the cube, which is "not 
 foreshortened." This line is behind the picture plane, 
 
 &H 
 
 ' ^
 
 PERSPECTIVE PRINCIPLES. 
 
 97 
 
 and so does not appear its real length. The exact 
 length can be obtained by setting off the actual length of 
 the diagonal on a horizontal line through the lower end of 
 the front edge, and by drawing from its ends, lines to the 
 point opposite the eye. The intersections of these lines 
 with the lower lines of the drawing give the lower ends 
 of the side verticals. 
 
 Any known length can thus be measured on the pic- 
 ture plane, and carried into the picture by means of 
 parallel lines, which vanish at C, the point opposite the 
 eye. 
 
 Figure 34. The cube, with its lower face on the level 
 of the eye, and its vertical faces extending to the left at 
 30, and to the right at 60. 
 
 The left face is nearest parallel to the picture plane, 
 and thus appears wider than the right face. The edges 
 A and B vanish downward at angles which depend on 
 the distance of the eye from the object, but the angle of 
 A must ahvays be less than that of B. For equal dis- 
 tances of the eye, the width of the appearance must be 
 less.when the faces are seen unequally, than when they 
 are seen equally. The apparent width decreases as the 
 cube is turned toward the position in which only one 
 side is seen. 
 
 Figure 35. The cube with its vertical faces vanishing 
 
 equally, its top being four feet below the level of the eye. 
 
 |Q(X A/ t Here the sides appear of equal width, and the " angles 
 
 / 3. 
 
 Jk 
 
 I 
 
 f> r 
 ' J 
 
 > 
 
 />^o
 
 98 FREE-HAND DRAWING. 
 
 of inclination" and convergence are alike on each side of 
 the central edge. There are four parallel edges extend- 
 ing to the right, and four to the left. Parallel horizontal 
 lines appear to converge toward a point on the level of 
 the eye, and there will be two vanishing-points. Since 
 the edges are at equal angles with the picture, they will 
 incline at equal angles, and the vanishing-points will he 
 equi-distant on each side of the central edge. 
 
 In this position of the square, which is the base of the 
 cube, one diagonal, 1-2, is parallel to the picture (" not 
 foreshortened ") and appears a horizontal line. The 
 other diagonal, 3-4, appears a vertical line, and the 
 farther angle of the square seems directly over the nearer 
 one. M'hen the /<>/> of the cube is seen in this wa\\ the 
 risible sides alwavs appear of equal width. 
 
 The diagonals are perpendicular to each other, and it 
 is seen that if two lines are perpendicular to each other, 
 and one is "not foreshortened," the right angles appear 
 right angles. 
 
 Figure 36. The cube above the eye, its horizontal 
 edges extending to the left at 60, and to the right at 
 
 30. 
 
 Both sets of edges vanish at points in a horizontal line 
 at the level of the eye (called the horizon), the point at 
 the left being nearest to the drawing, for the line at the 
 greatest angle with the pie tare appears (lie sJiortest. The 
 diagonals of the horizontal surfaces vanish. Point 2 is
 
 N 
 
 S3 
 
 99 
 
 left. The 
 to be its 
 
 2, on the 
 ouml, the 
 tical face 
 
 when the 
 45 to the 
 >e vertical 
 s directly 
 i i and 2 
 >isect the 
 ht at the 
 spectively 
 .earer enil 
 i vanishes 
 ing-point, 
 ines. 
 
 below the 
 aring the 
 
 It is thus 
 , and the 
 nish more 
 .han tliose
 
 PERSPECTIVE PRINCIPLES. 99 
 
 the nearer end of 1-2, which vanishes to the left. The 
 other, 3-4, vanishes to the right, for 3 is seen to be its 
 nearer end. 
 
 Figure 37. The cube resting on an edge, 1-2, on the 
 ground, with four of its faces at 45 to the ground, the 
 eye being above the object, and the right vertical face 
 being visible. 
 
 The edge on the ground vanishes to the left, when the 
 right vertical face is seen. If four faces are at 45 to the 
 ground, the diagonals of the other faces must be vertical 
 and horizontal lines. The upper edge, 3-4, is directly 
 over the edge on the ground, and verticals from i and 2 
 contain 3 and 4. The horizontal diagonals bisect the 
 vertical diagonals, and vanish toward the right at the 
 level of the eye. Points 5, 6, and 7, 8, are perspectively 
 equi-distant from the vertical diagonals. The nearer end 
 of 5-3 is 5. This line vanishes upward, and 5-1 vanishes 
 downward. Parallel lines have the same vanishing-point, 
 and the other oblique edges vanish with these lines. 
 
 Figure 38. A cube resting on the ground, below the 
 eye, with its vertical faces visible and appearing the 
 widths AB and AC. 
 
 The face AC appears narrower than AB. It is thus 
 at a greater angle with the picture than AB, and the 
 horizontal edges extending to the right must vanish more 
 quickly, and at greater " angles of inclination " than those 
 extending to the left.
 
 100 FREE-IIAXD DRAll'lXG. 
 
 " 
 The Right Square Pyramid. 
 
 The axis of this pyramid is perpendicular to the base 
 at its centre. This point is found by drawing the diag- 
 onals. 
 
 Figure 39. When the base of the pyramid is horizon- 
 tal, the drawing may be tested by a vertical line from 
 the centre of the base. This should contain the vertex 
 of the pyramid. 
 
 When two sides, AB and CD, of the base are " not 
 foreshortened," they appear perpendicular to the axis, 
 and one side only of the pyramid is seen if it is long or 
 if it is above the eye. (Fig. 39.) If the axis is short or 
 wholly below the eye, three .of the triangular faces will be 
 visible, the two outer ones appearing alike. (Fig. 40.) 
 
 One, two, three, or four sides, or the base with one, 
 two, or three sides, may be visible at one time. 
 
 Figure 41. When two sides are seen, all the edges of 
 the base appear to vanish. When two sides appear 
 alike, the edges vanish at equal angles. The farther 
 slant edge is just behind the nearer. One diagonal of 
 the base, 3-4, appears to coincide with the axis of the 
 pyramid, and the other, 1-2, appears at right angles 
 to it. 
 
 Figure 42. When two sides are seen unequally, the 
 axis of the pyramid appears perpendicular to a line which 
 is parallel to the picture plane. A plan of the base and
 
 PERSPECTIVE I'KlXCiri.ES. 101 
 
 the picture plane will show the position of the line ab 
 with reference to points i and 2. It passes behind 2, the 
 nearer point, and in front of i, the farther point. When 
 the pyramid is vertical, ab appears horizontal. When 
 oblique, as in Fig. 43, the line ab has the same relative 
 position, passing in front of the farther angle of the base 
 i, and behind the nearer angle 2. 
 
 77ie Triangle, and tlic Triangular Prism. 
 
 Figure 44. When the triangle is equilateral or isosceles, 
 and its base is a horizontal line, the altitude of the tri- 
 angle is a vertical line, and intersects the centre^ of the 
 base. 
 
 Figure 45. When neither end of the prism is seen, its 
 long edges are " not foreshortened," and must be repre- 
 sented by parallel lines. Points i and 2 are in perpen- 
 diculars to the long edges, passing through the perspective 
 centres 3 and 4, of the lower edges of the triangles. 
 
 Figure- 46. When an end is seen with two sides which 
 appear alike, one edge, A, of the base is " not foreshort- 
 ened." The central, I>, of the receding edges appears at 
 right angles to this edge, and the end does not appear its 
 real shape. 
 
 Figure 47. When an end and a side are seen, the 
 drawing may be tested by a vertical line through point i. 
 This vertical should intersect 2-3, nearer 3 than 2, for
 
 102 FSEB-HAND DRAWING. 
 
 the nearer half of any retreating line appears longer 
 than the farther half. The edges of the end vanish in 
 the direction of their farther points, which are at once 
 seen except in the case of the edge 1-2. If line 3-7 
 appears to intersect the centre of 1-2, edge 1-2 is "not 
 foreshortened " and does not vanish. If 3-7 intersects 
 1-2 nearer 2 than i, point 2 is the nearer end of the edge 
 1-2. If 3-7 intersects 1-2 nearer i than 2, point i is 
 the nearer end. 
 
 The prism is so placed that the edges of the face on 
 the ground are at equal angles with the picture. The 
 length of the prism is twice that of the edge of its base. 
 The edges 2-3 and 2-6 vanish at equal " angles of incli- 
 nation." The nearer half of 2-6 appears as long as 2-3, 
 the farther half, a little shorter than the nearer. 
 
 The Regular Hexagon. 
 
 In the hexagon there are four sets of parallel lines, as 
 A, B, C, and D, in Fig. 48. Its diagonal, 0-4, is divided 
 into four equal parts by the diameters D and the diagonals 
 B and C. A drawing of this form will be tested by seeing 
 that the parallel lines vanish in the directions of their far- 
 ther ends, and that the diameters intersect the diagonal 
 so that the points in it are perspectively equi-distant. 
 
 Figure 48 represents the hexagon when its centre is at 
 the level of the eye, and it is " not foreshortened."
 
 PERSPECTIVE riUXCU'LES. 103 
 
 Figure 49 represents the plane after it has been revolved 
 away from the spectator about angle o. A vertical line, 
 the real length of a. diameter, through o, will be a side 
 of the rectangle shown in Fig. 48 enclosing the figure. 
 The receding sides of this rectangle vanish at the level 
 of the eye. The farther side is a vertical through 4, 
 whose position is determined by comparing the apparent 
 width of the foreshortened figure with its height. The 
 diagonals of the rectangle give the centre of the hexa- 
 gon. A vertical, /', through the centre, bisects the 
 rectangle, and diagonals from b to o anil 4 give points 
 5 and 6 in the diameters of the hexagon. The di- 
 ameters intersect the sides, giving the length of the 
 sides A. 
 
 Figure 50 represents the hexagon in the same position 
 as Fig. 48, except that a diagonal is vertical. 
 
 Figure 5 1 represents the foreshortened hexagon, when 
 revolved back about side A. The enclosing rectangle is 
 drawn as in Fig. 49. Its diagonals give the centre of the 
 hexagon, through which passes the diagonal parallel to 
 side A. Its ends, o and 4. are angles of the hexagon. 
 The vanishing lines D, from the nearer side A, give the 
 farther side. 
 
 Figure 52. The hexagon having been sketched from 
 the object, to test the drawing (assuming the diameter 
 Al] to be correctly placed), 
 
 Draw CD, which will be horizontal, (parallel to AB,) 
 
 \
 
 104 1-KEE-1IAXD DKA //V.V(/. 
 
 when point 4 appears over o. Draw AD and BC. See 
 that o-i is greater than 1-2 and 3-4 less than 2-3. 
 
 Figure 53. To test the sketch (assuming the nearest 
 side to be correctly placed), 
 
 Draw the diameters AC and Bl), and the diagonals 
 AD and BC, giving point 2. Through 2 draw 0-4. See 
 that the points on this line are equi-distant, actually equi- 
 distant when the line is "not foreshortened," and per- 
 spectivety so when the line vanishes. 
 
 The Hexagonal Prism and Pyramid. 
 
 Figure 52 may represent the top of a vertical prism, 
 two of whose sides will be seen equally when 4 appears 
 just over o. The side o-A inclines at the same angle as 
 o-J), at both the top and the bottom of the prism, though 
 the angles of the lower lines are greater than those of the 
 upper. "When two sides are seen equally and the prism 
 is not vertical, the directions of the lines o-A and o-J> may 
 be determined by means of the diameters AB and CD 
 of the hexagon, which appear perpendicular to the axis 
 of the prism. 
 
 Figure 53 may represent the top of the prism when 
 three of its vertical faces are seen, the two outer ones 
 appearing of equal width. ^Yhen thus seen, the edges 
 AT. and CD of the ends appear perpendicular to the 
 axis of the prism.
 
 PERSPECTIVE PRIXCIPLES. 105 
 
 Figure 54 represents the prism when three faces appear 
 of unequal widths. The narrower A is the farthest from 
 the eye. Points a ami c are thus farther from the eye 
 than b and </, and al> and <</ vanish to the left. The 
 parallel hori/.ontal lines of the ends vanish in four points, 
 which must be the same distance above the drawing (at 
 the level of the eye). The equal spaces on 0-4 appear 
 unequal. The vanishing of the parallel lines brings the 
 lower base of the proper width, it being greater in this 
 case than that of the top. The invisible end of a prispi 
 may appear wider or narrower than the visible end (see 
 page in). 
 
 Figure 55 represents a prism whose length is twice that 
 of the diagonal of its base. The prism rests on one face 
 on the ground, and is below the eye. The edges of this 
 fice are at equal angles with the picture. 
 
 The diameters of the ends are vertical lines and with 
 the diagonals a(> and <</, give points i, 2, 3, etc., which 
 are perspectively equi-distant. The narrower face A is 
 the more distant, point a is the farther end of o-<c and 
 the edge vanishes upward. The " angle of inclination " 
 of I'd is the same as that of df. The side 0-5 is per- 
 spectively twice as long as the diagonal 0-4. To fully 
 test, draw the invisible edges, and the diameters and the 
 diagonals of the bases. Continue all parallel lines to see 
 that they vanish toward one point. 
 
 The question may arise " Shall the nearer half of the
 
 106 FREE-HAND DRAWING. 
 
 diameter <?</, be represented by a greater distance than 
 the farther half?" ; omitting the convergence of the ver- 
 tical lines makes the equal distances, ac and c t /, equal in 
 the drawing. 
 
 Figures 56 and 57. The tests for the pyramid are the 
 same as for the prism and the square pyramid. When 
 three faces are seen, the outer ones equally, the axis 
 appears perpendicular to a diagonal of the base. When 
 two faces appear equal, the axis appears perpendicular 
 to a diameter. When two or three are seen unequally, 
 the axis appears perpendicular to a line between the 
 diameter and the diagonal, as in Fig. 42. 
 
 The Circle. 
 
 The circle appears its real shape when it is " not 
 foreshortened," and this means any position in which the 
 circle is seen in a direction perpendicular to the circle at 
 its centre. It appears a straight line when the eye is in 
 the plane of the circle. In other positions, in which its 
 entire circumference is seen, it appears an ellipse. If 
 we suppose the picture plane to be a plane surface, the 
 cone of visual rays will be intersected by it in a pei feet 
 ellipse, but if we suppose the picture plane to be a sphere 
 or other curved surface, the section will not be an ellipse ; 
 practically, the circle appears an ellipse. 
 
 Figure 58 is an elevation representing the eye, a
 
 PERSPECTITE PRrXCIPLES. 107 
 
 horizontal circle C on the level of the eye, and other cir- 
 cles, A, B, D, and E, above and below the level of the eye. 
 
 Figure 59 is a plan of the same. The circles are 
 tangent to a vertical picture plane. In the elevation, 
 lines to the ends of the horizontal lines representing the 
 circles, represent the visual rays, by which their appar- 
 ent heights are seen. These rays, intersecting the pict- 
 ure plane, give the short axes of the ellipses of Fig. 60. 
 In the plan, the lines tangent to the circle represent visual 
 rays, and intersecting the picture plane at i and 2, they 
 give the length, 1-2, of the long axes seen in Fig. 60. 
 
 As the circle is dropped or lifted from the level of the 
 eye, the length of the short axis increases, and within 
 ordinary limits this is true of the appearance of all 
 horizontal circles. 
 
 Figure 61 represents a square, two of whose sides are 
 " not foreshortened." A circle inscribed in the square 
 must be represented by an ellipse, tangent to the square at 
 its diameters in points i, 2, 3, and 4. The centre of the 
 square is at the intersection of its diagonals, and appears 
 nearer 2 than i. The centre of the square, that is, the 
 centre of the circle, is not the centre of the ellipse. In 
 other words, the diameter of the circle does not appear 
 as long as a chord in front of the diameter, and the long 
 axis of the ellipse is not a diameter of the circle. 
 
 Figure 62 is an elevation representing the eye, the 
 picture plane, and the ground, with the circle upon it.
 
 108 FREE-HAND DKAiriXG. 
 
 Figure 63 is a plan of the same, both views correspond- 
 ing with Fig. 61. The visual rays r, r, to points i and 2, 
 determine at the picture plane the short axis of the 
 ellipse. The line P, bisecting the angle between the 
 rays, gives the centre of the ellipse, and continued to 
 the ground, gives the position of the chord MM, which 
 appears the longest line of the circle. 
 
 The eye is above the ground, and thus in the plan, the 
 visual rays r, r do not come tangent to the circle at 
 points M and N. 
 
 All lines whose ends are unequally distant must appear 
 to vanish. In any circle there can be but one diameter 
 which is "not foreshortened." This is the one which is 
 perpendicular to the direction in which the circle is seen. 
 
 Such a horizontal line appears horizontal, and thus a 
 horizontal circle always appears a horizontal ellipse, tor 
 though the diameter does not appear the long axis of the 
 ellipse, it is parallel to the chord which appears the long 
 axis, and this chord is thus " not foreshortened." 
 
 The short axis of an ellipse is perpendicular to. and 
 bisects the long axis. The short diameter of the ellipse 
 appears a vertical line in the case of a horizontal circle, 
 and in any circle appears to coincide with a line per- 
 pendicular to the circle at its centre. 
 
 Conversely, the long axis of any ellipse appears per- 
 pendicular to a line which is at right angles to the plane 
 of the circle at its centre.
 
 PERSPECTIVE PRINCIPLES. 109 
 
 Figure 64. The vertical circle A, when its centre is 
 on the level of the eye, appears a circle, or an ellipse 
 whose long axis 3-4 is vertical, for a horizontal line on 
 the level of the eye appears horizontal, and this line 
 determines the direction of the long axis of the ellipse. 
 
 B and C are vertical circles of the same size as A, 
 directly over and under A, and in the same plane. 
 Horizontal lines, perpendicular to these circles at their 
 centres, vanish at the level of the eye. These lines 
 determine the directions of the long axes 7-8 and 
 ii-i2 of the ellipses which represent B and C, and it is 
 seen that the axis cf an ellipse which represents a verti- 
 cal, foreshortened circle, on any level except that of the 
 eve, must be an inc/incif line. 
 
 The circles, being of the same size and in the same 
 vertical plane, will be tangent to two vertical lines which 
 are represented by vertical lines R and S. In order 
 that the upper and lower ellipses shall be tangent to 
 R and S, their short axes, 5-6 and 9-10, must be shorter 
 than 1-2, that of the central ellipse. The width of the 
 ellipse decreases as a vertical circle is raised or lowered. 
 
 The long axes 7-8 and 11-12 appear a little shorter 
 than 3-4. Whether this difference shall be represented 
 or not is a question similar to that considered on 
 page 51.
 
 110 FREE-HAND DKAM'IXG. 
 
 The Cylinder. 
 
 When an end only is seen, it is " not foreshortened," 
 and appears its real shape. If an end and the curved 
 surface are seen, the end is foreshortened, and appears 
 an ellipse. Less than half the curved surface of the 
 cylinder can be seen at one time. 
 
 Figure 65. When one end of the cylinder appears a 
 straight line, the other appears an ellipse, B. 
 
 When neither end surface is visible as a straight line, 
 or as a surface, both ends appear narrow ellipses. The 
 cylinder A is then " not foreshortened." 
 
 When one end of a vertical cylinder is visible, the 
 other is invisible, and appears a wider ellipse than the 
 visible end (see C and D). 
 
 The elements of a vertical cylinder appear to converge 
 when the cylinder is not on the level of the eye, but are 
 represented by vertical lines. 
 
 The long axis of the ellipse representing any circle is 
 perpendicular to a line which is at right angles to the cir- 
 cle at its centre. In the cylinder this line is its axis, 
 and in any drawing of the cylinder the long axes of the 
 ellipses must always be at right angles to the axis of 
 the cylinder. Generally, the fact that the centre of the 
 ellipse is not the centre of the circle may be disregarded, 
 and the line connecting the centres of the ellipses be con- 
 sidered the axis of the solid.
 
 PERSPECTIVE PRINCIPLES. Ill 
 
 The visible end of any cylinder is nearer the eye than 
 the invisible, which must thus appear smaller than the visi- 
 ble. The elements connecting the two ends appear to 
 converge, as any parallel lines. The question of the com- 
 parative widths of the visible and the invisible ends has 
 caused much trouble. Figures 22 and 23 show that the 
 wUths are dependent upon the position of the cylinder. 
 When it is at an angle less than 45 with the picture, the 
 invisible base appears the wider, as in the vertical cylin- 
 der as generally seen. When the cylinder is at a greater 
 angle than 45 with the picture, the invisible base appears 
 the narrower. This, however, is not exact for angles near 
 45, and refers to common positions of the object. For 
 unusual conditions, as a very long object near the spec- 
 tator, or for a number placed in a line extending for 
 some distance, it cannot apply ; as the distortion caused 
 by the use of any one picture plane would then be very 
 great. It is best not to attempt to draw an object which 
 is so near as to create a visual angle of over 30. 
 
 Figure 66. The invisible base A is always at a less 
 angle to the plane which gives the appearance than the 
 visible B ; that is, the visual rays to the invisible base 
 make greater angles with it than those made by the vis- 
 ual rays to the visible base. The invisible base is nearer 
 to the position in which it is " not foreshortened " than 
 the visible, and though it appears narrower than the 
 visible base, when the cylinder is at a greater angle than
 
 112 FREE-HAND DRAWIXC. 
 
 45, it also appears shorter, and always appears propor- 
 tionally wider than the visible. This is the only rule that 
 can be given. The difference between the apparent sizes 
 depends upon the distance of the eye, and decreases as 
 the distance increases. When the distance of the eye is 
 short, the difference is marked. 
 
 Figure 67 represents a horizontal cylinder on the level 
 of the eye. The cylinder extends to the left at 45 with 
 the picture, and its base extends to the right at the same 
 angle. Its length is twice its diameter. 
 
 The short axis 1-2 of the visible end A is a perspec- 
 tive half of the element 1-3. The contour elements con- 
 verge toward the left. 
 
 Figure 68 represents the same cylinder, still at 45 to 
 the picture, but inclining upward to the right instead of 
 being horizontal. 
 
 The appearance is the same as that in Fig. 67. An 
 object at an angle with the picture will present the same 
 appearance as long as this angle is unchanged. It may re- 
 volve through a circle, and the only change is in the posi- 
 tion of the appearance with reference to a horizontal line. 
 
 Figures 69 and 70 represent horizontal cylinders 1! and 
 C, respectively over and under, and the same size as the 
 horizontal cylinder A in Fig. 67, which is here repre- 
 sented by dotted lines. The ends are circles situated as 
 those in Fig. 64, and the ellipses representing them must 
 be tangent to two vertical lines.
 
 PERSPECTIVE PRINCIPLES. 113 
 
 Figure 71 represents a horizontal cylinder below the 
 eye, and extending directly away from the spectator so 
 that its axis appears a vertical line. 
 
 The end appears an ellipse, whose long axis being at 
 right angles to the axis of the cylinder is a horizontal 
 line. The tendency is to represent the end by a circle 
 but it can appear so only when no part of the curved 
 surface is seen. 
 
 Figure 72 represents a cylinder of the same size and 
 parallel to that of Fig. 71, the ends of the cylinders 
 being in the same planes. 
 
 In Fig. 71 the elements converge on the level of the 
 eye. To this point the axis and elements of the parallel 
 cylinder appear to extend. The centres of the ends are 
 best represented by points in horizontal lines through the 
 centres of the ends of the first object. The long axes of 
 the ellipses pass through these points perpendicular to 
 the axis of the cylinder. The short axes will be shorter 
 than those of Fig. 71, for the ellipses must be tangent to 
 horizontal lines, which are tangent to the ellipses of 
 Fig. 71. 
 
 The Cone. 
 
 The cone appears a circle when its axis would appear 
 a point ; a triangle, when its base is seen as a straight 
 line. The entire curved surface is visible when the 
 cone points toward the eye ; none of the curved sur-
 
 114 FKKE-IIAXD HK A II' IXC,. 
 
 face is seen when the cone points directly away from 
 the eye. Between these positions any part of the 
 curved surface may be visible, the circle appearing an 
 ellipse. 
 
 The base of the cone being at right angles to the axis 
 as in the cylinder, it appears an ellipse whose long axis is 
 perpendicular to the axis of the cone. The contour ele- 
 ments must appear tangent to the ellipse of the base. 
 
 Figure 73 represents three cones of the same size, 
 A, B, and C, on a horizontal surface below the eye. 
 
 Cone A is vertical. The long axis of the ellipse of 
 the base appears horizontal. The contour, elements arc 
 tangent to the ellipse above its long axis, showing that 
 more than half of the ellipse represents the visible edge 
 of the base. 
 
 Cone B rests on an element on the ground. The 
 base is visible, and appears wider than that of A. The 
 axis thus appears shorter than that of A, and noting 
 the tangent points of the elements, we see that less than 
 half the curved surface is seen. 
 
 Cone C inclines toward the spectator. Its base 
 appears wider and its axis shorter than that of B. Much 
 more than half the curved surface is seen. 
 
 To draw the cone, cylinder, or any similar object, 
 the methods explained on page 33 should be followed. 
 The mass should be drawn first, and visible lines before 
 imaginary ones. The axis, (which is an imaginary line,)
 
 PERSPECTIVE PRINCIPLES. 115 
 
 should not be drawn first, as is often recommended. 
 After the position and proportions have been obtained, 
 the axis may be indicated as a test before the drawing 
 is accented, but on no account should this line be drawn 
 first. 
 
 Concentric Circles. 
 
 Concentric circles appear ellipses whose long axes 
 are parallel, but since the centre of the circle is not the 
 centre of the ellipse, the long axes of the two ellipses 
 will not coincide. 
 
 Figure 74 represents in perspective and half plan 
 concentric squares with tangent circles, the inner ones 
 being half the diameter of the outer. 
 
 The angles of the inner square are in the diagonals of 
 the outer, and are given in perspective by drawing the 
 receding sides of the inner from the points 2 and 3 of 
 the half plan. EF is the short axis of the ellipse tangent 
 to the larger perspective square. GH, the short axis of 
 the smaller ellipse. The long axes bicect the short, and 
 it is seen that AP>, that of the larger ellipse, comes in 
 front of the centre of the square O, and also in front of 
 IK, the long axis of the smaller ellipse. 
 
 Points E, G, O, H, and F are equi-distant in the 
 diameter of the larger circle, and divide it into four 
 equal spaces, which appear perspectively equal. The 
 diameter CD of the circle is " not foreshortened," and
 
 116 1-KEE-UAXD DKAM'IXG. 
 
 the equal divisions upon it appear equal. The diameter 
 CD is not the long axis of either ellipse, but is parallel 
 to them, and generally there is so little space between 
 them that practically we may say that the equal divis- 
 ions on the diameter of the circle appear in the long 
 axis of the ellipse, and if the distance Al between the 
 ellipses, measured horizontally, is one-fourth of the 
 entire long axis Al>, the distances EG and HF are per- 
 spective fourths of the entire short axis EF. 
 
 The apparent distances at front and back, between 
 ellipses representing concentric circles, are always the 
 same perspective parts of the entire short axis, that the 
 distances between the ellipses on the long axis are of 
 the entire long axis. 
 
 The distance between the long axes of the ellipses is 
 equal to one-half the difference in length of HF and 
 EG. 
 
 Figure 75 represents concentric circles more nearly ;-s 
 they generally appear, the distance FG being but little 
 shorter than Al, and the long axes of the ellipses thus 
 being very near together. The distance 5-6 is one-sixth 
 of the axis 0-6, and shows that the spaces A1J and FG 
 must be perspective sixths of the short axis AG. The 
 drawing shows that the retreating parallel circles do not 
 appear to converge except beyond the centre of the cir- 
 cle. Thus, curved parallel retreating lines 'may appear 
 to converge or diverge.
 
 PERSPECTIVE PRINCIPLES. 117 
 
 Figure 76 represents a circular ring, a cross-section of 
 which is a square. 
 
 The circles are concentric on each side of the ring. 
 The distance 4-8 is actually one-seventh of the long axis, 
 and the distance 2-9 is a perspective seventh of the short 
 axis. The square which is the section of the ring appears 
 very nearly its real shape at the ends, the horizontal 
 side 4-8 appearing a little longer than the vertical 3-4. 
 The distance 1-2 at the front, is longer than 3-4, and at 
 the back 5-6 is a little shorter. The invisible lines should 
 always be sketched, so that the lines which are seen may 
 have the right direction. Care must be taken not to 
 exaggerate the distance between the long axes of the 
 ellipses. In many cases it will not be necessary to draw 
 more than one line as a test for both ellipses. 
 
 Tlic Frustum of the Pyramid and the Cone. 
 
 When any pyramid is cut by a. plane parallel to its base, 
 the section is similar to the base and the lines of both 
 figures are parallel. 
 
 Figure 77 represents the frustum of a square pyramid. 
 This is a form frequently found in furniture, chairs, tables, 
 etc. The drawings from these objects may be tested by 
 seeing that the slant lines, when continued, meet at a 
 point over the centre of the base, and that the lines of 
 the upper base are parallel to those of the lower.
 
 118 FREE-HAXD DRAW IXC,. 
 
 Figure 78 represents the frustum of a cone below the 
 eye, with the larger base A visible. 
 
 The contour elements of the cone appear tangent to 
 the ellipses of both bases and, when continued, meet at a 
 point in the axis of the cone. The smaller base is invisi- 
 ble, and thus, being more distant, appears proportionally 
 wider than the visible. 
 
 Figure 79 represents the same object, but seen from a 
 nearer position, the ellipses appearing wider. 
 
 The contour elements are tangent to the ellipses farther 
 from the ends of their long axes, and thus less of the con- 
 vex surface is visible. A circle A, half-way between the 
 two bases, is represented by an ellipse tangent to the con- 
 tour elements, and perspectively half-way between the 
 ellipses of the bases. The nearest element of the 
 cone appears a vertical line and extends from its upper 
 end b away from the eye. Its centre i thus appears nearer 
 a than b. The farther element of the cone is nearer the 
 position in which it is " not foreshortened," and point 2 
 is practically midway between c and d. The width of 
 the ellipse is proportionally greater than that of the upper 
 ellipse, but less than that of the lower. 
 
 Figure 80 represents the cone with its smaller base 
 visible and a conical band about its surface. The ele- 
 ments are tangent to the ellipses behind the ends of 
 their long axes, and more than half of the convex sur- 
 face is seen. As already shown, the visible curved sur-
 
 PERSPECTH'E PRINCIPLES. 119 
 
 face 01 the cone may vary from none to all. Circles or 
 bands about the convex surface will be visible in the same 
 proportion as the surface of the cone ; less than half the 
 ellipses being seen when the larger base of the cone is 
 visible, and more than half when it is invisible. The 
 apparent thickness of the ring or band, at the short and 
 long axes of the ellipses, is given by the test for concen- 
 tric circles. 
 
 Figure Si represents a frustum of a cone and a circle 
 between the two bases. 
 
 The apparent width of bands A and B varies with the 
 angle of the cone and the position of the eye ; but this 
 is a question of little importance, for the proportions of 
 the ellipses can always be easily determined as explained, 
 and the ellipses being correctly placed, the spaces be- 
 tween must be correctly represented. 
 
 Figure 82 represents a dish of conical form. 
 
 The nearer side of the dish is foreshortened more than 
 the farther, and thus appears much narrower. The rela- 
 tive widths depend wholly upon the position of the eye. 
 If lifted, the front appears narrower until it is seen edge- 
 wise, and if farther raised, all the inner surface is visible. 
 
 An elevation of the object, representing the position of 
 the eye, the picture plane, and the visual rays will assist 
 in obtaining the proportions of the model drawing when 
 it is made without the object. When drawing from the 
 object, if the appearance of any part is not clearly under-
 
 1 >U l-REE-HAXD DR. 1 II r /NC . 
 
 stood, this elevation will often help to make the princi- 
 ples clear. 
 
 Figure 83 represents a double cone, composed of 
 intersecting cones A and B, whose bases are four inches 
 in diameter, and whose axes are six inches. The whole 
 length is eight inches. 
 
 The elements converge to points in the axis of the 
 double cone, which are equidistant from the bases and 
 from the intersection of the two objects. The smaller 
 circle is common to both cones, and the ellipse which 
 represents it must be tangent to the elements of both 
 cones. Less than half the surface of A and more than 
 half the surface of B is visible. It follows that the ele- 
 ments of the farther cone, B, must appear to intersect 
 those of the nearer one, A. When the cones are much 
 foreshortened this point is prominent, as in the sketch at 
 the left. 
 
 The Torus and Ring of Circular Section. 
 
 The torus is a convex moulding frequently found in 
 architecture, and in many common objects. 
 
 Figure 84. An easy way to draw this form is to sketch 
 the ellipses representing the circles, which may be con- 
 sidered its bases. The section of the surface connecting 
 these bases appears nearly its real shape at the ends 
 of the long axes of the ellipses. (The semicircle in this
 
 PERSPECTIVE rRIXCIl'LES. 121 
 
 position below the eye appears half of a horizontal 
 ellipse.) The curved contour of the moulding will be 
 represented by a line tangent to the semicircle, and 
 nearly so to the upper and lower ellipses, or, if the ellipses 
 are wider, farther above and below the ellipses. 
 
 Figure 85 represents the ring. This object will be rep- 
 resented by concentric circles, when it is "not foreshort- 
 ened," but when foreshortened, its outlines will not be 
 ellipses. This is due to the fact that the outer visual rays 
 are tangent in front below the centre of the ring, and be- 
 hind above the centre. Thus the line on the ring which 
 is on the contour is not a circle. When much foreshort- 
 ened, the inner outline of the farther part will pass behind 
 the outline of the nearer part, as in the drawing. 
 
 The centre line of the ring is a circle which, if seen, 
 would appear an ellipse. Suppose a sphere of the diam- 
 eter of the section of the ring to move, with its centre in 
 the circle, around the circle. The sphere would describe 
 the surface of the ring. The sphere will be represented 
 in all its positions by a circle. '\Yhen behind, by a circle 
 slightly smaller than when in front. The outline of the 
 ring must be represented by a line tangent to the circles 
 representing the sphere. Its outlines arc thus ray nearly 
 parallel to the ellipse representing the centre of the ring. 
 It should be noted that if a line is parallel to an ellipse, 
 it is not an ellipse. Parallel ellipses are impossible.
 
 122 FKEE-1IAXD DKA II /.\ G, 
 
 Frames. 
 
 In the frames of regular shapes are found concentric 
 polygons. The angles of the inner figure being in the 
 diagonals of the outer, this point enables us to test draw- 
 ings of these objects. 
 
 Figure 86 represents a cubical frame. 
 
 The diagonals of any face, as ABCD, contain the 
 angles of the inner square, any line of which being 
 drawn, gives points in two other lines. Any angle of the 
 object is an end of three lines. Thus, from E extend 
 EF, EG, and EL. Continue any inner line to an outer 
 edge of the object, and a point in the continuation of a 
 second inner line is found. Thus, EG continued to AB 
 gives point i, which is in IK, and EF continued to the 
 top, gives a point in an inner edge which extends to the 
 left. 
 
 Figure 87 represents an equilateral triangular frame. 
 
 The angles of the inner triangle are in perpendiculars 
 to the centres of the opposite sides. These lines inter- 
 sect each other at the centre of the triangle. Any side 
 of the inner triangle, as A, gives points i and 2 in the 
 other sides, B and C. Any side, as A, may be continued 
 to the outer triangle, giving 3. From 3 a parallel to the 
 short edges gives 4, which is in the edge D, parallel to A. 
 
 Figure 88 represents a square frame with a circle \ 
 tangent to the inner square.
 
 PERSPECTIVE PRINCIPLES. 123 
 
 The student will probably draw the long axis of the 
 ellipse representing this circle parallel to either the side 
 or the diagonal of the square. The long axis is parallel to 
 the side, when one outer side only, as B, of the square 
 frame is seen. It is parallel to the diagonal only when 
 two sides, as B and D, are seen equally. It is generally 
 parallel to neither. 
 
 The long axis is perpendicular to the axis of the cylin- 
 der, of which the circle is the base. The direction of the 
 axis of the cylinder is that of the short edges of the 
 frame. A parallel to these lines, through the centre of 
 the square, will be the short axis of the ellipse. The 
 ellipse is tangent to the square at points a, l>, c, and d in 
 vertical and perspectively horizontal lines through the 
 centre e. The long axis is perpendicular to, and bisects 
 the short, and comes in front of the centre of the square. 
 
 Figure 89 represents a reading-glass, and illustrates 
 the fact shown above, that the direction of the long axis 
 of the ellipse must not be referred thoughtlessly to any 
 other lines of the object. 
 
 The student who does not observe, will draw the long 
 axis of the ellipse in the direction of the handle of the 
 glass. It may, by chance, have this direction, but its 
 direction may be very different. The handle radiates 
 from the glass, as a spoke from its hub, and its direction 
 may be that of any one of the many spokes in the wheel. 
 
 Figure 90 is an elevation, and Fig. 91 a model draw-
 
 124 FREE-HAND DRA \VL\G. 
 
 ing of a cylindrical object having a moulding and grooves 
 about its surface. 
 
 Figure 90 represents the picture plane, and the visual 
 rays converging toward the eye. These rays intersect 
 the picture plane, and give upon it the positions of the 
 various points to which they pass. 
 
 The upper form, A, is that of the torus, explained on 
 page 120. 
 
 The central, B, is the reverse of this form. The cir- 
 cles appear lines, 5-6 and 7-8, in the elevation. The 
 rays to these points intersect the picture plane, and give 
 the short axes, 5-6 and 7-8, of the ellipses. The curved 
 lines N and M, if visible, end above the long axis ot 
 the ellipse. 
 
 Form C is that of the double cone, explained on 
 page 1 20. 
 
 ]~asr Forms. 
 
 Figure 92 is an elevation representing the vase shown 
 by the model drawing, Fig. 93, in which a common mis- 
 take is shown at the right side of the drawing, where the 
 line representing the body of the vase extends to the 
 long axis of the ellipse of the neck. The outline of 
 the body must at least pass tangent to the ellipse, as 
 at the left, and it may pass above the ellipse. The 
 neck of the vase thus extends inside the outline of the 
 body.
 
 PERSPECTIVE PRINCIPLES. 125 
 
 When the top of the vase is at right angles to the axis 
 its circles are concentric, and appear as in Fig. 75. 
 
 Figure 94. When a handle projects from the side of 
 the vase, its thickness breaks the outlines. When the 
 handle extends toward the eye, the line of intersection 
 appears fuller and more nearly its real shape, the more 
 the handle is foreshortened. 
 
 Figure 95 represents the bottom of a vase, whose 
 actual form is indicated by the light lines of the section. 
 The lines of the stem appear to end above the centre of 
 the ellipse, for any conical form which extends toward 
 the eye must have more than half of its surface visible. 
 
 Figure 96 is an elevation of a vase, the picture plane, 
 and the visual rays. 
 
 The rays, intersecting the picture plane, give the posi- 
 tions and the lengths of the short axes of the ellipses 
 representing the three plinths, A, B, and C. These 
 being drawn, the other lines of the model drawing, Fig. 
 97, are readily placed. 
 
 The curved lines of the neck appear above to intersect 
 the lower ellipse of plinth A, and below, they end above 
 the long axis of the upper ellipse plinth B. The body 
 of the vase is represented by a line tangent to or above 
 the lower ellipse of plinth B. 
 
 Figure 98 is an elevation of the lower part of a vase 
 with a spherical shaped body and a cylindrical base 
 having a curved moulding.
 
 126 FREE-HAND DRA ll'IXG. 
 
 The curved edge may be drawn as the torus. The 
 body of the vase is represented by a line tangent to the 
 ellipse of the upper base of the plinth, at points depend- 
 ing upon the position of the eye. When the ellipses are 
 narrow, the line will be tangent near the ends of the 
 ellipse, as in Fig. 99. 
 
 When wider, the tangent points may be near the short 
 axis (Fig. TOO). If still wider, the curve of the body 
 appears a continuous line covering part of the base (Fig. 
 101). 
 
 Figure 102 is an elevation of a vase whose appearance, 
 (to the eye situated at the point of convergence of the 
 visual rays,) is given by Fig. 103. 
 
 The elevation gives the positions and lengths of the 
 short axes of the ellipses representing the different circles. 
 The long axes are shorter than the actual diameters of 
 the circles, because they are behind the picture plane. 
 The upper edge of the vase is conical. The short, 
 straight lines, a, a, tangent to the two ellipses, B 
 and C, will be seen until the larger ellipse C is wholly 
 visible. 
 
 The student who has a knowledge of Orthographic 
 Projection may test his ability to draw from a description 
 of the form and its position, by taking any sheets of pro- 
 jection showing objects one after another, supposing the 
 objects to be seen from a certain point, and making 
 model drawings which shall represent them. Thus, Fig.
 
 PERSPECTIVE PRINCIPLES. 127 
 
 104 represents several objects, and their relations to each 
 other, and the planes of projection. 
 
 Figure 105 is a model drawing of the same, and sup- 
 poses the objects to be seen from the left and from 
 above, so that three faces of the cube are visible. 
 
 The cube is the first object, and any drawing which 
 shows the top, front, and left sides, answers the require- 
 ments. When the cube is correct, the ground-line which 
 is parallel to the edges extending to the right should be 
 drawn. 
 
 The cone is the next object. Its base is a circle of 
 the same diameter as the base of the cube. The best 
 way to place the ellipse, which is the appearance of this 
 circle, is to draw a square whose sides are parallel to 
 the base of the cube. The ellipse must come tangent 
 to the square at its diameters. The distance between the 
 cone and the cube is equal to half the side of the cube. In 
 perspective this distance 1-2 will be found by drawing the 
 diagonals of the right front face of the cube. Setting off 
 this distance on line AB, from 2 to 3, gives the nearest 
 angle of the square. Its sides extending to the right are 
 continuations of, and are perspectively equal to those of 
 the first square ; and the sides extending to the left are 
 parallel to those of the first. It should be remembered 
 that these lines continue, and vanish at right and left in a 
 horizontal line at the level of the eye, and all parallel 
 lines should be continued as far as the drawing will
 
 128 FREE-HAND DRAWING. 
 
 allow, so that they may be given the proper convergence. 
 The student should not attempt to have the vanishing- 
 points come on the paper. The diameters of the base 
 give the tangent points of the circle and square, and 
 through them the ellipse must pass. The circle is ]iori- 
 zontal, and the axis of the ellipse is a horizontal line. 
 The distance between the centre of the ellipse and the 
 centre of the square is so slight as to be hardly notice- 
 able. The long axis of the ellipse is, however, in front 
 of the centre of the square ; and in a larger drawing, 
 where the ellipse is wide, if the axis should be drawn 
 through the centre, the difference would be very notice- 
 able. The axis passes through the centre of the square, 
 and must be represented by a vertical line. Its length 
 is readily determined by reference to the vertical edges 
 of the cube, which are half as long as the axis. 
 
 The cylinder is next to be considered. The nearer 
 circle is in the plane of the front face of the cube, and it 
 will be best drawn by means of the square which circum- 
 scribes it. The sides of the square are parallel and equal 
 to those of the right front face of the cube. Of course 
 the distance 5-6 must be less than 3-4, as 3-4 is less than 
 0-2, and 4-5 is less than 2-3 (see Fig. 24). The 
 diagonals of the square give its centre, and through this 
 point the axis of the cylinder is drawn. The vertical and 
 horizontal diameters give four points in the ellipse, whose 
 long axis is a little in front of the centre of the square.
 
 PERSPECTIVE PRINCIPLES. 129 
 
 and at right angles to the axis of the cylinder. In the 
 same way, the farther end may be drawn. The length of 
 the cylinder being twice the side of the cube, the dis- 
 tance 7-8 is perspectively equal to 5-7. 
 
 The hexagonal prism is the last object. It is vertical, 
 with one face in the plane of line AB. A diagonal of 
 its base is parallel to AB. Its length may be placed on 
 AB, from 9 to 10, perspectively equal to 5-6, the dis- 
 tance 6-9 being perspectively equal to 4-5. Points n, 
 12, and 13, (dividing 9-10 into four perspectively equal 
 parts.) being placed, the diameters of the hexagon extend 
 from IT and 13 toward the left-hand vanishing-point. 
 The side 14-15 having been drawn, the diagonals 11-15 
 and 13-14 give the centre of the hexagon. Through 
 this point the diagonal parallel to 11-13 passes, and the 
 lines from 9 and 10 place in it the two remaining angles 
 of the base, 16 and 17. The left vertical face A appears 
 narrowest. This shows that 16 is nearer than 13, and 
 the diameter 16-13 inclines upward slightly from 16. 
 
 These drawings call for lines at definite angles with the 
 ground and the vertical plane. Such angles may be de- 
 termined by means of the cube, and for this reason it 
 will be well to draw this object first, even when it is not 
 called for. 
 
 The edges of the cube, Fig. 106, being perpendicular 
 to the two planes, the diagonals of its faces are at 45. 
 If smaller angles are desired, they can be obtained by
 
 130 FREE-HAND DRAWING. 
 
 subdividing the angles of 45. In making this division, 
 it must be noticed that equal angles never appear equal 
 u'hen occupying different positions u>ith regard to the pic- 
 ture plane. 
 
 Figure 107 shows that equal angles appear unequal, 
 and larger, the more the lines of the angles are foreshort- 
 ened, so that to divide Any angle, the part which is most 
 foreshortened must be represented by the greater angle, 
 and as equal angles approach the position in which they 
 are " not foreshortened," they will appear smaller. 
 
 By holding a triangular card, the student will see that 
 an angle less than 90 may appear greater than 90, 
 when its sides are much foreshortened. In fact, the small- 
 est angle may appear any angle up to 180. An angle 
 greater than 90 may in the same way appear any size 
 up to 1 80. 
 
 When the plane of the angle is foreshortened more than 
 the sides of the angle, the angle appears less than its real 
 size, and any angle may appear the smallest possible to 
 be measured. It is thus seen tliat an angle ma\ appear 
 an\ angle from the s in a I lex t up to 180 
 
 Such practice will more quickly than any other work 
 show the student whether he really understands the prin- 
 ciples, or has been merely memori/.ing them. The latter, 
 which unfortunately is the only way many study, will be 
 found entirely useless, and those who have been working 
 thus, must start again with the determination to see with
 
 PERSPECTIVE PRIXCIPLES. 131 
 
 their own eyes, and to accept nothing which they have 
 not verified by careful study. 
 
 The principles which have been explained enable one 
 to see as it is impossible to see without them, to draw 
 without the objects, to draw from memory, and to design 
 geometric forms of any size and in any position. They 
 are of so much value to the practical draughtsman that 
 he cannot afford to be without them, even were it very 
 difficult to obtain this knowledge. The principles are, 
 however, so simple that there is no excuse for violations 
 of the few essential ones ; yet such violations are found 
 very frequently, not only in the work of the amateur, but 
 also in that of the professional draughtsman. 
 
 Although the principles must be carried out in all good 
 drawings, theory alone should be depended upon only 
 when designing or drawing imaginary subjects. When 
 Nature can be studied, the rules may be applied after 
 careful consideration of the appearances, and it is not 
 intended or supposed that the principles will render this 
 study of Nature unnecessary. When understood, they 
 are of most value in assisting the mind to accept the 
 image of the eye, and arc unconsciously applied. 
 
 Rei'icii.1 of Important Principles. 
 
 Any line whose ends are equally distant from the eye 
 appears its real length. Any plane whose angles are 
 equally distant appears its real shape.
 
 132 FRl-.E-lIAXD DKAll'lXG. 
 
 2- Parallel, retreating lines appear to converge, or vanish 
 toward a point called their vanishing-point. 
 
 ? Of two parallel ami equal lines which do not vanish, 
 the nearer appears the longer. 
 
 u. Equal spaces on any retreating line appear unequal, 
 the nearest appearing the longest. 
 
 All lines whose ends are unequally distant from the eye 
 are lines which appear to vanish. 
 
 Horizontal, retreating lines, above the eye, appear to 
 descend, or vanish downward. 
 
 Y Horizontal, retreating lines, below the eye, appear to 
 ascend, or vanish upward. 
 
 X' Parallel, retreating horizontal lines appear to vanish 
 
 at the level of the eye. 
 
 4 A horizontal line at the level of the eye appears hori- 
 zontal, and a horizontal plane at this level appears a hori- 
 zontal line. 
 
 /(j The vanishing-point of any set of parallel lines is in a 
 parallel to them passing through the eye. Hence, to see 
 the vanishing-point of any lines, we must look in their 
 direction. 
 
 f~ Of two parallel and equal lines which are foreshortened, 
 
 the nearer may appear the shorter. 
 
 /^ Of two equal lines which are perpendicular to each 
 other and have one end common, the one at the greater 
 angle with the picture plane appears the shorter, and 
 vanishes at the greater angle.
 
 PERSPECTIl'E PRINCIPLES. 133 
 
 If one side of a square vanishes toward the left, the 
 other side vanishes toward the right. 
 
 When the sides of a square make equal angles with 
 the picture plane, they appear of equal lengths, and the 
 " angles of inclination and convergence " are equal. 
 /f The " angle of inclination " of any retreating line 
 depends upon the level of the eye and its distance from 
 the line, but it is always much less than the real angle 
 that the line makes with the picture. 
 
 / The convergence of parallel lines is in the direction of 
 their farther ends. These are points of the invisible 
 faces of any right square prism. 
 
 i*f If both ends of any edge are points of invisible faces, 
 the edge must be considered as " not foreshortened," 
 even if its ends are unequally distant from the eye. 
 y Straight lines must generally be represented by straight 
 lines, and vertical lines by verticals. 
 
 If two of the vertical sides of a cube or prism are seen, 
 ' both sets of horizontal lines appear to converge. 
 
 When one diagonal of a horizontal square appears a 
 vertical line, the other appears a horizontal line, and the 
 sides vanish equally in each direction. 
 ^/ When the pyramid is vertical, its vertex is in a vertical 
 
 line through the centre of the base. 
 & 2- The vertex of an isosceles or equilateral triangle is in 
 
 a perpendicular to the base at its centre. 
 ^ ^ The diameters and diagonals of the regular hexagon
 
 134 FKEE-HAXD DRAWING. 
 
 divide the diagonal which they intersect into four equal 
 parts. 
 
 The circle generally appears a circle, a straight line, or 
 an ellipse. 
 
 A horizontal circle, above or below the level of the eye, 
 appears a horizontal ellipse. 
 
 The centre of the circle does not appear the centre of 
 the ellipse, and the long axis of the ellipse is not a 
 diameter of the circle. 
 
 The foreshortened vertical circle, when above or below 
 the level of the eye, appears an ellipse whose long axis 
 is not a vertical line. 
 
 j & The long axis of the ellipse appears perpendicular to 
 
 a line which is at right angles to the circle at its centre. 
 
 o d Only one end of a cylinder can appear a straight line 
 
 at one time. The other end appears an ellipse. 
 3d If any of the curved surface of the cylinder with an 
 
 end is seen, the end does not appear a circle. 
 ?/ If the visible end appears an ellipse, the invisible end 
 
 appears an ellipse proportionally wider than the visible 
 end. 
 o ^ The long axes of the ellipses are perpendicular to the 
 
 axis of the cylinder. 
 
 ? 3 Any part of the convex surface of the cone may be 
 seen at one time. When the cone is vertical and below 
 the eye, more than half is visible ; when above the eye, 
 less than half.
 
 PERSPECTIVE PRINCIPLES. 135 
 
 ty When the base appears an ellipse, its long axis appears 
 perpendicular to the axis of the cone. 
 
 2j- The contour elements of the cylinder and cone appear 
 tangent to the ellipses of the bases. In the cylinder, 
 the tangent points are frequently not in the axis of the 
 ellipse. In the cone, they are never in the axis. 
 
 I/ The apparent distance, measured on the short axis, 
 between the ellipses representing concentric circles is 
 the same perspective part of the short axis that the dis- 
 tance between the ellipses, measured on the long axis, is 
 of the entire long axis. 
 
 3** The lines which represent a foreshortened vertical 
 
 * ring are nearly parallel to an ellipse which represents its 
 centre line. They are not ellipses. 
 
 a - The angles of two polygons, whose centres coincide, 
 and whose sides are parallel, are in the same diagonal 
 lines. 
 
 o An angle may appear of any size, large or small, 
 7 
 
 according to whether the sides or the plane of the sides 
 
 is foreshortened. 
 
 The above are most of the points essential to the draughtsman; 
 and those not teachers, and those unable to follow all the chapter, 
 and those not interested in the subject for itself, may find that the 
 review includes nearly all that they need.
 
 CHAPTER VII. 
 QUESTIONS FOR EXAMINATIONS. 
 
 To be answered by drawings, supplemented, if necessary, by writing. 
 Unless otherwise stated, all drawings are to be Model Drawings. 
 
 1. Illustrate by diagrams representing the eye, the 
 picture plane, and a sphere, the different positions of 
 the picture plane which produce " true " and distorted 
 pictures. 
 
 2. How do parallel retreating lines appear? Illus- 
 trate by a cube all of whose lines appear to converge. 
 Show by arrows the directions in which the lines vanish. 
 
 3. Illustrate by sketch of a cube the way parallel, 
 retreating horizontal lines appear. 
 
 4. Represent a horizontal square plane, whose sides 
 extend to the left at 30, and to the right at 60, when 
 the plane is on the level of the eye. 
 
 5. In any background, how is the position found of 
 the point where parallel lines appear to vanish? Illus- 
 trate by sketch of any room, with a box upon the floor, 
 and write any points which the sketch may not make dear. 
 
 6. How do vertical lines above the eye appear, and 
 how should they be represented ? Illustrate by sketches 
 of a cube. 
 
 136
 
 QUESTIONS FOR EXAMINATIONS. 137 
 
 7. Make a sketch of a cylinder or a square prism, 
 which shall show that the more distant of two parallel 
 and equal lines may appear the longer. Mark the 
 nearer line AB, the farther CD. 
 
 8. The " angles of inclination " of the lower visible 
 edges of a cube which is below the eye, and rests on a 
 face on the floor are equal. Represent the cube. 
 
 9. How do parallel straight lines in Nature appear? 
 Illustrate by representing the actual appearance of each 
 of three cubes, placed first, in a straight line upon the 
 floor ; second, in a vertical line, one being on the floor, 
 another on the level of the eye, and the last above this 
 level. 
 
 10. By sketches of the three cubes in the above 
 positions, show how straight lines should generally be 
 represented. 
 
 T i . Give the actual appearance of a horizontal cylin- 
 der whose length is 2, diameter i, 1 when below the eye, 
 and so placed that the left-hand base appears a vertical 
 line. 
 
 12. Show by a sketch of an interior when this appear- 
 ance would be the best drawing of the cylinder. 
 
 13. As a representation of simply the cylinder, what 
 drawing is better than the actual appearance? 
 
 14. Represent a cube above the eye, with four edges 
 vertical, when three of its sides are visible as surfaces. 
 
 1 The cylinder may be drawn of any size but of these proportions, 
 and the same for following problems.
 
 138 FREE-HAND DRAWING. 
 
 15. The same cube when a diagonal of its visible 
 horizontal face appears a vertical line ; and a vertical 
 square prism, whose length is 3, diameter i, having upon 
 it a square pyramid whose base is 2, axis 2. The axes 
 of the solids coincide, and the edges of the bases are 
 parallel. The lower base of prism on level of eye. 
 
 1 6. Above solids when the eye is on the level of the 
 centre of the prism, and a face of this object is "not 
 foreshortened." 
 
 17. The same solids and conditions, except that two 
 faces of the prism are seen equally. 
 
 1 8. A prism whose ends are equilateral triangles 
 whose sides are half as long as the prism, rests upon 
 a face upon the floor below the eye. The sides of the 
 face on the ground extend to right and left at equal 
 angles with the picture. The left base is visible. Show 
 all tests of the drawing, and the directions in which all 
 the lines vanish. 
 
 19. The same when the object is above the eye. 
 
 20. The same object when above the eye, and the 
 ends of its horizontal face are " not foreshortened." 
 
 21. A regular hexagonal card, horizontal and above 
 the eye, with one diagonal " not foreshortened." 
 
 22. The same card vertical and on the level of the 
 eye, and vanishing to the right. Its diameters are " not 
 foreshortened." 
 
 23. The prism shown in Fig. 55, when it is horizontal 
 and above the eye.
 
 QUESTIONS FOR EXAMINATIONS. 139 
 
 24. The same when it is below the eye, and horizon- 
 tal, with its long edges "not foreshortened." 
 
 25. The pyramid of Fig. 56 when it is above the eye, 
 with the diameters of its base "not foreshortened." 
 
 26. Place under the pyramid (Fig. 56) a cube, one 
 diagonal of its top coinciding with the marked diagonal 
 of the base of the pyramid. The square is to be larger 
 than the hexagon. 
 
 27. Represent when below the eye a horizontal hex- 
 agonal plinth, a square pyramid placed upon its top, and 
 a hexagonal pyramid resting obliquely upon the floor 
 and the plinth. 
 
 28. A cube with inscribed circles tangent to each 
 square, when below the eye with first, two surfaces 
 visible ; and second, three surfaces visible. 
 
 29. Show by a horizontal circle above the eye that 
 the centre of the circle is not represented by the centre 
 of the ellipse. 
 
 30. The long axis of the ellipse is what line of the 
 circle ? 
 
 31. How do equal spaces on any retreating line 
 appear? Illustrate by an "elevation." 
 
 32. A horizontal circle is seen by several persons who 
 are the same distance above, and away from the circle. 
 Does the same line of the circle appear to the different 
 observers the long axis of the ellipse? Illustrate by a 
 " plan."
 
 140 FREE-HAND DRAWIXG. 
 
 33. Sketch a spinning-wheel which is below the level 
 of the eye. 
 
 34. A vertical cylinder whose visible end is above the 
 level of the eye. 
 
 35. A horizontal cylinder on the level of the eye, the 
 cylinder " not foreshortened." 
 
 36. Why do not the long axes of the ellipses in Fig. 
 68 vanish? 
 
 37. Represent a horizontal retreating cylinder above 
 the level of the eye, and so situated that its axis appears 
 a vertical line. 
 
 38. A parallel cylinder on the same level and to the 
 right of the last object, the ends of the cylinders in the 
 same planes. 
 
 39. The retreating vertical side of a building which 
 has in it three semicircular arches in the same vertical 
 line, the eye on the level of the centre of the central 
 arch. (See Fig. 64.) 
 
 40. A vertical cylinder, diameter i, length 2, with a 
 cone upon it, the bases coinciding ; eye on level of the 
 centre of the cylinder. 
 
 41. A horizontal circle is represented by an ellipse, 
 whose long axis is 4" long, whose short is i" long. A 
 concentric smaller circle appears an ellipse which inter- 
 sects the long axis of the outer at points |" from its 
 ends. 
 
 42. Represent a horizontal retreating pipe below the
 
 QUESTIONS FOR EXAMINATIONS. 141 
 
 level of the eye Its inner diameter half of its outside 
 diameter. 
 
 43. A horizontal cylinder, diameter i, length 2, its 
 axis on the level of the eye, and extending to the right 
 at an angle of 45 with the picture, and a second equal 
 cylinder just below, its ends in the same planes as those 
 of the upper. 
 
 44. A vertical cone, resting upon the centre of a 
 horizontal square plinth whose vertical sides are seen 
 unequally, and a circular ring square in section, resting 
 obliquely against the plinth. 
 
 45. The pyramid of Fig. 77 when above the level of 
 the eye. 
 
 46. The same for the cone of Fig. 80. 
 
 47. A conical pail, of which the curved outer surface 
 with the inner surface of the bottom is visible. 
 
 48. A cuspidore of double cone form when below the 
 eye. 
 
 49. The double cone of Fig. 83 when it is horizontal, 
 below the eye, and at a large angle with the picture 
 plane. 
 
 50. The ring of Fig. 85 when it is vertical, and on 
 the level of the eye, and more foreshortened than in the 
 figure. 
 
 51. The frame of Fig. 88 when the axis of the ellipse 
 representing the tangent circle is parallel to a side, as B. 
 
 52. The same when the axis is parallel to a diagonal 
 of the square.
 
 142 FREE-HAND OR A \VI.\G. 
 
 53. A triangular frame when it is horizontal and 
 below the eye, with the most distant sides of the trian- 
 gles " not foreshortened." 
 
 54. A vertical, foreshortened hexagonal frame below 
 the eye. 
 
 55. A table with a square top and inclined legs. 
 
 56. A vertical cylinder below the eye, with a mould- 
 ing half round in section at the top, one square in sec- 
 tion at the bottom, and a groove square in section cut 
 in the centre of the cylinder. Diameter of cylinder i, 
 length 2. Width of bands |. 
 
 57. The vase of Fig. 92 when seen from below. 
 
 58. The same when seen from above, and very near 
 so that the ellipses are wide. 
 
 59. The vase of Fig. 96 when the bottom is visible. 
 6b. The same for Fig. 98. 
 
 61. The same for Fig. 102. 
 
 62. Sketch an interior representing the floor and two 
 walls, with a table or other objects. 
 
 63. The same, showing in addition the ceiling, or 
 horizontal objects above the eye. 
 
 64. Sketch an interior representing three walls and 
 furniture. 
 
 65. An interior representing one wall, with objects 
 parallel to the wall, and on each side of the spectator. 
 
 66. The same when spectator is near an end of the 
 wall.
 
 QUEST fONS FOR EX.-l ML\ T . I 77O.YS. 143 
 
 The following questions are for those who understand 
 Orthographic Projection and Scientific Perspection. 1 
 
 67. Illustrate the difference in appearance between a 
 perspective drawing of a cube placed at the left, below 
 the eye, and with one face parallel to the picture plane, 
 and a model drawing of the same. 
 
 68. The same for a cone at the right and vertical. 
 
 69. The same for a horizontal cylinder parallel to the 
 picture plane, and its right base visible. 
 
 70. Make a perspective drawing of a horizontal square, 
 which shall show that the perspective of a retreating line 
 may be longer than the line. Make a model drawing of 
 the same square. 
 
 71. Illustrate by means of the perspectives of a sphere 
 the distortion found in a Plane Perspective representing 
 objects above, below, or to the left or the right of the 
 point opposite the eye. State briefly the difference 
 between a Perspective and a Model Drawing. 
 
 72. Represent the objects shown by Figs. 104 and 
 105 when they are seen from the right instead of from 
 the left. 
 
 1 An illustrated pamphlet comparing Plane Perspective and Model 
 Drawing will be mailed on receipt of fifteen cents, to those teachers who 
 wish more on this subject than this book contains.
 
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 SUGGESTIONS FOR FIRST LESSONS IN THE PUBLIC SCHOOLS. 
 
 [These objects and similar ones should be studied in different positions until they can be well and easily drawn.] 
 
 Square Card. 
 
 Circular Card. 
 
 Square Card. 
 
 Triangular Card. 
 
 L 
 
 \ 
 
 Square Card. 
 
 Rectangular Card. 
 
 Rectangular C?.-d. 
 
 Rectangular Card. 
 
 Triangular Card. 
 
 Hexagonal Card. 
 
 Hexagonal Card. 
 
 Triangular Card. 
 
 Horizonla! and Vertical Squares. 
 
 Horizontal Squares. 
 
 Vertical Squares. 
 
 Horizontal Circles. 
 
 Vertical Triangles.
 
 (E 7 
 
 THE LIBRARY 
 UNIVERSITY OF CALIFORNIA 
 
 Santa Barbara 
 
 THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW. 
 
 MAY 3 1989 
 
 1989 H 
 
 Series 9482
 
 A 000 647 340 9