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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.
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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