Full text of "How To Use Creative Perspective"

DRAWING BY ALDREN A. WATSON FOR GULLIVER'S TRAVELS

Illustrated Junior Library
Gr asset & Dunlap, Publishers

HOW TO US

CT I VE

Ernest W. Watson

REINHOLD PUBLISHING CORPORATION

N*u> York

19 55

RKINHOUD PUBLISHING CORPORATION

J*rtt*d i I/JSU4., JLrffrvwry of Con&r+mm Cmtalop Cmrd A^tt-mber 5S-628O
second, pri-nting. 1957

This book is gratefully
dedicated to my wife Eve,
partner in its preparation

contents

INTRODUCTION 9

i MATERIALS AND PROCEDURES 17

ii THE STRUCTURAL APPROACH 25

Hi THE SQUARE AS A UNIT OF MEASURE 31

iv THE PICTURE PLANE 39

v THE CUBE 47

vi FORESHORTENING AND CONVERGENCE 51

vii THE CIRCLE 69

viii THE CONE 89

ix THE HOUSE OF SEVEN VANISHING POINTS 95

x FLOOR TILES 99

xi UP STAIRS AND DOWN 105

xii UP HILL AND DOWN 111

xiii THREE-POINT PERSPECTIVE 115

xiv REFLECTIONS 129

xv SHADOWS 133

xvi FURNITURE 141

xvii UNIVERSAL PERSPECTIVE 147

xviii FIGURES IN PERSPECTIVE 151

xix PROBLEM OF THE BRIDGE TRUSS 157

INDEX 158

introduction

awing by the author
an advertisement
Eldorado Pencils.

WHAT IS CREATIVE PERSPECTIVE?

The answer will be found in the work of top contemporary illustra-
tors whose work is reproduced and analyzed in this book. As their
pictures are studied, it will be seen that they are more dramatic and
more convincing because the artists took broad liberties with textbook
rules, often violating the academic methods of scientific perspective.

How to violate perspective (profitably) is fully as important for
a practicing artist as are the rules of perspective, which are quite
simple. When rules are violated and perspective effects are achieved
through the artist's own devices, his methods can be called "creative."

This book has been written for the student who, while in no less
need for thorough knowledge of academic method, ought also to learn
that by using perspective creatively he can bend it to his uses rather
than be limited always to strict conformity.

Another factor which makes this book timely is the very great influ-
ence upon picturemaking-hence on perspectiveof the airplane, the
cinema, and modern photographic concepts. They have introduced new
ways of looking at our familiar world, ways that have made us radically
revise some concepts of perspective appearance.

Then there is "modern art" which defies tradition and projects revo-
lutionary viewpoints into the art of picturemaking, freeing the artist
from slavery to conventions that formerly were considered inviolate.
All of these influences have made the older texts obsolete in part.

Although the creative aspects of perspective are emphasized in this
book, the academic precepts are demonstrated sufficiently to give the
student of freehand perspective what theoretical knowledge he needs
to have of conventional practice having in mind the beginner who first
needs step-by-step introduction to this subject.

Fifteenth century woodcut by an
artist who had no knowledge
of scientific perspective.

The facts of perspective, to repeat, are quite simple. They can be
learned readily by anyone of ordinary intelligence. The only difficulty
lies in their effective use by the artist. By effective use I mean some-
thing other than their correct application to picturemaking in a photo-
graphic sense. Such use may not be effective at all. Effective perspec-
tive more often than not is to be had in violation of photographic
reality and the so-called "rules" of mechanical procedure. (Through-
out the book the term photographic reality or photographic appearance
is used to refer to such a transcript of nature and objects as is recorded
by the camera.) Photography comes nearest to being what we see, or
think we see, with the physical eye. In reality, no picture photographic
or otherwise-can duplicate what our eyes see. For one thing, the
camera picture is recorded on a flat plate or film ; the retina of the
human eye is concave.

All pictures, we must recognize, are a compromise with what the
eye actually sees. The assumption in perspective theory is that the
artist's direction of sight does not change in the making of his picture.
As a matter of fact, it is never static; his eye restlessly darts here
and there over the entire area of the scene without being conscious
of doing so. It has to, because the eye can focus only upon a single
point and a very limited one-at one time.

In spite of this inconsistency, we have been taught to predicate our
method upon the erroneous assumption that every picture is in reality
the record of what can be seen without shifting the gaze from point
to point. We establish what is known as the center of vision f and give
the picture t plane a fixed relation to it. There are exceptions to this
procedure, as we shall see.

Some of the greatest art of past centuries-yes, most of it-has been
produced by artists who have been either ignorant of or indifferent to
scientific methods of representation. Long before the early Renais-
sance when modern perspective procedure was first used, painters
were employing a sort of perspective that suited their purposes very
well indeed. Some moderns might even maintain that truly creative
painters were better off without the "tyranny of rules" which, admit-
tedly, has weakened the work of many painters in periods when slavish
adherence to scientific perspective has been regarded as essential to
good picturemaking. Although unaware of the rules of perspective as
taught today, the old fellows knew enough about appearance to make
their pictures sufficiently realistic. The Chinese, the Japanese and all
oriental artists throughout the centuries got along very well without
perspective rules and gave the world much of its greatest art. But, in
recognizing this, we must at the same time remember that before the

"Abandoned Powerhouse" an oil painting by Julian Levy,
collection of A.L. Simmons.

In this picture the artist, being familiar with scientific
perspective, violated it for the sake of design.

invention of perspective the painter's public was used to these strange
to the modern eye-methods of representation. The entire concept
of picturemaking was quite unlike that of our present era, which
demands the appearance of reality in illustration as people have come
to conceive it in terms of photographic appearance. But even the
concept of photographic reality has recently changed. Modern photo-
graphic practice has accustomed us to the camera distortion of close-
ups and odd angle exposures which not so long ago would have violated
our sense of reality.

And modern art-I am speaking of painting now-f rowns upon nat-
uralism. The modernist actually flouts scientific perspective, goes out
of his way to avoid it. In this philosophy, nature painting is not art
at all and the further the artist gets away from it the better. At any
rate, perspective as used by the modernist is quite different from that
employed by the naturalistic or illustrative painter. The latter uses
perspective to give a realistic appearance of distance of going back
into the picture. The modernist distorts scientific perspective in order
to flatten out the depth effect into two-dimensional pattern. He tries to
keep his painting "on the picture plane" ; that is, on the surface of the
canvas.

Conservative painters continue to employ perspective devices that
give emphasis to photographic appearance. But the best of these con-
servatives are by no means slaves to mechanical rules. They take many
liberties with perspective that to the layman's eye may not be obvious.

What I have just been saying applies particularly to the painter.
The illustrator's problem is entirely different; his function, usually,
is to depict the facts and events of the familiar world with as much
realism as possible. He must make his pictures look natural. Photo-
graphic perspective that is, scientific perspective is indispensable to
his purpose. Yet even the creative illustrator is not a slave to his per-
spective. Although he has to be thoroughly conversant with theory,
in practice he favors design when design is in serious conflict with
perspective. And he has adopted, to a considerable extent, the mod-
ernist's intentional distortion. Such distortions have indeed become
a vogue in contemporary drawing. A large body of present-day illus-
tration, which might be typified by Richard Erdoes' drawing, achieves
a liveliness and design distinction while it ignores perspective rules.
But Erdoes is as thoroughly versed in perspective as anyone could
be ; what is more, he could not have achieved the beauty of this "art-
less" drawing were he not a master of perspective.

The existing conflict between design and perspective in picture-
making may be a new thought to beginners, but the serious art student

"Street Scene in Morocco"
from Column Magazine, by Richard Erdoes.
An exciting drawing by a top
illustrator, in which scientific
perspective has been flouted for the
sake of an amusing design.

soon becomes aware of it. More and more he discovers that the demands
of designthat is, the arrangement of lines and tones needed for
effective composition and for the clear expression of his idea force
him to violate perspective rules ; and his picture actually may be more
convincing when his lines do not conform to photographic reality.

Every one who draws or paints, in whatever manner, ought to be
completely conversant with the laws of scientific perspective. Unless
fortified with this knowledge the artist is ill-equipped either to draw
accurately or to take liberties with the facts of appearance. The great
majority of artists, and all illustrators even those who most often
seem to do without it frequently are called upon to put the facts of
scientific perspective to meticulous use in their work. Without intimate
knowledge of it and great skill in its practice, no one can pose as a
professional illustrator.

In all learning processes there is theory and there is practice. Each
is dependent upon the other : they should go hand-in-hand. The busi-
ness of the author and teacher is to present theory ; practice is up to
the student. In the classroom the instructor can dictate to his students
the kind and extent of practice he considers necessary ; on the pages
of a book he can only advise.

So, I advise the serious student of perspective to spend a great deal
of time putting into practice the procedures demonstrated on these
pages. He will need a lot more than the reading and understanding
of the theory that he will find set forth in this book. He will need
practice, and plenty of it. One acquires skill in drawing only by draw-
ing, drawing, drawing and more drawing.

By way of emphasizing the effectiveness of concentrated practice,
I am tempted to offer my own learning experience during my first six
weeks of art study in The Massachusetts Normal Art School in Boston
(now the Massachusetts School of Art).

The first day of school we were ushered into a large studio, in the
center of which was a disordered pile of wooden grocery boxes of

Advertising drawing by Eric Fraser

for the American Rolex Watch Corporation.

A meticulously accurate drawing was

required for this particular

type of advertising illustration.

assorted shapes and sizes. Chairs and drawing tables -were arranged
in a wide circle around these uninspiring models. We were directed to
draw the boxes. That was our only instruction; we were given no
perspective theory, no hint of any kind of procedure.

We assumed that this exercise was merely a device to keep us occu-
pied during the confusion of the opening day, and we looked forward
expectantly to the morrow when something more exciting would be
forthcoming, perhaps drawing from a living model. Imagine our dis-
may to find the situation unchanged except that the boxes had been
knocked about a bit. We were told to draw them in this new arrange-
ment. The next day it was the same, and the next. Sometimes each
drawing was limited to an hour, sometimes to two hours. A monitor
was chosen to rearrange the boxes at stated intervals.

This went on for six weeks without any theory -whatsoever! We
were told nothing about foreshortening or about convergence of lines ;
"we were merely instructed to draw what we observed. The accuracy of
our observation, I should explain, was checked and corrected by the
instructor who admonished us to use our eyes more expertly. At the
end of six weeks we were finally taught the scientific facts of perspec-
tive appearance.

When, years later, I began teaching perspective at Pratt Institute,
I remembered this grueling and uninspiring six weeks, and I was
critical of the method. I reasoned that it would have been better had
we, at the outset, been given some theory that would have warned us
what to look for as we drew those rectangular forms day after day.

I soon changed my opinion. I discovered that my own students very
readily mastered the theory I was offering them, but still they couldn't
draw. That was because they lacked the very attitude that was forced
upon me by that six weeks' grind which taught me so well how to
use my eyes. I came to the conclusion that theory and practice should
be mixed in the proportion of 1 part theory to 50 parts practice, and
I suggest to the reader that this premise be kept in mind.

Much drawing from objects without dependence upon theory cul-
tivates the habit of three-dimensional thinking. One acquires the feel-
ing of form : the feeling of lines and planes actually receding and not
merely fooling the eye by their direction or shape on the paper. The
professional artist forgets the surface of his paperthe picture plane
as soon as he begins to draw or paint upon it. When he sets down lines
or masses to represent distance he actually thinks and feels distance.
He projects himself right through the paper, figuratively, into a limit-
less beyond.

In drawing the outlines of those boxes as they actually looked in
relation to each other, rather than trying to determine the convergence
of their lines by considering how they ought to look (according to the
vanishing points of perspective theory) we youngsters were getting
just the kind of training needed to develop the sense of "form in space,"
without which no one ever becomes a good draftsman.

I make a good deal of this at the outset because the beginner does not
realize how much practice he needs in drawing from objects. He is
likely, especially when a book is his instructor, to believe that the
theories set forth therein are his salvation. He does not fully appre-
ciate the truth that all theory can do for him is to offer certain mechan-
ical aids to his own observation and his own skills. Certainly he can
do without theory better than he can dispense with practice.

Today the illustrator makes extensive use of photography in his
work. And photographs of just about everything under the sun are
available for his useeven for copying, if he chooses. Does he need
an extensive knowledge of perspective, without which artists in pre-
camera days were helpless?

There are many occasions, it is true, when he can and does literally
copy his subject from photographs ; but the present-day illustrator still
needs as much skill in perspective as ever. Fred Ludekens once made
many illustrations for Hiram Walker whiskey. 'These involved the
drawing of innumerable barrels in all sorts of positions. Ludekens
thought his assistant, with photographs before him, might relieve
him of the tedium and time involved; in the end, Ludekens had to
draw the barrels himself.

As a teacher at Pratt Institute, I asked to have my first perspective
course labeled, Structural Perspective. That was to emphasize the
necessity of developing a structural sense, an engineering sense that
enables an artist to analyze every object, no matter how intricate, in
terms of its simple geometric basis.

The development of this analytical skill is really the most important
task before the student of perspective drawing. No matter how thor-
oughly conversant he may be with the facts of perspective appearance,
he will be quite incompetent without a large degree of this engineering
skill. Many problems that will seem very puzzling to the uninitiated
call for some very keen detective work, even by a mind that is trained
in a mechanical as well as a freehand approach.

6 Preliminary drawing by Albert Dome for his

illustration in color for Collier's.

Note the meticulous drawing of every detail,

demonstrating this master's amazing knowledge and facility as a draftsman.

This brings us inevitably to the use of mechanical views the cus-
tomary approach of engineers and architects. These include top, front,
side and sectional aspects of the subject which supply information that
is indispensable for much illustrative drawing. To deal with this con-
structive phase of our work we need to make use of at least elementary
instrumental drawing. And of course there are occasions when the
illustrator has to resort to somewhat involved instrumental strategy.
Such occasions may be the rendering of a factory interior or the nave
of a cathedral, projects that involve knowledge of instrumental per-
spective that can be found only in books wholly devoted to that subject.

It will of course be understood that no competent illustrator has to
follow the mechanical procedures that are here presented for purposes
of instruction in the solution of many problems. Such, for example, as
those demonstrated in the chapter on Shadows, and in the analysis of
Peter Helck's drawing. But it goes without saying that the procedures
involved are not only thoroughly understood by the illustrators but
that they are actually in operation at least in the subconscious mind.
Just as a skilled musician has long since mastered the elements of
his craft and can concentrate on the purely creative aspect of his art,
so the perspective procedures of a professional artist's work become
very nearly automatic.

There is such a phenomenon as "photographic vision." By this I
mean the gift possessed by a few artists of just naturally knowing how
to draw anything correctly without recourse to the kind of thinking
and analytical study here demonstrated. This however is a rare gift;
it is one that would better not be counted on by the student.

I believe the most valuable contribution of this book will be found
in the study of pictures by prominent illustrators reproduced on the
following pages and accompanied by analytical diagrams that demon-
strate the solutions to many different perspective problems. These
examples reveal the kind of resourcefulness and the graphic strategy
that enter into the illustrators' art.

It is said that Paolo Uccello (1397-1475), the Italian painter, was
largely responsible for perfecting the science of perspective. At any
rate he was hypnotized by it and, according to Vasari, he begrudged
time for sleeping and eating. He neglected his painting seriously and
when his wife remonstrated, he would only reply, "Oh, this delightful
perspective."

Of course I do not anticipate that my book will infect any readers
with that degree of fanaticism, but I do hope that it will help to make
the subject as pleasurable as it has been to me and to innumerable
students. For, when the study of perspective is given the right ap-
proach, it can be as fascinating as crossword puzzles or other games
that challenge the wit and stimulate the intellect.

Ernest W. Watson
January 1955

chapter i lr

MATERIALS AND PROCEDURES

Although we are dealing with freehand perspective in this book,
it will be necessary as explained in the introduction to use some of
the procedures of instrumental perspective in the development of our
experiments. Hence, the student should be supplied with the following
minimum items of equipment.

A drawing board about 16 by 24 inches is recommended. A piece of
illustration board the same size, tacked to one side, will give a pleas-
anter surface on which to work ; and when drawing on tracing paper,
the white illustration board underneath will be especially appreciated.

Drawing paper 16 by 12 inches or thereabouts is recommended for
many drawing exercises. Larger sheets will sometimes be necessary,
as smaller drawings-particularly when instrumental work is involved
will not be so accurate. The smaller the drawing, the greater the
probability of inaccuracy.

A T-square of good quality, and 45 and 30-60 degree triangles-all
of the transparent type-are essential. Two brass-edged rulers, one 24
inches long, a draftsman's compass and a pair of dividers will suffice
as a minimum instrumental outfit.

When making instrumental diagrams, pencils with leads of hard
degree are needed-H or 2H grades. These should be sharpened with a
knife to points much longer than are produced by mechanical sharpen-
ers. The leads should be kept well-pointed during all instrumental
work, in order to avoid inaccuracies that would invalidate the whole
procedure. For free sketching the softer leads will be preferred.

A large pad of tracing paper (about 19 by 24) is indispensable. Get
samples from your dealer and select the most transparent sheet. There
is a wide range of transparency in tracing papers. The student often
will want to lay the transparent sheets over photographs and repro-
ductions of artists' work, in order to analyze them by tracing the con-
verging lines and extending them until they find their vanishing points.
In this way much will be learned, not only of natural appearances as
recorded by the camera but of illustrators' strategy in changing the
rules to meet the needs of special situations. More about this later.

Many times, in making these analyses, it will be found necessary
to fasten several sheets of paper together with scotch tape in order to
secure a large enough area for the location of vanishing points which
may be some distance away from the picture on either side. In this
event, a yardstick may be substituted for the ruler in drawing the con-
verging lines. When the vanishing points are found to be even beyond

the edges of the drawing table, the drawing can be laid on the floor and
the lines projected by means of strings or threads extending from pins
stuck in the picture, as shown in fig. 7.

In such a case we might assume that the illustrator who made the
original drawing established his far-flung points by the same method.
However, the chances are that once he had established his vanishing
points with strings from two converging lines on each side, he resorted
to the following device to get directions of all other converging lines
without actually carrying them out to the far-flung points.

Extending a very thin wire string is unsuited because it stretches
from pins stuck in at the vanishing points (already located, as in fig. 7)
and attaching the other end to pencil points, arcs are inscribed on the
drawing board as shown in fig. 8. (Good wire, as fine as thread, comes
on spools.)

Templates are then cut with a sharp knife or razor blade, after
having traced the arcs made on the drawing board and transferred
them to thick cardboard. These templates are tacked firmly to the
drawing board so that the arcs of their curved sides coincide with
the arcs drawn by the wire compass demonstrated in fig. 8. Now the
blade of a T-square placed against the curved side of a template (fig.
9) will always radiate from the vanishing point as it is moved along
the arc ; that is, its center line will. All one needs to do is to remove the
bladeby removing the screws and reset it on the stock so that one
edge will be centered on the stock, as seen in fig. 10. Of course the
blade must be set at exact right angles to the stock. By moving the
T-square back and forth along the arcs, the direction of any line in
the perspective drawing can be quickly and accurately drawn.

When a vanishing point is on the drawing board, a pin stuck upright
at the vanishing point (as in fig. 11) will facilitate the drawing of
converging lines. The straightedge can be placed against the pin and
swung at any desired angle.

Fig. 12 demonstrates how strips of heavy cardboard, cut as shown,
can be attached by pins to the vanishing points and used in place of
the straightedge. Note that the pinhole in the strip must be in line with
its drawing edge.

In fig. 13 we see another device for finding correct line directions
when one or both of the vanishing points is beyond the edge of the
drawing board. The right VP (vanishing point) is within range; the
left VP is far out of bounds since the front lines of the cabinet are
nearly horizontal.

We extend the vertical line of the nearest corner (1-3) upward to
the eye-level (4). At any distance beyond the object at the left (the
further the better) we drop a vertical from the eye-level to converg-
ing line (A) whose direction has been determined freehand. This ver-

REILLY

tical (1A-4A) is shorter than the nearer vertical 1-4, but if it is
divided proportionately into the same divisions as 1-4 we have points
through which converging lines would pass on their way to their
vanishing points far to the left. Thus the top of the cabinet (3) is
half the height of 1-4. On the 1A-4A line we mark off a point (3A)
halfway up that line. Point 2 on the cabinet is one-quarter the height;
on 1A-4A we give 2A its corresponding position. Any number of meas-
urements on 1-4 can be duplicated proportionately on 1A-4A.

A camera and a projection machine are indispensable tools in the
contemporary illustrator's equipment. Still more indispensable is such
an inventive faculty as Frank J. Reilly brings to the solution of many
of his illustration problems, of which the subject of this demonstra-
tion is an examplea picture of a marshalling yard, which Reilly
painted for a Pennsylvania Railroad advertisement.

The picture illustrated the catch line, "An aircraft carrier goes by
rail, before it goes to sea." It dramatized the part the railroads play
in transporting material for the building and outfitting of a "flattop."

It was specified that a certain number of freight cars should appear
in the picture not as simple a result to achieve as one would imagine,
says Reilly.

After futile experiments with pencil sketches in an effort to include
the required number of cars, Reilly went to the lumber yard and
brought back to his studio an armful of wood strips approximately
one inch square in section. Upon these he marked off car lengths, care-
fully proportioning the lengths to the widths in order that his models
would be in correct scale. Then he laid the strips on the floor in parallel
rows to represent freight trains in a marshalling yard (fig. 15).

Reilly mounted a stepladder with his camera, and counted the num-
ber of "cars" that appeared upon the ground glass within a vertical
mask that he had carefully cut to the proportion of the advertisement.
Experimenting with the distance of his camera from the models, he
soon discovered the position from which to take a photograph that
would include exactly the specified number of cars, and allow for a
few locomotives and some empty track.

He pasted the 3% x 4% -inch print that resulted from this process
upon a large sheet of paper, tacked to his drawing board, and-
projecting the converging lines of the print located the three vanish-
ing points. The photo print was so small that all three points fell
within the area of the drawing board (fig. 16).

From each vanishing point he then swung an arc on the paper, near
the edge of the photographic print, as illustrated (fig. 16) .

The next step was to enlarge the picture to the size of the intended
painting. He did this in the following way. He made a photograph
of the photo print also the paper with the arcs upon which the print
was mounted; and, from the film, projected all onto the surface of

.VP 1

Advertising painting
for the

Pennsylvania Railroad
by Frank J. Reilly.

his paper (fig. 17). He then traced the main lines of the car models
on the projected enlargement with his pencil, tracing the arcs as well.

On the enlarged drawing (thumbtacked to a large drawing table) ,
templates cut of thick cardboard were tacked, their curved edges
identical with the arcs of the projected enlargement (fig. 18). The
T-square, traveling along the curved arcs of the templates as shown,
served for all converging lines, many of which, in addition to those
of the photographic print, were needed for the detailed drawing.
Note, however, the necessity of resetting the blade of the T-square
so that one edge of it bisects the stock and becomes what otherwise
would be the center line of the blade.

The lower vanishing point (fig. 19) is located in a vertical that
passes through the vertical lines of the picture-quite near its left
edge. Study the chapter on three-point perspective in connection with
this, pages 114-127.

The advisability-indeed the necessity-of drawing from models
cannot be overemphasized. For flat models (21 to 28) use a heavy card-
board that will not warp. The heavy cardboard will not do for three-
dimensional models that have to be scored, folded and assembled. For
these, select a reasonably heavy bristol board that is rigid enough not
to buckle and warp, yet is easy to work. A little experimenting with
papers will reveal the most suitable one.

If the flat, geometric models are used constantly by the student the
correct drawing of these basic forms will soon become second nature.
Take the triangle, for example. This figure, as demonstrated on later
pages, can be drawn quite easily by semi-mechanical procedure ; but
mechanical means can often be dispensed with by the student who
with sufficient practice has acquired an authentic visual concept
through practice drawing from the model (fig. 24) . It is safe to say
that one who makes 50 careful drawings from this model, turned in

all possible angles and placed at different heights in relation to the
eye, will have acquired a knowledge of this figure's appearance that
will serve him well in years to come.

The same can be said for models 25, 26 and 27 ; especially fig. 26. The
reason for this will be apparent later on when it will be seen how
important it is to know how to relate correctly the right angle (ABC)
to the circle seen in perspective (an ellipse).

The illustrator often has the problem of drawing several circular
objects that are lying on the ground. A splendid exercise as training
for this kind of assignment is drawing from dinner plates or phono-
graph records arranged on the table or floor. For some drawings use
plates of the same size, for others select plates of different sizes.

If drawing these models seems to be tedious .exercisecomparable
perhaps to the pianist's five-finger exercises the student who really
wants to learn how to draw will attack them eagerly since they assure
greater facility and authority in all subsequent work for the rest of
his life.

A four-inch model of a cube is easily made from stiff paper (see
diagram on next page) . After the flat pattern has been cut out a razor
blade and brass-edged ruler will do this best the parts marked for
folding should be scored. Scoring can be done with a letter-opener or
similar instrument. Fold so that the scoring is on the outside of the
model. Transparent scotch tape is ideal for securing free edges. Before
folding, inscribe a circle on at least one side and blacken it with india
ink. It is not necessary to make a paper model of a cylinder though
that is relatively simplebecause cylindrical cans and boxes of all
shapes and sizes are available in the kitchen.

The cone can be easily constructed as indicated on the next page.
After the base has been trimmed level (at right angles to the altitude)
a circular piece of heavy cardboard can be fitted to it and secured with
scotch tape.

Fig. 31 illustrates a model that is very important; a rectangle
preferably a square attached to a cylinder. This is another model
that ought to be drawn many, many times, turning it in all positions.
The importance of practice with the model will be evident in numerous
problems encountered in this book.

Sometimes special models like that pictured in fig. 33 are of great
help. The aim of such models is a geometric analysis of the object
rather than its facsimile. An analytical model is one which represents
the simplest geometric forms from which the object can be developed.
Oftentimes the most successful model is one which least resembles the
object, thus model 33 gives no hint whatever of the object for which
it was made the wagon wheels (fig. 36).

Another word about tracing paper. Illustrators make extensive use
of it. They often correct a first drawing on a sheet of overlaid tracing
paper. A third or fourth correction is frequently made in this way.
The final drawing is then transferred to illustration board for ren-
dering in any required medium.

Good transfers can be made by blackening the back of the tracing
paper with a 6B pencil and rubbing the tone smooth with the fingers
or a wad of tissue paper. Carbon paper is not practical because the
carbon line is hard to erase. A sharply pointed hard lead is used to go
over the lines of the drawing in making the transfer. If such a transfer
is carefully made, with sufficient pressure, transferred lines will be
so black and definite that it may not be necessary to go over them with
pencil or ink in order to strengthen them. Albert Dome paints colored
inks, which are transparent, right on top of such a tracing without
touching the transferred lines. In the reproduction they appear to
have been made with india ink. Another advantage of working on
tracing paper is the possibility of studying the drawing in reverse.
Errors are often detected and corrected in this way. Studying the
drawing in a mirror gives the same result, although without the same
ease of correction.

It goes without saying that those who draw a great deal from
objects, indoors and out, will make the most progress. A certain
amount of drawing from photographs is recommended too. These will
involve subjects presenting structural problems that otherwise may
not be brought to one's attention. But, it must be realized, photographs
are often distorted impressions, quite unlike the images the same
scenes would produce upon the retina of the human eye. Thus all pho-
tographs should be questioned in the light of what is demonstrated on
the following pages, as well as from one's own observation of things
seen and experienced. Comparisons of photographic effects with illus-
trators' drawings will prove interesting.

It is suggested that the student make a file of pictorial scrap illus-
trating the points covered in the various chapters. For example, when
working in the cylinder chapter, collect as many pictures of cylindrical
objects as possible. Analyze them on tracing paper overlays. This is
equivalent to enlarging the scope of the book and extending the oppor-
tunity it offers for study. Some may prefer to paste such scrap in a
loose-leaf notebook, along with analytical studies of the pictures.

The making of such picture collections will do more than anything
else to make one "perspective conscious," to cause one always to be
on the lookout for interesting applications of the principles being
studied, to observe and understand, not merely to see.

chapter ii

It will help the drawing student if he thinks of himself as a builder
or a structural engineer. While he does not handle wood, steel, or con-
crete, with his pencil he does construct on paper the forms created by
these materials. The more he can develop his engineering sense, the
surer and speedier will be the growth of his power as an illustrator.

Illustrative skill involves considerably more than the training of
the eye and hand to see and record the correct appearance of things
observed, essential as that is. There are those who can make reasonably
good drawings of things they are looking at, but who are lost when
they try to construct objects "out of their heads/' They have a photo-
graphic eye, but they lack imagination.

Imagination, as it relates to our problem, is the faculty of compre-
hending the structural basis of all objects. It is the ability to analyze
objects no matter how complicated or cluttered with detail in terms
of the simplest geometric forms to which they are related : the cube,
the sphere, the cylinder and the cone. It is the ability to see around and
through objects. The illustrator must possess an x-ray vision ; for him
there can be no invisible lines. Like the engineer he deals with plans
and elevations ; like the mechanical draftsman he develops the habit
of dealing with mechanical views top view, side view, front view,
and sectional view. These views give him information needed to clarify
his problem. This structural sense is his very first need ; without it,
knowledge of perspective principles will not amount to much.

I used to send my students out with their rulers and notebooks to
get structural facts of such objects as letter-boxes, furniture, the
concrete mixer at work on the street, a wheelbarrow, the newsdealer's
booth on the corner. They came back, not with perspective sketches of
these things but with top views, front views and side views, together
with their measurements. From this data they made perspective draw-
ings in the classroom.

Such exercises are a means of developing one's imagination and
an engineering sense. They constitute the structural approach. The
student will do well to follow this prescription for basic training. This
kind of study of simple objects such as those mentioned will provide
the right habit of approach to all problems, no matter how complicated
they might seem to be.

TO? VIEW

"Safety Poster."

Let us see how this structural approach applies to a few specific
problems. Take the elementary problem of a ladder leaning against
a building.

In the City Safety Council poster the painter is warned to set the
ladder at a safe angle. The artist, in drawing it, needs to "watch the
angle" in a different way. He has to visualize the ladder as one side
of a triangular prism pushed against the wall. Otherwise his drawing
is guesswork. There is no other way for him to test his drawing.

In fig. 38 we see the triangular prism correctly drawn, its base line
AB parallel with the sill line CD and converging with it to the right
vanishing point. (See Chaps. IV and VI for instruction on convergence
of parallel lines.) Hence we know that the foot of the ladder rests
where it should on the ground. In fig. 39 the error is obvious ; the ladder
rests in an impossible position, since AB is not parallel with CD as it
should be.

The engineering approach has to be applied to the drawing of as
simple an object as a mallet. The top and side views in fig. 40 tell us
that the handle is at right angles to the cylindrical head, and that we
find point B on a line extending from A into the cylinder's axis (D).

Getting the direction of the handle is the first step in the perspective
view. This is best done by drawing imaginary line AC, which is directly
under the handle on the ground. It is much easier to find point A by
this indirect approach. Line AC must, of course, be at right angles to
the cylinder's axis. There is no mechanical means of establishing this

A drawing by Thomas Rowlandson.

angle; it is a matter of freehand judgment. Whether the correct line
is the one shown in fig. 41 or whether one of the dotted lines is more
accurate is something that can be known only through the artist's
experience. It involves the ability to draw a right angle in any position
in relationship to the cylinder in certain positions. (See fig. 31, page
24.) The acquisition of this ability is of first importance to the student.
Once line AC has been established, the rest is mechanical procedure.
We have to cut a section, as it were, through the cylinder at its center
(fig. 42) in order to find point B.

The analysis and procedure in the hinged box cover (fig. 43) is one
that is applied to many situations, of which the open door (fig. 44) is
perhaps the most common.

The trained artist always looks for a simple geometric basis for
every object he draws. Thus the scotch-tape holder (fig. 45) obviously
is a combination of two cylinders with a cylindrical hole in the larger
one.

The proper way to draw the coach is shown in the analytical diagram
in fig. 46 ; a large cylinder for the rear wheels and a smaller one for
the front ones. It is natural and helpful to sketch an ellipse as a guide
for the drawing of the curved body line, although only an arc of the
ellipse is involved. Thomas Rowlandson, an 18th century English
artist, drew the accompanying coach. It is strange that an illustrator
who was such a perceptive observer and delineator of life and charac-
ter should have completely failed in the drawing of the wheels of his
coach.

B 49

8 51

FRONT VIEW
56

More Than 8,900 Advertisers Use T. &
To "Stffaw Their Advertising Program"

SIDE VIEW
57

The drawing in this advertisement

for Thomas Register

was made by illustrator W. N. Hudson.

HUDSON

Many times the solution of a problem is facilitated by imagining
that the object is carved out of, or contained within, geometrical solids.
The lawn sweeper (fig. 48) might be analyzed in this manner. Study-
ing its side view (fig. 49) we discover that the handle, extended to
the ground (A) forms a triangle ABC. If, then, we draw in perspective
a triangular prism (50) of correct proportion, we have a basic geo-
metric form which, if accurately drawn, solves our problem.

In order to draw that triangle in correct proportion we have to have
some way of measuring it. In the next chapter it will be seen that we
measure things in perspective by means of the square. Now we see in
fig. 51 that the rectangle (ABCD), which encloses the triangular
form, is wider than it is high. Fig. 51 demonstrates that it is one square
(AEGD) and one quarter in width. If, then, we construct a square
(AEGD) in perspective (fig. 52) and add a quarter square to it we
shall have a rectangle of correct proportion within which our triangle
is inscribed. The important thing here is to estimate properly the
square, a simple matter for one who, through much practice in drawing
squares, has acquired this facility.

In fig. 53 we draw the wheels, noting, by referring to fig. 49, that
they are of such size and in such position on the handle AC, that they
just touch a vertical at A. The completion of the drawing from this
point on is merely a matter of detail.

Now consider illustrator W. N. Hudson's problem when he was
asked to make the drawing of scales for the Thomas Register adver-
tisement. For this subject he did not have a model from which to draw ;
probably all he had to go on was a rough layout made by the art direc-
tor to indicate what was wanted or perhaps just a verbal suggestion.
So he had to build the scales ; that is, build them with his pencil.

In the first place, he had to design the scales much as an industrial
designer would do. This necessarily involved thinking about the object
in terms of "views," in order to establish the facts of its construction
in top, front and side view sketches (see figs. 55-57) . Probably he made
several such trial sketches, varying the proportions of the box, and
varying the size, the height and the position of the pans in relation
to the box. Doubtless he tried out these various designs in perspective
sketches before finally deciding on the one to use.

From the first, he would have automatically analyzed the problem
as a box set down between two cylinders (fig. 58).

Next, he would sketch the plan of the object in perspective as in
fig. 59-two circles with a rectangle between. Working from plans in
this way is common perspective practice. This is an important step
and it involves expert knowledge of what these geometric figures would
actually look like in perspective. A beginner attempting this would
do well to test his drawing by reference to models. (Two cardboard
disks or dinner plates and a rectangle of cardboard will serve nicely. )

Next (fig. 60), the box is drawn in correct proportion to the design
decided upon, and a vertical plane ( ABCD) is passed through its center
to establish the height of the two cylinders whose top circular planes
will be drawn as ellipses on the diameters, XY. The arms connecting
the pans with the box will be drawn in this vertical plane.

All that remains now is to draw the top ellipses of the cylinders.

It is not to be supposed that any professional illustrator would care-
fully go through steps similar to those outlined in this chapter for
simple objects which he could draw almost automatically. But the
kind of thinking here demonstrated applied to more complicated situa-
tions is indeed common professional practice.

chapter iii

THE SQUARE AS A UNIT OF MEASURE

An object must be measured before it can be represented accurately
in a drawing. This is as true in freehand sketching as in instrumental
drawing-. In instrumental work the exact dimensions must be known,
the lengths of all lines in feet and inches being required before the
draftsman can make his drawing either full size or to scale.

The artist making a freehand drawing must measure the object just
as carefully, but in an entirely different manner. He does not ask to
know the height, in feet and inches, of the building he chooses to
sketch ; nor is its exact width important to him. But he must know
the relative lengths of these lines the proportion of one to the other.
Proportion is, therefore, his principal concern in the analysis of his
subject. He must have some infallible method of measuring proportion.

The study of proportion has not been included in books on per-
spective, but it is so inseparably related to perspective in practice that,
logically, it should be a part of any program of drawing instruction.

The student is frequently seen holding his pencil at arm's length
and squinting his eyes as he moves his thumb along it in an effort to
measure the lengths of lines. The amateur feels confident in the efficacy
of this device. If the proportion of his drawing is criticized he is likely
to say, "It must be right ; I measured it." This method of measurement
is dangerous because it convinces the beginner he is right when he
is probably quite wrong. Pencil measurements are unreliable. An inch,
measured off on the pencil, represents an eight-foot window sill across
the street. To measure exactly is almost impossible: the hand is
unsteady ; it unconsciously moves closer to the eye at times ; the body
moves forward or back-ward slightly ; the pencil may not be at right
angles to the direction of sight. Any one of these imperfect conditions
can account for serious errors when % inch on the pencil represents
a foot of the line measured. In my classes, pencil measurements have
always been taboo.

How then shall the object be measured? In the first place there must
be a unit of measure. All scientific measurements are based upon some
logical unit of measure. For the purposes of the artist in measuring
proportion, the obvious unit of measure is the square. We can say,
truthfully, that the square is the only possible unit of measure, whether
or not the object is foreshortened.

Draw in outline a 2-inch square in india ink on a small piece of
window glass or transparent plastic. Hold this measuring glass up
and, closing one eye, look through the square at the building across
the street.* By moving the glass nearer or farther away, the size of
the square will conveniently appear larger or smaller and so will serve
as a measure for large or small areas. Remember that we are measur-
ing areas, not lines.

If you were thus studying the proportion of the gate (fig. 62), you
would find your square exactly fitting the gateway. The square would
enclose the chest of drawers (fig. 63). The outlines of the mantel
(fig. 64) would not fit in your square, but you will note that the fire-
place itself is a square. In making your sketch of the mantel you would,
therefore, start your layout with the square opening, it being a simple
matter to relate the other dimensions to it when the square is indi-
cated on the paper. Similarly in fig. 65, you would find a square at
once, and readily observe that the balance of the ornamental iron
screen above takes up one-half of a square.

Imagine now that you are in the garden about to sketch the garden-
house (fig. 66). You find that the square exactly encloses the entire
structure, except for the chimney and steps. And you note that the
eaves' line falls halfway down the square. The rectangular portion of
the ell does not quite fill the square-the dotted line in fig. 68 indicates
the top of the square but its window opening just fills your square
measure, as do the ends of the entrance steps (fig. 69).

SQUARE

The drawings on page* $2 through 35 were

made by the author in a aerie* of advertising drawings

for Eldorado Pencils. Courtesy Joseph Dixon Crucible Co.

*I have in my possession a square reducing glass, across the face of which are
engraved lines that cross each other at right angles, forming a series of smaller
squares. When viewing objects through this glass they are automatically measured
in terms othe square. The glass is of French manufacture and so far as I know
is unobtainable in this country.

Now measure the ballroom window (fig. 70). The shade is con-
veniently pulled halfway, making the measurement a simple matter.

Next let us study the Italian subject (fig. 72) . As you move the glass
about, letting the square play over the structure, the only square you
discover is the entrance portico. This square is too small to help much
in finding the proportion of the building. But, if by now you have be-
come "square conscious," you will quickly discover that the right-hand
line of the tower projected down through the building makes a square
(A, fig. 73) which gives you the right start. Your measuring glass
will certainly pick up the partly enclosed space 8, which helps decided-
ly in sketching the tower. Play your square over the tower itself. Note
that the top of the central window conveniently cuts off a square (fig.
73A) . You readily estimate that the remainder is about one-third of a
square.

It is always desirable to make the first measurement include as
much of the area of the subject as possible. The garden-house (fig. 66)
was entirely enclosed within our first square. The Italian subject
(fig. 72) did not suggest an enclosing rectangle because of its broken
contour. The square A was deemed a more practical measure as a
basis for the sketch.

8 !

The first glance at Coutances Cathedral (fig. 75) reveals the large
square X. The upper portion of the building is not so readily meas-
ured, but, having the correct proportion of the lower part, it is easy
to measure the tower masses. You can hardly fail to pick up square A,
as your measuring glass moves over the facade. This is a very useful
measurement. The structural lines of the tower practically cut the
large square X into three equal vertical spaces, and B is close to being
a square.

The square measurement units that were used to make illustrations
78, 81, 83 and 85 are shown in the drawings accompanying them.

The employment of the square in determining proper proportions
will be found especially useful in memory drawing. If in memorizing
an object to be drawn later we carry in mind a geometric framework
based upon a reliable unit of measure, we can have greater assurance
that our drawing will be a faithful illustration.

S.MARIA

DELIA SALUTE

first 9 /art re

>ie

desir&bte as a-
first'

WELLS CATHEDRAL
78

The student will find that after studying proportion for some time
with the measuring glass, he has acquired an accurate concept of the
square and, dispensing with it, will discover that he has become
''square conscious" and possessed with an infallible method of meas-
uring proportion.

We have used architectural subjects only in these demonstrations
but of course the procedure applies to all objects equally well, and
the student is advised to practice measurements on all the common
things that surround him in the home and on the street. Pictures in
magazines make excellent practice material. They can best be analyzed
by laying tracing paper over them.

Thus far we have used the square only to measure objects seen in
front view, or elevation, where no foreshortening is involved. Can this
unit of measure be applied to subjects seen in perspective, like the little
country church (fig. 86) ? It can.

This sketch shows the measuring glass being held at right angles to
the direction of sight, resisting the tendency to turn it in the direction
of the plane being measured. This of course is not a true measurement
of the front of the building which is considerably wider than its height
at the eaves : it merely tells us what the width of the f a$ade on our
sketch paper should be in relation to its height.

But fig. 87, where our square encloses nearly the entire structure
(by bringing the glass closer to the eye), gives us a measurement we
would do well to make at the beginning. Whenever we can enclose
the whole object within the square, we have a convenient means of
placing the drawing on the paper and blocking-out the main lines.
Figs. 88 and 89 indicate still other measurements that are quite
obvious.

Now as we have said, this procedure, although it is an aid in making
our sketch, tells us nothing about the actual measurements of the sub-
ject itself. For that reason its usefulness is limited.

Suppose, for example, our task were to draw the church not from
observation but from specific measurements : width 30 feet, depth 40
feet, height at the eaves 20 feet (fig. 90) .

The long side is a rectangle twice as long as its height, or two
squares. The width of the front is half as much again as its height, or
a square and one half. How are we to measure these dimensions in
perspective, on foreshortened surfaces?

The architectural renderer lays out his perspective drawing instru-
mentally and projects actual measurements ; the illustrator's measure-
ments have to be estimations, but if he knows what a foreshortened
square looks like he will come very close to exactness in his freehand
sketch.

The first step, then, in measuring the front of the church after the
directions of the converging lines has been indicated (fig. 91) is to
establish the estimated width (X) of a square (fig. 92) whose height
is fixed at the corner of the building. How accurate is this figure? Is it
a square?

Now it is easier, even for the practiced eye, to judge the foreshort-
ened square when it is visualized as the face of a cube. So let us indi-
cate the other visible face of the cube on the long side of the building
(fig. 93) . This face must be wider-in our sketch-than the other be-
cause, as the steeper convergence of the front lines indicate, the front
plane is turned away from us at a greater angle and all horizontal
measurements on it therefore are more foreshortened ; hence, on the
right side, less foreshortened and wider.

Even the beginner, who, before, might have been undecided about
the X rectangle (supposed to represent a square) now sees at once
that fig. 93 is far too wide to represent a cube and that X, consequently,
cannot be a square. Fig. 94 certainly looks more like it and this cube
will serve in establishing the widths of both front and side walls of
the church. The church's dimensions can now be determined geomet-
rically as shown at fig. 94.

Two distinct methods of measuring with the square have been dem-
onstrated. One employs the square on an imaginary transparent plane
(an actual piece of glass for the beginner) at right angles to the
direction of sight; the other dispenses with the glass and uses the
square in perspective. Which is better?

Each method has its value, but since the experienced illustrator
always thinks of what he is drawing as three-dimensional, he usually
makes his measurements in perspective. He never thinks of the flat
surface of the paper upon which he is working ; he is always project-
ing his image through the paper, as it were. To rely to any extent upon
the methods demonstrated in figs. 86, 87, 88 and 89 is, for him, a rather
artificial method ; it contradicts his whole attitude of three-dimensional
thinking. That is not to say that he never resorts to it by way of check-
ing against his perspective measurements. Chances are that most illus-
trators do just that.

The student is advised to use both methods simultaneously. Until
he has had much practice in drawing cubes and has learned unmistaka-
bly what a cube looks like under all conditions, he will experience much
difficulty in perspective measurements.

chapter iv

THE PICTURE PLANE

Almost everyone, as a child, has demonstrated the function of the
picture plane by tracing upon the windowpane, with wax crayons, the
outlines of the house across the street. In his tracing, the child thus
achieved a reasonably correct, if crude, perspective representation of
the structure, provided the position of the eye was not changed during
the drawing.

And so the picture plane can best be conceived as a sheet of glass
through which the artist observes his subject and, in imagination,
traces its outlines ; the lines actually being drawn on a sheet of paper
which thus takes the place of the transparent glass.

It should be said at the outset that for anyone who has much apti-
tude for drawing, the concept of the picture plane is wholly unneces-
sary in practice. It would not have been introduced into this book were
it not useful now and then in demonstrating certain phenomena and
various procedures otherwise difficult to explain. The person who
draws naturally does not even think of a flat plane. To him the paper
upon which he draws is not a flat surface : it is space. When he sets
down lines to represent distance, his pencil pushes those lines right
through the paper-twenty feet or half a mile. The retreating line
reaching toward the horizon may be only three inches long on the
paper, but to the artist it feels just as long as the street or the railroad
track or whatever he may be drawing.

Hosts of artists have never given the picture plane a thought, and
even children in their first drawings are able to think of the drawing
paper as space rather than a flat surface.

So it seems very unwise to put too much stress upon the concept
of the picture plane in teaching freehand perspective, although it is
absolutely essential in instrumental perspective. An illustrator called
upon to make drawings of buildings or other structures that demand
accuracy of measurement must resort to the same kind of instrumen-
tal procedure that is employed by the architectural and engineering
Tenderer. The student of freehand perspective who intends to become
a professional artist will do well to consult a good text on instrumental
perspective. Here, we can only indicate in the simplest diagrams the
basic principles in instrumental procedure.

When we do think of the picture plane it is important to remember
that it should be imagined at right angles to the central direction of
sight, and that its position should not change in any given picture.
9 6 That is the basic rule but there are exceptions to it, as we shall see.

97 The whole theory of scientific perspective is predicated upon the

assumption that the direction of sight, hence the position of the picture j
plane, remains constant in the picture. The theory is consistent with
photography, which records a wide-angle scene upon an immovable
picture plane-the camera's plate or film.

But the human eye sees things quite differently. Its direction of
sight is constantly shifting; it has to, because our eyes can focus only
upon a single point at one time. As I write, I look down from my
studio at the florist's window on the street corner. I am very conscious
of shifting my gaze in trying to distinguish the various items in the
window within the space of seven or eight feet. Automobiles not thirty
feet from the store window, just around the corner on each intersect-
ing street, are mere blurs. All that I can tell about them without per-
ceptibly changing my direction of sight is their color and their general
type truck or passenger car.

Thus we see that an immovable picture plane violates the whole
process of seeing. Yet, considering the inconsistency, it serves remark-
ably well provided the artist understands its inconsistency under
certain conditions and knows how to compensate. The skillful artist
is always taking liberties with scientific perspective, violating its rules
for reasons of design or for a more truthful impression.

The diagrams in this chapter demonstrate the basic procedure of
the instrumental method. In fig. 97 we look down upon the picture
plane. Think of it as a large sheet of glass standing vertically on the
ground. Seen from above its top edge would appear as a thin line*
The gray rectangular form represents the plan or foundation of a
building. It touches the picture plane at B. This is not necessary ; it
might be placed at a considerable distance behind the picture plane,
but it is given this position here for a special reason that will appear
later.

The "station point" represents the eye of the observer. It may be
any distance from the picture plane according to the effect desired in

98 the perspective rendering.

From the station point, lines are drawn to the picture plane parallel
with the sides of the building, lines AB and BC. This means, of course,
that the angle at the station point (shaded) is a right angle. These
lines from station point to picture plane locate the two vanishing
points and, as seen in our diagram, they are projected down for the
perspective drawing in figs. 98 and 99.

It will be evident that the placing of the station point controls the
perspective effect. The nearer it is, the more "violent" the perspective.

To avoid this and to get a more normal effect, the distance of the
station point from picture plane can be increased. This automatically
extends the vanishing points further to right and left because the

99 station point angle (shaded) is always a right angle.

Jf **** / Mod*m Art, Atao York.

101

The station point also can be located laterally wherever desired. Its
position taken here is purely arbitrary ; it might have been any dis-
tance to right or left. Try moving the station point both laterally and
more distant from the picture plane and see what happens. What does
happen when the station point is close to the picture plane is seen in
fig. 102, and in fig. 100 where we get violent and distorted images. The
near corner of the rectangle in perspective (fig. 102) is a very acute
angle, an effect never seen in normal vision. Experiment with a rec-
tangle on the floor. It will be found that the near corner is always an
obtuse angle ; it can never be seen as an acute angle as in fig. 102.

Therefore it is usually advisable to locate the station point far
enough away from the picture plane to avoid such distortion. That, as
we have stated, will throw the vanishing points further to the right
and the left, widen angle X (fig. 102) and give a normal appearance.
There are times, to be sure, when the artiat deliberately employs dis-
tortion for a good purpose, as in the Curare drawing on page 122.
Indeed this is very commonly done.

Everyone who has used a camera is aware of what happens when
the picture in taken close to the object, as was the case in photograph-
ing the Museum of Modern Art (fig. 101) . The result of a close camera
range like this is the same as that achieved in drawing when the
station point is near the picture plane. Although it is an "unnatural"
effect, we have become so accustomed to such photographic exaggera-
tions that they are more readily accepted than formerly. If the camera
had been at a great enough distance to give a more "normal" perspec-
tive to the museum building, the picture would have failed to show
sufficient detail. The fact that but a little of the right side shows in
the photograph is a compensating factor. Had it been standing alone,
as in fig. 100, the distortion would have been more noticeable.

Having established our station point and vanishing points (in fig.
97), lines are drawn from the station point to the several corners of
the plan (A, B, C, D, E, G and H in fig. 97). Think of these lines as
beams of light that connect the eye with the object. Where the beams
cut through the picture plane we have points a, &, c, d, e, g and h that,
projected down to the perspective drawing in fig. 98, establish the
correct relative dimensions of the plan in perspective. To fix our van-
ishing points in fig. 98, we have dropped verticals from the vanishing
points already established in plan (fig. 97) until they meet the eye-
level. The eye-level can be placed higher or lower than shown in fig. 98,
according to the vantage point from which we wish to view the subject.

102

Now in practice one would erect the building directly upon the per-
spective plan (blacked-in) in fig. 98, and develop the entire drawing
there. To simplify the procedure and avoid the confusion of a compli-
cated drawing we make a separate diagram (fig. 99). The a, 6, c, d, e,
g, h points have been projected down to this diagram from fig. 97.

The height of the building and its smaller element (C, G, E, H in
the plan) are indicated in the side elevation. Projecting horizontals
from it to the perspective drawing we have points X and Y on the
nearest vertical XB. These are the only measurements needed. When
point Y is projected back to VP 2 on the horizon, it indicates the height
of the small element.

As previously stated, the building touches the picture plane (point B)
for a special reason. Had it been set back from the picture plane we
could not have projected the vertical heights from the elevation (fig.
99) -which is drawn on the picture plane-to the building's near cor-
ner. In that case it would have been necessary to project either line AB
or line CB in fig. 97 forward until it touched the picture plane, giving
us a vertical line on the picture plane upon which we could measure
heights. We could then project our measurements from the side eleva-
tion to that vertical line and project them back toward vanishing
points, as we have done at Y (in fig. 99), to find the height of the
small element. All vertical measurements have to be taken on the pic-
ture plane and projected back into the distance on the foreshortened
planes.

Until relatively recent times the picture plane was invariably con-
sidered a vertical plane ; no one thought of tilting it to look up or down
at objects. But, of course, we do that constantly in viewing things that
surround us. And, when we do, we see objects in 3-point perspective.
There is convergence not only in their horizontal lines; the vertical
lines converge as well-upward or downward as the case may be. A
photograph taken with a tilted camera produces effects of 3-point
perspective with which we are all familiar. This aspect is demon-
strated in a later chapter, therefore we shall not discuss it at this point.
Now let us come back to the reference of a child making a perspec-
tive drawing on the windowpane of a house across the street. He
would have learned, had it been pointed out, that any set of the build-
ing's lines which recede into the distance would, if continued, meet
at a point. That point would be found to be on the exact level of the
observer's eye on the window glass.

Hence the perspective fact, all horizontal, parallel receding lines
converge and meet at a point on the eye-level, or at the horizon-which
is the same thing.

FAWCETT This is demonstrated in illustrator Robert Fawcett's drawing of
the housewife standing at the old kitchen range (105). In that draw-
ing there are four sets of parallel lines, hence there are four different
vanishing points (VP 4 lies outside the ptoge). The long lines of the
stove, the lines of the wall against which the stove is placed and the
short edges of the table (against the back wall) are all parallel to
each other ; therefore they converge to the same vanishing point ( VP 1 )
on the eye-level at the right. The short lines of the stove, the other
wall and the long lines of the table constitute another set of parallel
lines ; they converge to VP 2 , on the eye-level at the left.

The serving table, just behind the figure, is turned at an angle to
the lines just mentioned. As demonstrated, its long parallel lines con-
verge to VP 8 and its short ones to VP 4 . If this table were moved to
the position indicated by the dotted rectangle, its vanishing points
would have still different locations on the eye-level.

In this drawing the eye-level happens to pass through the eye of
the cook. That is merely because the illustrator assumed that he was
standing in the room as he drew and that his height was the same as
that of the woman. Had he assumed a sitting position the drawing
would have been as shown below. The horizon line would have dropped
to his lower eye-level.

104

Tki drawing for an advertitement for Child*
wan wade by illuttrator Robert Fawceti.

106

chapter v

THE CUBE

It will be increasingly evident to the student that familiarity with
the cube is extremely important in both simple and complicated struc-
tural developments. In later chapters we shall find ourselves needing
great facility in drawing cubes when confronted by a variety of forms
that can best be rendered by relating them to this basic geometric
solid. In the chapter on the circle, for example, the cube helps us to
determine the proportion of ellipses that represent circles in various
positions.

So the student should be continually drawing cubes with the model
before him, of course-until he can almost draw them with his eyes
shut.

On pages 38 and 46 there are suggestions for cube practice. Consider
first page 46. Here we work with a cube that, when subdivided as
shown, is made up of 64 smaller cubes. Before proceeding with the
various arrangements-and others that will suggest themselves-be
sure that your cube is absolutely correct to begin with. Drawings should
be made at least one-and-one-half the size of those on the printed page.

First sketch the cubes freehand, drawing directly from a model of
the cube. When the drawing looks right test it by extending the con-
verging lines till they meet on the eye-level. Use T-square and triangles
for these tests. It may be necessary to lay the drawing on another
very large sheet in order to find the vanishing points at considerable
distance from the cube. The lines extending at the right should, of
course, meet at the same point ; those at the left at another point on
the same horizontal eye-level. When the converging lines have been
corrected the question still remains: "Is it a cube?" It might be too
narrow or too wide.

One way to check on proportion is to lay a windowpane over the
drawing and, with an architect's ruling pen and india ink, trace the
cube lines carefully. The glass surface is not easy to draw upon but
it will actually take the ink. (You will need a brass-edged ruler.)

Now hold the glass at the side edges near the top so that it will hang
vertically and at right angles to your direction of sight as you view
the cube through it. You are really looking through the picture plane,
and if your drawing is correct its lines will cover those of the model.
If they do not, correct the drawing and test it again.

This may be a tedious business, for you may have to make several
tests before you get a perfect drawing. But it is time and effort well
spent. Many artists go through life making cubes too wide or too
narrow because they never really learned what a square hence a
cube-looks like in perspective.

The student with a camera with a lens that will take close-ups will
find it profitable to take many pictures of the cube in different posi-
tions. These photographs can then be used as a means for checking
108 his drawings.

110

Now try doing a page of cubes like those on page 38. Of course it is
not necessary to render the cubes in wash as shown but it is excellent
practice and is more fun. Lamp black is diluted with water and applied
with a No. 5 sable brush. If the cubes are first drawn in line on tracing
paper, then transferred to a good sheet for the shaded drawings, the
result will be better.

The cubes on the black background will give an even greater test
of cube skill. The student may want to compose his own arrangement
instead of copying the plate ; but that is unimportant. It will not be
practical to carry out these drawings instrumentally. This test throws
one entirely upon his freehand judgment.

A day or so after completing them, look at your cubes critically
with a "fresh eye." You will be certain to make some corrections. Do
this for several days until you can no longer find fault with them.

When the cube is seen in direct front view, so only its front face and
top are visible, the beginner finds it difficult to realize how greatly the
top face is foreshortened ; usually he makes it too wide from front to
back, as at A, fig. 109. To appreciate the extent of the error in this
figure we have only to project lines down from cube A to show how this
figure would look (B) when seen at a lower level, where its proportion
can be more accurately judged. Instead of a cube, we now see that we
have drawn a rectangular solid more than five times as long as its
square end (E).

The cubes C and D were drawn by the author from actual measure-
ments taken in the manner shown in fig. 110. The cube D rested on a
table just twenty inches below the author's eye-level and three feet
away. Squinting along the edge of a ruler, the front to back width of
its top face appeared to be slightly over one quarter the cube's height.
The cube C rested on a shelf only eight inches below eye-level, hence
its top face appeared much narrower.

If the cube had been nearer, the top face would have shown greater
depth because the nearer to the eye, the more nearly one looks down
upon it. This kind of meticulous measurement is occasionally advis-
able ; it helps in educating the eye to such an accurate judgment that
109 the use of the model can soon be dispensed with.

A number of elementary perspective facts are demonstrated in fig.
111. Cube No. 1, placed midway between its vanishing points 1 and 2
presents two equal vertical faces. That means that the diagonals AB
and CD (dotted lines) are horizontal and the diagonals EF and GH
are vertical.

No. 2 cube has been set off to the right so that its right vertical face
is turned considerably more toward us ; so much so that its long con-
verging lines vanish at a point far off the page at the right, while
those of the left face turned sharply away-find a vanishing point not
far to the left of the cube. Its AB, CD diagonals now are not horizontal ;
if carried out to the left, being parallel they would meet at a vanishing
point on the eye-level far off the page.

No. 3 cube is one-quarter the size of No. 1, whose left face has been
divided into quarters by the intersection of the diagonal line ( AG) with
a horizontal bisecting line from K. Note that although the small cube
has not been turned-having merely been pushed forward from cube
1, as it were its right face is wider than its left.

Note also the directions of the EF and GH diagonals of cube 3;
they converge with the EF diagonal of the parent cube because those
diagonals are actually parallel. That geometric relationship is often
useful, as it was here in determining the location of the small cube's
point F. Points E and G were found by projecting forward from and
P of cube 1. Next SO was projected forward, giving the correct width
of the narrow face.

It will be seen that the further the cubes are placed to the left, the
wider their right faces and the narrower their left. The opposite
applies to cubes at the right of the center.

Incidentally, the drawing of cubes placed like 4, 5 and 6 offers a
means of testing the accuracy of cube 1. If through error of judgment
cube 1 had been made too wide, a cube in the position of 4, 7 or 8 might
present a wide face actually wider than its height.

EYE i r v r i

ill

cm H o R i s o N

chapter vi

112

FORESHORTENING AND CONVERGENCE

I suppose it would be an unpardonable break with tradition not to
use the railroad track to demonstrate the simplest of all perspective
facts : the fact that objects appear progressively smaller as their dis-
tance from the eye increases-the railroad ties and the telegraph poles
and the fact that, therefore, the rails and the wires converge and
(in a picture) come together at a vanishing point on the eye-level. The
space between the ties and between the poles decreases progressively
with the increase of distance.

The position of the observer in fig. 112 is in the center of the road-
bed, between the tracks ; and as he looks straight ahead toward the
horizon (the level of his eye) all the railroad ties are at right angles
to his direction of sight. That is the way they would look in a photo-
graph. In one-point perspective all such parallel, horizontal lines in
the subject (according to the rule) are represented by horizontal lines
in the picture. There are exceptions, as we shall see.

When the observer steps off the tracks to the left of the roadbed and
views the tracks from that position, what he sees is illustrated in fig.
113. The rails converge to a point at the left; and the ties, instead of
appearing as horizontals, take a slanting direction and converge to a
point on the eye-level outside the picture at the right. This is known
as two-point perspective.

In fig. 114, which represents the observer's relation to the scene as
pictured in fig. 112, the direction of sight is at right angles to the ties
which are parallel with the picture plane. In fig. 115, which represents
the observer's relation to the scene in fig. 113, the ties are not parallel
with the picture plane ; their left ends are nearer the picture plane and
the eye than are their right ends. Hence they converge to the right.

In fig. 112 (and in fig. 114) the observer is exactly in the center of
the picture. What happens when, as in fig. 116, he moves over to one
side, but not beyond the tracks as in figs. 113 and 115?

In theory his direction of sight remains parallel with the rails and
at right angles to the picture plane and to the ties. Now the left ends
of the ties actually are further from the eye than are the right ends ;
but both ends are equidistant from the picture plane which, in theory,
is the determining condition. Therefore, in the drawing, the ties,
according to the rules, should be drawn as horizontal lines. Hence
there would be but one vanishing point, as in fig. 112.

CHANCE But a drawing made that way would not look as satisfying as it does
in the drawing (fig. 117) by Fred Chance, where the observer stands
on the track in about the position indicated in fig. 116. From that posi-
tion it certainly is natural to turn the eye to the left of the vanishing
point, particularly since the picture's interest the horn and whistle-
lie in that direction. The camera would practically reproduce what Mr.
Chance has done if it were held in the same position taken by the artist
as his point of observation. If, however, a third track were to be added
(in Mr. Chance's picture) at the right side, the situation would be the
same as in fig. 112; then the ties would have to be made horizontal.
Prove this for yourself by tracing Mr. Chance's picture; sketch the
third track at the right and give the ties the same direction as those
of the other two. Note the unnatural effect.

113

Drawing by Aldren A. Watton.

114

115

116

PICTURE

PLANE

Drawing by Fred Chance.

Courtesy American Locomotive Company.

117

118

119

Just to demonstrate further how Fred Chance's drawing violates
the strict rules of scientific perspective, we have laid a rectangle say
a panel of wallboard-upon the track (traced from his picture), see
fig. 118. Now place a rectangle of paper on the table before you so
that you view it as the tracks are viewed in fig. 116. Can you turn it
in such a way that it resembles the rectangle in fig. 118? No, as soon
as line A is slanted up from the horizontal (as in fig. 118) line B takes
a direction indicated by the dotted line in fig. 118 and by the drawing
in fig. 119. Yet if you experiment further by laying a piece of white
paper (cut like the rectangle in fig. 118) on the track in Mr. Chance's
drawing, it probably will look natural enough.

It would be interesting for the student to experiment further with
this subject by making a drawing similar to Mr. Chance's but drawing
the ties horizontal. The advantage of the Chance procedure will be
quite evident in the comparison of the two effects.

If Mr. Chance had established his vanishing point but slightly to
the right, just outside the picture (as in fig. 119) he would have con-
formed strictly to the "law" of two-point perspective. Then, you see,
the rectangle laid on the track would have met the test. But it is obvious
that by keeping his vanishing point within the picture he concentrated
interest upon the horn and whistle as he could not have done so suc-
cessfully by following the plan in fig. 119.

The old rule stated, in effect, that we cannot have two-point per-
spective with one of the vanishing points within the picture's limits.
As we shall see, it is a rule that is constantly and effectively violated.

Interestingly enough we have another Fred Chance railroad draw-
ingthe Fortune cover (fig. 120) in which the vanishing point of
the track is in almost the identical position as in fig. 117. In this design
he has followed the rule which says that when a vanishing point falls
within the picture, other horizontal lines at right angles to the retreat-
ing lines must be horizontal in the drawing. Thus we see that the illus-
trator uses his judgment in these matters; he is much less governed
by perspective rules than by what suits a particular situation.

Cover design by Fred Chance.

Reprinted by special permission of the editors of Fortune.

120

FAWCETT

In the painting for an advertisement for the Association of Ameri-
can Railroads (fig. 121) we see a violation of the rule laid down at
the beginning of the chapter : the rule that in one-point perspective all
horizontal lines should be parallel. We note in this picture that the
ties on the tracks at the sides are not parallel ; those on the right con-
verge to a point on the eye-level at the right ; those at the left seek a
vanishing point on the left. In this "one-point" perspective we have
three vanishing points, an effect contrary not only to scientific perspec-
tive but to what the camera would give us.

Here we should remind ourselves again of the difference between
the camera eye and the human eye. The camera, with its lens pointed
straight ahead will focus upon every detail within the frame of that
picture; it will see each detail clearly. The eye to take in the same
scene must change its direction, looking to the left to take in the left
part, and to the right to see that clearly. One would even have to turn
the head to do it. When we look at the picture of this scene we do the
same thing. When we look toward the right it is natural for us to expect
the convergence of the ties we see there. Focusing upon them we are
but vaguely conscious of the left tracks, even of the center track. It
would be interesting for the student to make a drawing of this situa-
tion, "correcting" the picture by making all the railroad ties horizon-
tal, then judge for himself which effect looks better. That, after all,
should be the determining factor.

Another very interesting handling of the railroad problem will be
found in the drawing by George Giusti and design by Bradbury Thomp-
son on page 63. We encounter this modification of one-point perspec-
tive in many situations, notably in the rendering of interiors as demon-
strated on pages 56 and 57, where we have experimented with differ-
ent methods of drawing a kitchen in perspective, borrowing Robert
Fawcett's illustration of the woman and stove as our motive.

121

Courtesy Association of
American Railroads.

frOO*

122

123

124

125 A

125 B

126

Courtesy Abbott Laboratories,
North Chicago, Illinois.

127

Visitor* Information Center,
Portland, Oregon*

In the interior (fig. 122), we adhere strictly to the rule for one-
point perspective, sometimes called parallel perspective because the
planes at right angles to the eye (the facing wall and the end of the
stove and the front of the cabinet in the drawing) are parallel with
the picture plane. In this drawing the eye-level is the same as that of
the wonjan, and the vanishing point is in the center of the room. This
is the effect that would be produced by photography when the lens of
the camera is viewing the room from the same vantage point.

Now if we move over to the right of the room, rather close to the
wall, and direct our camera somewhat toward the door, we get an
effect like that in fig. 123. The facing wall is no longer a rectangle;
its floor and ceiling lines converge to a point on the horizon far to the
left, as do all other lines parallel to them. This is a much more agree-
able effect for the simple reason that an arrangement of lines and
shapes, as in fig. 125B, is more interesting, less static, than that in
fig. 125A. Abbott Laboratories' Brief Summaries (fig. 126) is a good
illustration of the superiority of a design layout based upon the per-
spective procedure of fig. 125B. This is a violation of the old per-
spective law as is the photograph of the Visitors' Information Center
in Portland, Oregon (fig. 127) .

There is no reason why, if the effect in fig. 123 is agreeable, we
should not keep the observer's position in the center of the room and
converge the facing wall lines to a left vanishing point as we have
done there. But we have to be careful not to bring the left vanishing
point too close to the picture, as has been done in fig. 124, where the
drawings of the cabinet and the chair become very distorted. In this
kind of problem, as in all others, the illustrator's judgment will rule.

We have to find a way of measuring every piece of furniture in the
room ; the heights of the stove, the chair, and the cabinet in relation
to the figure (see fig. 122). We are assuming here that the housewife
is a little over five feet, her eye exactly five feet above the floor. Since
the height of the range is the same, we have a five-foot measurement
on the wall. Any vertical on that wall between the floor and the eye-
level likewise is five feet long AB for example. Dividing AB into five
one-foot parts we can measure on it the height of the chair (18 inches
--one and one-half feet) . A line on the wall from this point to the VP
cuts the corner of the room at X. A horizontal on the facing wall,
through X, dictates the height of the chair seat. The cabinet dimen-
sions are 30 inches high to the top of the drawer section ; almost six
feet from floor to top of cabinet. We carry these measurements around
the walls in the same way. We make the door seven feet high.

128

An advertisement for
Hanes Hosiery, Inc., by Bobri.

BOBRI Bobri, the creator of the interesting advertising illustration (ftg.
128) , is one of our most skillful draftsmen, as well as a highly original
designer. In this picture he has taken liberties with perspective which
enhance his design without appearing to violate natural effect.

Let us look first at the buildings and the checkered pavement. We
might naturally assume that all converging lines of these objects are
parallel and therefore seek a common vanishing point at the eye-level ;
as, indeed, they appear to do at casual glance. But, laying our tracing
paper over the drawing and testing these lines, we discover that instead
of one vanishing point there are two, as shown in fig. 129. They are
not very far apart, to be sure, but from the standpoint of design the
variation is important. Fig. 130 shows how awkwardly violent the
light side of the structure on the right would be if its lines converged
to VP 1 . The design is better as Bobri has arranged it.

What he has really done is to give that building (fig. 128) the shape
of a parallelogram. Side Y in fig. 132 is parallel to the horizontal lines
of the pavement, but side X cuts diagonally across them.

Another interesting violation of scientific procedure is seen in the
direction of the lines of the battlements of the building on the left
(indicated by heavy lines) in fig. 129. These, being parallel to the
picture plane, might be expected to be horizontal in the drawing;
instead they slant down to the left and all of them are parallel. This
might seem to be an accidental minor detail, but to a meticulous
designer like Bobri nothing in the picture is accidental.

Now we come to something that is indeed surprising. That is the
relation, in size, of the figures. We are at once aware, of course, that
the girl's figure is out of scale with other elements in the picture and
for an obvious reason ; but we are not so conscious-if at all-of the '
gigantic size of the guard with the halberd in relation to the distant
figures and the height of the building itself.

But fig. 131 demonstrates that this personage is about three times
the height of the distant figures. Projecting lines forward from VP 1
through the feet and head of one of the distant figures until they reach
the plane in which the guard standsthe tinted plane-reveals the
proper height for the guard, if Bobri had wished to be photographi-
cally correct instead of a designer.

When we see such things done by an expert they seem so simple,
as do most things that are right, and it is hard to realize how subtle
these adjustments between design and perspective are. It is only when
the beginner makes his own attempts that the skill of the experienced
designer-draftsman in these matters is appreciated.

GIUSTI George Giusti's drawing (fig. 133) shows the solution of an interest-
ing problem. As shown in Westvaco Inspirations, this advertisement
spread across two 12 by 9-inch pages. That factor in itself will explain
certain "irregularities" in perspective procedure.

First, let us look at the tonal section in the upper-right corner. That
rectangle isolates what might be called a normal view : it covers about
as much terrain as might comfortably be included in a picture of this
kind. As a matter of fact it tells the whole story. It is extended beyond
its borders only to create an unusual layout and thus further dramatize
the idea.

129

Pi ^

ll 't

eye

180

182

Thit it a plan of tk* building and pavement
09 Bobri ha* drawn them.

131

Now if a student presented that drawing (the tonal section) in a
perspective class, his instructor might point to his error in the render-
ing of the railroad ties. These, he might say, should be horizontal lines,
since the subject is drawn in parallel perspective with the vanishing
point nearly in the picture's center. And he could demonstrate the
logic of that rule by drawing two diagrams (figs. 134 A and B) in which
converging lines to the right of the track are made into additional
tracks. He could point out that if the direction of the ties of track X
(fig. 134A) is correct, those of tracks Y and Z, being parallel with
them, must be drawn as shown. But the absurdity of that effect is evi-
dent. The device of a third vanishing point for the right track (fig. C)
seems equally so. (However, please refer to the painting of locomotives
on page 55 where this device has been employed successfully. But in
that picture the slant of the ties of the side tracks is so slight that the
divergence is scarcely noticeable.) The logical rendering of the two
tracks is that seen in 134B. The fact that actually these other tracks do
not exist in Giusti's drawing does not justify him theoretically for
what he has done. But in breaking the rules he has done the most
effective thing.

When the converging lines of the ties (within the tonal area) are
extended, it will be seen that they meet at a vanishing point far to
the left. But, it will be noted, there is no convergence at all of the tie
lines outside the tonal area ; they are mostly parallel. Indeed some in
the foreground diverge slightly. Furthermore, it is the work of two
persons. The tonal picture is a drawing by Giusti for a Gruen Watch
Company advertisement; the extended tracks and the figures below
the picture were added by designer Bradbury Thompson in creating
a two-page spread for Westvaco Inspirations, for which he is art direc-
tor and designer. Therefore, what we have here is really not a picture
but a design, a design which involves two distinct views, one toward
the right-hand page of the spread, the other toward the left page.
While the attention focuses upon one page the other is out of focus,
hence not really a part of a unified picture, although it is part of a uni-
fied design. Although one would expect the perspective inconsistency to
be disturbing, it is not because the reader, turning from the train
which is the focal point of the spread to follow the rails as they come
forward on the opposite page, turns the head as he would if he actually
were on the spot staring at the rails themselves. Thus there are two
separate focal points in a single picture, a feat that demands arbitrary
handling of perspective devices.

Another interesting point in this design is the treatment of the
figures. Note that while the figures diminish in size perspectively, those
in the distance are much larger than they would be if treated realisti-
cally in perspective. Converging lines drawn through all the extended
hands find a vanishing point considerably above the horizon line. Who
cares? The effect is much stronger than otherwise. In this connection,
refer again to Bobri's figure treatment in the Hanes advertisement,
page 58.

134 A

134 B

134C

Two-page spread in Westvaco Inspirations

around a Gruen Watch Company advertisement

by George Giusti.

FAWCETT This dramatic picture by one of America's top illustrators reveals
interesting perspective tactics involving four vanishing points. The
horizontal lines of the room in which the action takes place converge
toVPl.

Now the casual observer senses that the wall of the further room
(gray in our diagram) is parallel with the corresponding left wall of
the near room. But when we carry out the converging lines we discover
that they seek a vanishing point considerably to the right ( VP 2) . This
means that the further wall is not parallel with the near one; the wall
is turned more toward us.

Why should this have been done? The answer is obvious. The effect
is more pleasing than if the wall were in more violent perspective,
in that case affording less opportunity for the display of its fine panel-
ing, a most interesting background feature. Oddly enough, however,
the floor line of that room converges to VP 1, thus strengthening the
impression that the far wall is actually parallel with the near one
a very subtle treatment !

The table, we note, is not parallel with the wall of the room as we
would expect it to be and as the casual observer suspects ; its long sides
converge to VP 3. This is a matter of design ; imagine how awkward
it would be, had that long line converged to VP 1 !

We have still another vanishing point; that of the opened door
VP4.

Until one has analyzed this picture as carefully as the author has
done, tracing some of its details, he cannot appreciate the perfection
of the drawing of every incidental object. Study the lamp, for example,
and the still life objects on the table. Nothing is slighted ; each prop
is authentic and convincing. And to demonstrate how this illustrator
makes even inanimate objects respond to the action that is taking
place, note the tilt of the liquor in the near bottle a minor bit of strat-
egy to be sure, but a master does not overlook the importance of "bit
parts."

136

136
Illustration for Collier's by Robert Fawcttt.

ATHERTON

137

An advertising illustration
for Coty, 7nc.>
by John Atherton.

In fig. 138, which is shown above, the chaise longue is drawn as it
actually would appear when viewed from the angle which the artist
assumed when he established the direction of the long side (X). This
can be substantiated by observation of any rectangular piece of furni-
ture. When seen in this position, the short side of the chaise longue
(Y) comes into full view.

But had the furniture been drawn in the "correct" manner (as in
fig. 138) the design of the picture would have been scattered and
ineffective, with the distant door thrown outside the range of interest
that should of course be focused on the girl.

Had the same relative position of door and chaise longue (as in
Atherton's drawing) been maintained as in fig. 139 and had the chaise
longue been drawn "correctly," the design would have been most awk-
ward. In fact, it would have been impossible.

Now suppose that, insisting upon a "correct" drawing of the chaise
longue we turn it as shown in fig. 140. In this positionthe long side
being horizontal-the end lines converge "normally" to the distant door
which is their vanishing point. But, as is obvious, the design is static;
it lacks the grace of Mr. Atherton's drawing.

Although this is a relatively simple bit of perspective strategy it
represents the practiced skill of one who knows how to distort natural
appearance in order to achieve unity and elegance of design.

yp MOR/ZOW

chapter vii

141

The figures give scale to the tanks
which are ten times the height
of the figures, or sixty feet.
The scene is drawn as though the artist
is on some eminence that brings his eye
about eighteen feet from the ground
-three times the height of the figures.
The figures beside the oil truck were
drawn first. Their height carried
horizontally to Aon tank $ and then
projected forward, giving
the proper height for
the foreground figures.

THE CIRCLE

How infrequently a circular object is viewed from the one direction
-"straight on"-in which it appears as a perfect geometric figure that
can be drawn with a compass ! But of course a circle always looks like
a circle whatever its relation to the direction of sight ; and if the ellipse,
which is its perspective appearance, is correctly rendered by the artist
it will indeed look like a circle. If, however, its ends are made either too
pointed or too rounded it certainly will not look like a circle. Nor will
it if it is not perfectly symmetrical.

The student should, at the outset, acquire facility in drawing ellipses.
Otherwise his progress in working out problems involving the circle
will be greatly hampered. He should do a lot of drawing from models-
cardboard circles, plates or other circular forms laid on the floor, the
table, and at various other levels.

Try sitting back from the drawing board and swinging in the ellipses
with full arm movement. While at first this will be awkward and the
first ellipses thus made will fall short of being perfect figures, they are
likely to be better than those constructed laboriously by finger move-
ment.

The tracing of ellipses from photographic reproductions in maga-
zines and newspapers will help to develop the correct concept of ellip-
tical figures. Keep up your practice until the drawing of ellipses is
really easy and until you are sure that you are making true figures.

A practical test of the symmetry of the ellipse is to fold it on its
short diameter to see if one side falls exactly over the other, as it
should ; and to fold it again on the long diameter to test the similarity
of the front and back halves. The drawing, of course, has to be on
transparent paper for this test; if not, a tracing of it on transparent
paper can be made quickly.

Fig. 141 demonstrates some of the perspective facts of the circle
when it is associated with the cylinder. At the eye-level (which is also
the horizon line) the circular section lines of the tanks appear as
straight lines. Above and below this level they appear as ellipses that
are progressively "rounder"-to coin an adjective that is useful in
discussing proportion-as their distance above and below the eye-level
increases. The top ellipses of the tanks are more nearly round than the
bottom because their distance from the eye-level is greater.

The proportion of the ellipsesthe proportion of short to long dia-
meters-also depends upon the distance of the cylinder from the eye.
The nearer the eye, the more nearly round ; the further away, the thin-
ner. Seen at a considerable distance they appear as nearly straight
lines.

Another point to be noted here is that the long diameter of the
ellipse is at right angles to the axis of the cylinder (shown by white
line) . We must draw ellipses of all upright cylinders-this means all
circles on horizontal planes-upon horizontal long diameters. They
always look that way to us, though not always to the camera. A photo-
graph of the tanks would show the ellipses with long diameters slanted
down toward a vanishing point at the left on the horizon. The effect
would be one of unnatural distortion.

This is one of many differences in camera and human eye vision.
It must be said that some distortions of camera vision are not as objec-
tionable to the average person as they were before photography began
to accustom the eye to unnatural odd angle effects which fill our picture
magazines. Our eyes have been re-educated or conditioned, as it were.
Artists have adopted some of these camera distortions and they use
them in common practice, as we shall see later. But the rule that the
ellipse, representing a circle on a horizontal plane, must be drawn on
a horizontal diameter is inviolable ; here the camera distortion is not
acceptable to the human eye.

What about the ellipses of cylinders seen in the positions other than
upright, standing on their circular ends? The drawing in fig. 143,
traced from a photograph of rolls of newsprint paper, demonstrates
that regardless of the position of the cylinder the long diameter of its
ellipse appears at right angles to the cylinder's axis.

The photograph of the grinding wheels (fig. 142) and the diagram
(fig. 144) a tracing from the photograph reduced in size reveal some
interesting additional facts.

First we note that the long diameters of the ellipses are at right
angles to the axis lines of cylinders of which they are the circular
ends. This relationship of diameter to axis is constant no matter what
the position of the cylinder ; axis and diameter of ellipse are always at

I Courtety Penninaular Grinding Wheel Company.

143

JBH8

> <**

right angles to one another. When the ellipse to be drawn represents
a circle that is not actually part of a cylinder, as the circular face of
a rectangular clock (fig. 145), the artist imagines the cylinder whose
sides and axis line converge with the side lines of the rectangular solid
which they parallel.

Always we must remember that the long diameter of the ellipse is
not a structural line of the object: it is merely an imaginary line-
useful only for drawing purposes. It is never the same as the geometric
diameter of the circle which the ellipse represents. We note, for
example, that ends of the ellipses' diameters in fig. 144 do not touch
the circles where they rest upon the ground or at their uppermost
points. And we see that the numerals VI and XII on the clock's face
are located on its structural, vertical diameter, having no reference
to the ellipse's long diameter which changes direction as the clock is
turned one way or another and raised and lowered.

Referring again to fig. 144 we observe that the long axes of the three
ellipses are not parallel to each other : that of cylinder 1 deviates from
the vertical slightly more than number 3. All three diameters converge
upward and, if extended, would meet at a point somewhere in a ver-
tical line, called a vanishing trace, through VP 1 which is far off the
paper at the left. The vanishing trace is demonstrated in Chapter IX.

In fig. 144 the side lines of cylinder 1 have been projected backward,
to the right, toward their vanishing point ; and two other ellipses have
been drawn within them to indicate how the proportion of ellipses
changes (length of long diameter to short) according to distance from
each other and from the eye. The photograph of the freight car wheels
(fig. 146) illustrates this very clearly. The camera appears to have
been quite close to the wheels. A picture taken at a greater distance,
though from the same direction, would show less difference in the
proportion of the ellipses of the two wheels. Refer to fig. 164 on page 77.

145

147

Advertising drawing of
Sydney Harbour, Australia,
for the British Commonwealth
Pacific Airlines, Ltd.

148 A

In the drawing of the bridge (fig. 147) we have an interesting
application of the principles we have been discussing throughout this
chapter. Although the lines of the bridge are not perfect arcs of circles,
they are sufficiently related to circles to make the accompanying anal-
ysis useful. It shows how essential is our knowledge of the appearance
of the circle in all situations where it is even but a part of the object's
form. Without such knowledge the artist can make serious errors, even
when he has photographs to use ; these will not always illustrate his
subject in the position in which he is required to view it.

Our analysis (fig. 148 A) represents, at least approximately, the
relation of the bridge's span to circles which appear to carry the curve
of the trusses for some distance. The perspective diagram (fig. 148B)
is self-explanatory. We see that the long diameter of the ellipse (dotted
line) is at right angles to the axis line of an imagined cylinder and
that it lies considerably in front of the circle's actual center (Y), a
phenomenon that is discussed presently.

Come back to this subject later when studying reflections. Making
a drawing of the bridge with its reflection in the water will be a
rewarding exercise.

148 B

150

The Observatory on Palomar is another good illustration of the same
principles. Here, the ellipses' long diameters slant but slightly from
the vertical since the cylinder's axis line, being not far above the eye-
level, is nearly horizontal. As in the bridge drawing, only segments of
the ellipses become parts of the structure but we need to draw the
entire ellipses in order to be accurate with the segments.

Refer to the Peter Helck drawing in later pages for further study
of this phenomenon.

Many beginners, especially those who are mechanically minded, are
quite surprised to be told that the diameter of a circle and the long
diameter of its elliptical appearance are never the same lines ; and to
discover that the long diameter of the ellipse is always in front of
(nearer the spectator) the circle's structural diameter.

Even more convincing than the diagrams here that prove it on
paper is a simple experiment with a cardboard circle, preferably a
very large one. Hold the model in a horizontal position at arm's length
a few inches below eye-level. Better yet, lay it on a shelf about ten
inches below eye-level. Now place the point of a pencil on the back
rim of the circle and slowly move it forward on the circumference
toward the front until it reaches a point that seems to be the extreme
right-hand boundary of the circle. Mark this point on the model. Do
the same on the other side. Now take the model down and connect the
two points with a line. That line, it will be discovered, is not the dia-
meter of the circle : it lies in front of it. Now draw the actual diameter
of the circle with a dotted line and put the model back on the shelf.
What is seen will resemble fig. 150.

The explanation is simple enough. Though actually shorter than
the circle's diameter, the long-axis of the ellipse looks longer because
it is nearer the eye. The closer the observer is to the circle the more
widely separated are the axis of the ellipse and the diameter of the
circle. This fact the student should verify by his own experiments.

The photograph of automobiles parked in a circle on Great Bear
Lake, on page 76, is an excellent demonstration of this phenomenon.

The Observatory at Palomar, California.

151

EVE' LEVEL

153

154

155

After these convincing experiments it seems hardly necessary to
demonstrate further the phenomenon by such diagrams as figs. 152 and
153 which represent the spectator viewing the circle from different
distances. However, there are other factors to be considered here.
In fig. 152 we see that the circle's diameter AB is a shorter line on
the picture plane than CD, the diameter of the circle's elliptical appear-
ance from that view point. Fig. 153 demonstrates how increased dis-
tance from the circle brings the two diameters closer together. And
when the circle is small-as in the clock's face (see page 71) -the
ellipse's diameter comes very close to the circle's structural center.
In larger objects like the bridge (page 72) the ellipse's long diameter
is likely to be considerably in front of the circle's structural center.

Now let us consider the problem of concentric circles which is illus-
trated in figs. 154 and 155.

Here we have three concentric circles which, in plan, fig. 154, are
seen to divide the diameters AB and CD into six equal parts.

After we have drawn the square in perspective and have found its
diameters and center, we can divide AB, the horizontal diameter of
the square, into six equal parts to give us points through which the
ellipses must pass on that line. On the greatly foreshortened diameter
CD these points must be so placed as to give a gradual diminution of
the six spaces (perspectively equal) between the ellipses from front
to back.

The ellipses, as we know, have to be drawn so that their long di-
ameters lie in front of the circle's center. The diameter of the smallest
ellipse is so near the center as to practically pass through it.
CHAPIN A practical application of this phenomenon is seen in the accom-
panying diagram of the solar system, the orbits of the planets forming
a series of concentric circles. That the artist knew his perspective
facts can be proved by testing the drawing on an overlay of tracing
paper.
156

TIME drawing by R. M. Ckapin, Jr.

Courtoty TIME. Copyright TIME, Inc., 1949.

160

161

The New York Times advertisement (fig. 157) presents yet another
illustration depicting the globe with the encircling plane which carries
the lettering. The top view (158) indicates the relative dimensions
of the plane and the globe.

Since we look down upon the globe, the poles (A & B) would not
be on its circular contour line; the axis would be foreshortened as
in fig. 159, and the center would be slightly below actual center.

In fig. 160 we see the globe encircled at this perspective center. It
requires a somewhat cultivated judgment to know whether the ellipse
is correct in proportion (long to short axes) considering the position
of the globe-below eye-level-which we established when we indicated
its poles. In fig. 161 we apply the procedure of fig. 155, consulting the
top view for the relative measurements of the various circles.

,^^;;

162 fee fUhinff on Great Bear Lake. Photograph Associated Free .

Hud9on type locomotive of the Chesapeake and Ohio Railroad

We now come to the consideration of another and most important
relationship of the circle and the square. It can conveniently be studied
on pages 78 and 79 in the problem of wheels on a railroad track.

Only one of the four ellipses can be correctly proportioned for a
wheel seen on that particular track and in that position on the track.
(The conditions are identical in all four diagrams.)

When the track is at right angles to our direction of sight; that is,
when our direction of sight parallels the ties, the wheels of course
appear as perfect geometric circles. On tracks that are viewed at an
angle the wheels are seen as ellipses varying in proportion (of short
to long diameters) according to the angle the track takes to our direc-
tion of sight. On a sharply receding track the ellipses are very thin.

164

TOP VfEW Or WHEELS

p/crusr PMMf

FOtf 01jSRVtt.

We are viewing all four tracks at exactly the same angle. The ques-
tion is, which of the wheels is correctly drawn? The person with a
trained and discriminating eye knows that only the ellipse seen in
fig. 166 can be correct. He does not need to be convinced by the experi-
ments on these pages which are intended to prove it for the inexperi-
enced student. Even our demonstration will not prove it for the student
who has not, through much practice drawing of cubes, learned exactly
what a cube looks like in perspective for, as we shall see, the cube
helps us here to make decisions.

However, we will assume that the student has in fact acquired a
reasonable concept of the cube's appearance in perspective views. He
will at once identify fig. 170 as a cube. That means of course that the
ellipse drawn on the side (which is the same as that of the wheel
in fig. 166) is the correct rendering for a wheel on that track. Fig. 169
is too wide to be a cube and figs. 171 and 172 are too narrow to be
cubes.

In order to make this experiment as simple as possible, the track
has been drawn so that the rail and the ties cross a horizontal (AB
in fig. 173) at the same angle. This means that a cube resting on the
rail will present two equal faces; that the diagonal of the top and
bottom faces (dotted lines) are horizontal and that the back corners
are vertically above the front ones.

Now let us extend the track as in fig. 174. Cube No. 2A occupies the
same relative position on the tracks as that in fig. 170 ; its two vertical
faces are equal. The other cubes are placed in such positions on the
tracks that the ellipses inscribed within them correspond with the
ellipses in figs. 169, 171 and 172. Thus we see that the proportion of
the ellipses on the same track depends upon their nearness to the eye.

An interesting application of this principle is seen in the locomotive
wheels (page 77) where the small front wheel is very nearly a circle
and the furthest driver is a relatively narrow ellipse. The camera man
who made the photograph from which this drawing was traced must
have been very close to the locomotive.

The diagram in fig. 164 illustrates the logic of this differential in
proportion of ellipses. Observers A and B view the two wheels from
different distances. The dotted lines represent the central directions
of their sight approximately central between the two wheels. The pic-
ture plane for each is, of course, at right angles to the direction of sight.
Note that the differential in width, in what would be seen as ellipses,
is greater for observer A than for observer B.

On the following pages we make an analysis of a very interesting
picture by Peter Helck which demonstrates many of the points covered
in this chapter.

173

I A

174

175

Advertising painting for the New York Central System
by Peter Helck.

HELCK No living American artist knows more about perspective or uses it
more expertly in his work than Helck. The subject here illustrated is
simple, compared with many that he is called upon to illustrate. Such
industrial scenes as the interiors of steel mills, with their intricate
machinery, involve about every kind of perspective problem that can
be imagined ; busy railroad centers, shipbuilding yards and the myriad
activities of business, farm, and commerce put Helck's knowledge and
skill to the acid test.

There can be no guesswork in the rendering of such illustrations as
the one chosen for this demonstration. As we proceed with our analysis
we shall see that every detail of the painting has been constructed with
such accuracy as can only result from meticulous observation of scien-
tific method.

Of course Peter Helck did not go through the steps presented in
this demonstration ; his knowledge of perspective is so thorough and
he has employed it so continuously over many years that the pro-
cedure here outlined was purely automatic. None the less it was active
in his subconscious mind as he made his painting.

The establishment of the eye-level is an important consideration in
every illustration; the picture's effectiveness depends in no small
measure upon the point of view from which the scene is to be viewed.
In order to dramatize the size and power of the large locomotive, Helck
established a low eye-level, such a vantage point as might be had by
a spectator standing in the ditch below the roadbed. The eye-level is
seen to be a little above the foundation slab.

Before discussing problems involved in the circular formsarches
of the bridge and the locomotive wheels-let us take a look at what
happens to the straight lines.

Vanishing points 1 and 2, we note, control all the horizontal lines
that are parallel either with the length of the bridge or its thickness,
also they control the lines of the locomotive on the bridge. But we
discover that the horizontal lines of the front of the lower locomotive
give us a different vanishing point. That point ( VP 8 ) is slightly below
the eye-level on the vanishing trace. How is this explained? (For
explanation of vanishing trace refer to Chapter IX.)

176

A heavy paper model of an engine
that would be useful to the student
in studying this problem.

It is explained by the fact that the locomotive is traveling on a
curved track. How do we know this? By the way the locomotive leans
as it does when rounding a curve, the inside rail of the curve being
lower than the outside rail. If the track were straight, and both rails,
therefore, on the horizontal ground plane, we would be able to see
the further rail, the roadbed being below our eye-level.

In order to demonstrate the perspective facts of this situation in
the clearest manner, let us reduce the problem to its simplest possible
terms by resorting to models (page 83) that represent the bridge and
the locomotive. We can use a rectangular prism for each, since we are
considering only their rectangular aspects. We have drawn the models
below the eye because by looking down upon them the points involved
can better be demonstrated.

Fig. 179 demonstrates the situation if the track were straight and
at right angles to the bridge as shown in fig. 177A. With the track
straight, the locomotive would not lean; its upright lines would be
vertical.

177B shows the tracks curved as in Mr. Helck's painting. But the
locomotive (in our plan) is seen to have the same position as when
the track is straight (assuming the center of the circle, of which the
curved track is an arc, to be on the axis line of the bridge) . Thus its
sides are still parallel with the bridge lines that vanish at VP 2 and
they would converge to the same point.

On the face of the bridge, in fig. 180 the slant of the leaning loco-
motive is indicated. The top and bottom lines, we note, seek a new
vanishing point (VP S ). This is located on the vanishing trace that
passes through VP 1 .

In fig. 181 the model of the locomotive has been completed by pro-
jecting forward from the rectangle drawn on the side of the bridge.
The darkened rectangle under it represents the plan, on the ground,
of the model before it was tilted to accommodate itself to the position
the locomotive takes on the curved track.

It appears that Helck's locomotive is not centered exactly under the
bridge as in our diagram. It is emerging from the arch and therefore
it would be at a slight oblique angle to the bridge. But the angle is so
slight as to be negligible. Had the locomotive proceeded a full length
further, it would have involved a more complicated diagram ; turned
at a pronounced angle it would have given us two new vanishing points.,

ypi

179

VP2

180

181

Let us consider the problems presented by the circular elements of
the picture. An analysis of the arches (fig. 182) reveals that they are
arcs of perfect circles but are not half -circles ; their centers are slightly
below the shoulders of the piers from which they spring.

If we visualize the arches as segments of enormous steel collars or
pipes, as indicated in fig. 182, it will help to clarify the problem. Think
of them as sections cut from long pipescylinders whose lines converge
to VP 2 .

The axis lines of these cylinders (dotted lines in our diagram) like-
wise converge to VP 2 and, drawing the long diameters of the two
ellipses (AB and CD) at right angles to them, we discover that they
have a pronounced slant from the vertical. Furthermore, long diameter
CD slants more than AB because the axis of the near cylinder inclines
at a steeper angle than its neighbor.

Now a tracing of the arches in Mr. Helck's picture shows that the
further arch was actually constructed according to the procedure just
described. But the nearer arch is the arc of an ellipse which has a
vertical long diameter, as the reader can demonstrate by a tracing
laid over the picture. Helck must have deliberately broken the rule
here in order to enhance the feeling of the locomotive's speed. Had
he constructed that arch on an oblique long diameter, as in our dia-
gram, its backward slanting direction would have opposed the loco-
motive's forward movement. As it is, there is a sympathetic feeling
of forward thrust in this arch. This may seem a very subtle device, t/
as indeed it is.

185

182

Let us next study the locomotive on the ground. In fig. 188, for
the sake of simplicity, we have placed the eye-level on the centers
of the engine's drivers although in the picture it is slightly below the
wheel hubs. If the tracks were straight, instead of curved, and the
locomotive, consequently, were in a vertical position as drawn in fig.
183, the long diameters of the ellipses would be vertical as shown,
and the further rail could be seen. But the lowering of the rail on the
inside of the curve changes this condition ; the axis lines of the cylin-
ders (which correspond to the axles of the wheels) slope downward
to VP 8 just below VP 1 . The long diameters of the ellipses, therefore,
must take a slanting direction (as shown in fig. 184) in order to be at
right angles to the axis lines as they should.

Here again Helck has taken some liberty ; he has exaggerated the
forward thrust of the ellipses, has slanted them more (fig. 185) than
they should be-according to rule-in an effort to force the impression
of speed.

The perspective facts of the locomotive on the bridge are quite
simple and need no explanation beyond what is shown in fig. 186. The
track is straight, of course, and the locomotive is erect as is indicated
by the vertical lines of its front. Note, however, that Helck has given
the verticals of cab and tender a decided thrust forward in order to
enhance the expression of speed. Analysis of the ellipses of the drivers
shows that their long diameters are at right angles to the axles of
the wheels as they should be. Observe that these diameters are not
parallel-the same situation as seen in fig. 182.

184

188

189

190

187 Advertising illustration for
the Axton-Fisher Tobacco Co.
by Albert Dome.

DORNE Coming now to Albert Dome's drawing for the Axton-Fisher
Tobacco Company we note that although the problem is a compara-
tively simple one, its successful solution imposes a thorough mastery
of perspective.

In the first place, we have a globe encircled horizontally and verti-
cally (fig. 188). If you lay tracing paper over the drawing it will be
seen that the feet of the three legs of the standard which, of course,
are located at the corners of an equilateral triangle (fig. 189) -are on
the circumference of a circle of approximately the same diameter as
the one that encircles the globe. Thus in fig. 190 we see a cylinder with
the sphere just fitting into its top opening, which is the first step in
the drawing of the base. The short diameter of the ellipse of the cylin-
der's base is obviously longer than that of the upper ellipse.

In order to draw correctly the triangle inscribed within the ellipse
one just has to know what an equilateral triangle looks like in a given
position. To an artist like Dome this is knowledge acquired years ago
before he earned a dollar as an illustrator. And one way to acquire
that knowledge is to make one hundred drawings from the model
of the triangle within the circle (fig. 24, page 22). Place the model
on the floor six feet away ; then eight feet away ; then ten feet. Set it
on a chair and draw it at those different distances. Do the same with
the model on a table. It pays to concentrate on this model to this extent
because once the correct image is fixed in the mind it is there for keeps.

While on the subject of illustrator Dome, I suggest turning back
to page 15 to study again his drawing for an illustration of a grocery
story incident. Note the meticulous way in which he has developed his
perspective of every smallest detail ; such as the spigot of the barrel
in the foreground. See how he has drawn the invisible lines of the
object, feeling out its construction with absolute accuracy. It would
be quite worthwhile for the student to copy this drawing faithfully,
enlarging it considerably. The experience would give him a better
appreciation of what it takes to make a master illustrator in this one
aspect of perspective skill alone.

chapter viii * g

THE CONE

It will help, in studying the cone, to think of it as enclosed within
a cylinder, both figures having the same base and the same axis (fig.
191). There are many situations (as in figs. 192 and 195) in which
this cone-cylinder relationship is useful.

Fig. 193 shows the cylinder lying on its side and in fig. 194 the cone's
apex has been dropped, allowing the cone to rest upon its sloping side.
Note that the long diameter of the ellipse representing the cone's circu-
lar base has been drawn at right angles to the cone's axis, a relation-
ship that is constant, as it is with the cylinder.

In fig. 198 we have a form composed of two truncated cones making
a spool-like object. Note here the way in which the side lines of the
cones become tangent with the bases. The sides of the upper cone
become tangent with the top circular base well in front of its diameter ;
the sides of the bottom cone become tangent with its base behind its
diameter. Note also the situation where the cones meet. The sides of
the lower cone become tangent behind the circle's center (ends of
dotted line) ; the sides of the upper cone are tangent at points in front
of the center (ends of full line). Looking down upon this figure it is
apparent that we see more than halfway around the lower cone where
it meets the upper one.

The saucepan in fig. 199 has a handle that slopes upward from the
rim at a pronounced angle. When the pan is revolved the free end of
the handle inscribes an imaginary circle which we can consider the
base of a flat cone, as indicated. The apex of this cone is useful in
determining the direction of a handle located anywhere on the rim
of the pan.

Perhaps it will seem that the demonstration of the perspective struc-
ture of Worms Cathedral towers are unduly complicated. "Who," one
may ask, "would employ this mechanical procedure in making such
a drawing?" The answer is, "No one would." Certainly the author did
not do so when he made the pencil sketch reproduced on the next page.
But the illustrator who carries such a structural basis in his mind will
use it-perhaps unconsciously-as he draws, even when he has the
object before him or, as in this instance, when working from a photo-
graph. Learning to draw is considerably more than training the eye
to observe accurately and teaching the hand to obey the eye. Many
demonstrations in this book are presented not with the expectation
that the illustrator will follow the procedures when he is doing profes-
sional work, but as training in constructive thinking which certainly
he will always employ in whatever he does. On the other hand, there
are many, many problems in advertising illustration where the artist
will in fact need to make use of intricate engineering strategy even
beyond anything covered in this book.

Each cathedral tower has six windows. The hexagon, mechanically
drawn in fig. 201, gives points that are projected up to the conical base.
These points (A, B, C and D) are the centers of the gable windows and,
from them, lines are drawn to the apex of the conical roof. Actually,
points C and D should not be located at the ends of the ellipse's di-
ameter as shown in fig. 201. Since they are structural points they should
be located at the ends of the circle's diameter not the ellipse's diameter.
This is shown in fig. 203, in a detail sufficiently enlarged to demonstrate

201

206

202

203

204

205

this phenomenon which is too subtle a point to be considered in the
small diagrams; so in figs. 201, 202, 204, and 205 we ignore this per-
spective fact. However, it is clearly observed in the pencil drawing
where the bases of the side gables are obscured by the cone's contour
lines.

We erect the side gables at C and D (fig. 201) as high as we want
them and connect their ridge lines (FM) by a horizontal line cutting
the cone's axis at E. Point E on the cone's axis then becomes the
center of two circles that we need for the construction of the two front
gables. The larger circle (dotted) establishes the gable's height; a
horizontal circular hoop would rest on points F,G,H,M and those on
the far side which we cannot see, so will ignore in our drawing. The
smaller circle, intersecting lines AX and BX, gives us the points where
the short ridge lines meet the conical roof.

In fig. 202 we locate the level of the gables' eaves at point 0. Project-
ing a horizontal line from into the cone's axis we get point Y, the
center of a circle which we need for locating points T, U, Z and Q on
the surface of the cone where the short eaves' lines of the gables will
go into the cone.

The width of the gables is projected up from the plan in fig. 201.

The points T, U, Z and Q do not actually fall upon radiating lines
from apex X, because lines ST and ZU, (fig. 203) are actually parallel
lines. However, lines ST and ZU, being parallel lines on a plane that
is slightly turned away from the observer, would show at least a slight
convergence. But the difference is so slight as to be ignored in draw-
ings. In figs. 204 and 205 are shown sections of the conical tower to
illustrate more clearly the structural facts.

RIGGS

208

207

209

It is not likely that Robert Riggs, the illustrator whose drawing is
reproduced on the opposite page, constructed a careful diagram like
that shown herewith. He is such an expert draftsman that he does not
require the mechanical aids needed by the inexperienced artist. No
doubt he had recourse to photographs for factual information.

At any rate, we find upon tracing his drawing that its lines,
extended, produce the accompanying diagram. Therefore, whatever
his procedure, the result checks exactly with our mechanical analysis.

Let us first consider the relationship of the three circles of the
listening "ears." Lines connecting their centers form a triangle. But
not an equilateral triangle. If it were, we would have an analysis more
like that of fig. 208. That is a reasonably true appearance of an equi-
lateral triangle on a plane such as rests against the three ears. We can
only conclude that the circles must be constructed on a triangle similar
to that of our diagram in fig. 207 and, in perspective, in fig. 208.

It will help the student, in considering the problem, to reproduce
this diagram (fig. 207) much enlarged on a piece of stiff cardboard
and hold it in a position that approximates the plane of the circles
in the picture. He should make the sides of the triangle ten inches
or so, and ink the circles to make them suggest those of the drawing.
He will discover that the circles on the cardboard do not look quite as
they do in the Riggs drawing. The long diameters of all three ellipses
on his model will be parallel, whereas in our fig. 208 they are seen to
take different directions. This is because in the object hence in the
drawing-the circular bases of the cones do not lie in the same plane;
they all tilt away from the triangular plane ABC due to the fact that
the axes lines of the cones converge to a point instead of being parallel.
Having discovered that the axes lines of the conical listening ears meet

Advertising illustration for

New England Mutual

Life Insurance Company

by Robert Rig 08.

211

at a common point, and that their bases form a triangle, we have the
triangular pyramid ABCD as seen in fig. 209.

The apexes of the truncated cones are located somewhere between
D and the triangular base ABC. These points (E, G, and H) are found
by extending the lines of the cones (as we have done in our tracing)
until they meet the axes lines AD, BD, and CD. Since the axes of the
three cones are the same length, a triangular plane connecting them
(E, G, and H) will be parallel to the triangular plane ABC.

Similarly, another triangular plane, parallel with the others, is
formed at K, N, and M ; points that indicate the centers of the small
ends of the truncated cones.

We have already noted that the three circular bases of the cones
do not lie in the same flat plane. The cone A being tipped toward us
more is represented by a base that is somewhat "rounder" than B
which is turned upward and away. The base of $me C being turned
away from us even more than B is a very narrow ellipse.

Furthermore, in our diagram (fig. 210), we observe a perspective
variation in the lengths of the truncated cones and their axes lines
AK, BN and CM, due to the different degrees of their foreshortening ;
the nearest one (AK) being the shortest because it is turned away
from us at the sharpest angle.

Finally, consider the long diameters of the three ellipses (fig. 210).
Each is seen to be actually at right angles to the axis of the cone as
is always the case regardless of the cone's position.

This analysis may seem quite complicated to the novice but to one
who has acquired enough skill to draw the object at all, the procedure
outlined is very simple. Most artists might use such a diagram as a
check on the correctness of a freely drawn illustration, rather than
as a preliminary framework upon which the final rendering would
be carried out.

V'AKIISHING TRACE

215

chapter ix

212

THE HOUSE OF SEVEN VANISHING POINTS

The House of Seven Vanishing Points may look confusing to the
beginner, but when studied step-by-step on the following pages it
should present no difficulties.

The student is advised to make an instrumental drawing of this
subject, perhaps half again as large as fig. 214, carrying out all of
the converging lines to their vanishing points. Since some of these
will fall at too great a distance to be located on the drawing, additional
sheets of paper will have to be cellophane-taped to the drawing to ex-
tend the field of operations. When drawing instrumentally one should
use hard leads that are kept well-sharpened to a fine point.

The main structure, of course, is as simple as fig. 212, a rectangular
solid topped by a triangular prism. The peak of the gable is on a vertical
line passing through the crossing of the diagonals of the rectangular
end.

The vanishing points of all converging lines other than the horizon-
tals that converge to VP 1 and VP- will be found in the vertical
vanishing trace which passes through VP 1 . The logic of the vanishing
trace is demonstrated in figs. 213 and 215. Fig. 213, it will be seen, is
fig. 212 turned so that the building stands on end. The horizon line of
fig. 212 becomes the central direction of sight in fig. 213 and the
vanishing trace becomes the horizon line.

In fig. 215 we have laid the house on its side to show how logically
the roof lines of the dormers, which are in the same plane as the
building's side, converge to the vanishing trace established by the
perspective of that plane. This figure had to be drawn here in violent
perspective in order to get the vanishing points on the paper. It will
be seen that the dormer roof lines of the large house converge very
slightly. That is because they are on a plane (the side of the house)
which, being turned but slightly away from the observer's direction
of sight, has its vanishing points ** great distance from the building.

HOklSON t/NE

217

216

The next step is to measure off the widths of the dormers on the
eaves line (AB in fig. 217) . To do this we have recourse to the simple
geometric device illustrated in fig. 216, where we wish to divide the
line AB into any number of equal parts-five for example. First we
draw AC, a line of indefinite length, at any convenient angle to AB.
On this we measure off five equal dimensions of any length from A.
These dimensions could have been larger or smaller, though it is best
not to have them too large. From C, a line is drawn to B, and lines
parallel to CB are drawn from the four other points on AC to AB.

Fig. 217 shows how we apply this device in perspective. The proce-
dure is different in some particulars though the principle is the same.

Instead of making the AC line of indefinite length, we establish its
length by a line from VP 1 through point B. This makes AC perspec-
tively equal to AB. On AC we now measure off the dormer widths and
the spaces between them. Since line AC is parallel with the picture
plane-hence is not foreshortened-we can use ruler or dividers to lay
out our measurements on it.

Lines drawn from the dormers, indicated on AC, to VP 1 are paral-
lel in perspective to line BC ; hence they translate our measurements
with perspective accuracy to line AB.

When the angle between the AB and AC lines is as acute as in
fig. 217, the converging lines that mark off the divisions on AB cross
it as such acute angles as to make accuracy more difficult than if the
BAC angle were wider.

If, instead of laying out our measurements on line AC in fig. 217,
we extend the building downward, imagining its base line to be DE,
we have a wider angle and the measuring lines that go to VP 1 cross
DE at a better angle (more nearly at right angles) for accuracy. The
points on DE can then be projected up to the eaves line. This is a very
useful device for measuring perspective distances on foreshortened
surfaces; the need for it is frequently encountered. If we wished to

218

VP'
6

219

locate doors and windows on our building, for example, we would do
it this way rather than working from the eaves line.

Now for the drawing of the dormers. By showing three dormers,
in fig. 218, in three stages of development, we can demonstrate each
step to be taken. In A we indicate the side lines on the roof that, being
parallel with gable line X, converge with it to VP H (see large drawing) .

Next we must find the ridge lines of the gables. We see, in dormer B,
the vertical center line OP and a line drawn from up the roof to
VP 3 . Where this line is intersected by the ridge line (which is parallel
with line Y, hence converges with it to VP 1 ) we have point S where
the ridge meets the roof.

We need but one other point, point N, at C. It is found by extending
the dormer's eaves line from M toward VP 1 . (The dormer's eaves as
well as their ridge lines are parallel with line Y.)

If all these operations are carried out accurately, we shall find by
testing the drawing that we have the various sets of converging lines
shown on our large drawing. The roof lines of the dormers (fig. 219)
converge to VP 4 and VP 7 as shown on the diagram in fig. 215. The
lines that converge to VP'-they are on the same plane as the roof-
come to a point rather close to the roof because the roof plane slopes
sharply away from the observer. These lines are not parallel with
the gable line X of the roof, so they do not converge to a point on the
vanishing trace.

If the dormers are correctly constructed as described, one does not
need to worry about the convergence of the gable lines that point to
VP 4 and VP 7 or about those that converge to VP 6 . It is quite unlikely
that an illustrator would carry these lines out to their vanishing points.

Note in fig. 219 that all the S-points are on a horizontal line that con-
verges to VP- ; likewise the N-points, the M-points and the P-points.
Knowing this, we do not have to go through all the structural opera-
tions here described for every dormer; having constructed one, the
others can be largely constructed by projecting these structural points
of the first as we have done in figs. 218 and 219.

The chimney is the one remaining detail to be considered. In fig. 220
two stages in its drawing are shown. At A we indicate the joining lines
of the chimney on the visible roof. At B we see lines drawn from points
D and H down the invisible sloping roof toward VP 5 , since they are
parallel with line X which converges to that vanishing point. From
points and P, lines are directed toward VP 1 . These lines are horizon-
tal and parallel with line Y which also points to VP 1 . We now have
the opening through which the chimney will project.

For the sake of greater clarity of demonstration, at B we have
projected upward the section of the building-imagining it to be solid-
that we have cut out to admit the chimney.

In this, as in all other perspective problems, the "X-ray vision"
which sees through the object and develops every point of construc-
tion is absolutely essential. We have to feel around and through the
object, thinking of it as a three-dimensional object rather than as a
flat drawing of it on paper. In this problem we must imagine ourselves
on that building, laying off the lines for the cut in the roof on the near
and visible slope, then going over the ridge and doing the same on
the other side. That kind of imagination develops our structural sense.

chapter x

Before making: the perspective drawings on page 98, it is advisable
to consider the diagram in fig. 221 which presents a framework com-
posed of four sets of lines. The vertical lines we will call AB lines;
the horizontal ones CD lines* Whether we wish to draw the squares in
one-point perspective as in fig. 222 or in two-point perspective as in
fig. 223, we use the same framework. In the first instance we view it
from position X ; in the second our line of sight is from Y.

In fig. 222, after laying out the width of the squares with ruler or
dividers on the nearest CD line, we draw the AB lines converging to
a vanishing point on the eye-level.

There is no mechanical method (in freehand perspective) of deter-
mining the placing of QR -the line that will measure off the front-to-
back dimensions of all the foreshortened squares ; we have to rely upon
our acquired knowledge of the appearance of squares seen at various
levels. So, using our freehand judgment, we draw one square (white)
which determines the position of line QR and the layout of the entire
framework. The diagonal CM which is an extension of the diagonal
of the extreme left square establishes points for all CD lines where it
crosses the AB lines, as in the diagram (fig. 221).

When we wish to lay the pattern as seen in fig. 223 (viewed in fig.
221 from Y) we draw our first square freehand and find its right and
left vanishing points on the eye-level. Then the EH lines are drawn to
serve as guides for the procedure in fig. 224 ; we first draw the dark
zig-zag lines, converging to their vanishing points; then the light
zig-zag lines. We now have the row of squares immediately behind
our first white one. We see in fig. 225 how the pattern is completed by
the drawing of all EH lines (see fig. 221) which pass through the
intersections of converging AB and CD lines and meet at a vanishing
point on the eye-level. This may sound confusing in the reading but
when drawing, all will be clear.

Now the drawing in fig. 223, although produced in "correct" scien-
tific perspective, gives a distorted pattern. The squares at the sides
certainly do not look like squares ; they are elongated rectangles and
their distortion increases with the distance from the center square.

Fig. 226 shows how this difficulty can be largely overcome merely
by raising the vanishing point for the EH lines considerably above the
eye-level. This is what the illustrator of the Coolerator picture (fig.
233) did with his floor pattern. Just how high that vanishing point
should be in any given situation is a matter for experimentation. The
student would do well to try lower and higher points.

This device is not perfect; it gives us some distortion at the sides
where the squares begin to look too long from front to back instead
of from side to side as in fig. 223. And they get too long from front to
back in the near foreground. But certainly the effect is much improved.

227

Interior of a Dutch house by Pieter de Hooch
(Dutch, 1629-C.168S). National Gallery, London.
If you will put tracing paper over the
painting by Pieter de Hooch and carry out all
converging lines, you will find that the
painter was meticulous in laying out
his perspective scientifically. But do his
square tiles look square? Are they not
somewhat too narrow from front to back?
Experiment by laying a few squares of paper
on the floor of your room. Then develop on
your tracing the "corrected" tile pattern.

101

Courtesy Maurice Weir.

In this photograph note the slight

distortion of the squares at

sides of the picture - evidence that

the camera does not see things as

does the human eye. Refer to the

second paragraph on page 10.

lot

229

233

Coolerator freezer advertisement
Courtesy Coolerator Company.

109

232

231

The hexagon pattern, fig. 230, is no more difficult than that of
squares. In fig. 231 we note how a hexagon can readily be constructed
within a circle by dividing the circle's diameter into four equal parts
and drawing parallel lines A, A, A vertically through the division
points.

Fig. 232 is the same operation in perspective. We divide the circle's
diameter into four equal parts and, after drawing the center A line
vertically and extending it upward to an estimated eye-level, project
the other A lines and B lines to the same point as seen in fig. 230. The
placing of the eye-level has to be judged according to the proportion
of the ellipse we start with ; the longer the vertical axis, the higher
the eye-level. When the eye-level is already known, as is the case when
we are laying a hexagonal floor in a room interior, it is the proportion
of the ellipse that has to be judged in relation to its distance below the
eye-level. This can be accurately done only after a lot of practice draw-
ing of circles at various levels.

After the first hexagon has been drawn and the A and B lines car-
ried out to their vanishing point on the eye-level, the pattern develops
itself, the diagonal lines to their vanishing points crossing in such a
way as to give all needed lines and points to complete the pattern.

104

234

PLAN OF STEPS

IN AvPEfcSPECTIVE

1O5

chapter xi

Our problem here is the drawing of two flights of steps (fig. 236) in
one-point perspective. Consult the plan as we proceed. We begin with
the lower flight (fig. 234).

The height of the rise XY we shall assume to be three feet. We
would have to determine how many steps of suitable dimensions are
needed. If we decide upon a 6-inch riser, we shall need six risers and
five treads. With a 6-inch riser an 11-inch tread is desirable.

First we draw line WY, which should be 55 inches long. The vertical
line XY, which is 36 inches high, will serve as a scale in making this
measurement. After dividing line WY into five equal parts (11-inch
divisions) we project lines upward. Lines projected forward (left)
from the 6-inch divisions of the line XY give the measurements for
the risers. The line OX passes through the projecting corners of the
steps. The line LM, drawn parallel with it, intersects the converging
lines of the steps and terminates them at their far ends. That is all
there is to it.

To draw the upper flight of steps (fig. 235) -we will do ^vell to make
a plan as we have done at fig. 234A. Then we can draw the same plan
in perspective (fig. 235) starting with that of the lower steps which
is a square. Having drawn that and the plan of the lower platform
adjacent to it, which is also a square, we can readily lay-out the remain-
ing two squares geometrically as suggested by the dotted lines.

Since the upper flight is to duplicate the lower, we can extend XY
upward and from X step off on it six riser heights equal to those of
fig. 234, giving us point Z. From point Z and from the five other meas-
urements we draw lines to the vanishing point.

What we want now are points K, the corner of the first step, and D,
the corner of the top step at the platform level. These points are found
by projecting points G and H up from the plan as illustrated. A line
from K through D to OVP (point opposite VP) gives us points for
the other steps as it cuts the horizontals from ZX to VP. The rest is
obvious.

In fig. 236 we have drawn a rail which should be 30 inches higher
than the treads of the steps. We can take our measurements from the
6-inch riser on the line NB. Point B is 36 inches from the ground and
SO inches above the tread. The rail BC can then be drawn parallel
with the rise of the stairs. Point E is easily established by a line from
C to the vanishing point OVP already established in fig. 235.

106

240

107

When the same stairs are viewed from an angle, as in fig. 237, the
procedure is the same, except that we cannot put a ruler on the line
WY as we did in fig. 234 to measure the widths of the treads. What
we have to do is to draw a rectangle XYTJW (shaded) that is 36 by 55
inches. In figs. 238 and 239 there is a. suggestion for doing this. First
draw a square in perspective against the vertical XY. By the use of
its diagonals, as in fig. 239, we get a 36 by 54-inch rectangle (a square
and a half) in perspective close enough to 36 by 55 inches. When we
have done this, we mark off by estimation five equal spaces (per spec -
tively) on WY.

Note that the actually parallel lines OX and LM, being on a receding
plane, converge ; as do the corresponding lines on the upper flight. In
fig. 240 we see these lines meeting at points directly above the right
and left vanishing points on the vanishing traces. Since the angle of
rise from the horizontal is the same in both flights of steps, both points
are the same distance above the two vanishing points.

242

Drawing by David Hendricksonfor

The Travelers Insurance Co.,

Hartford, Connecticut.

HENDRICKSON

There is really nothing new in the interior of the railroad station
(fig. 241). Note how the figures are scaled to the steps, which are
assumed to have 6-inch risers. The lower flight has eleven risers, giv-
ing the first platform a height of 66 inches. The figures have been
made about that height, which has been projected up to follow the
line of traffic along the platforms and up the other steps.

The heights of the risers of the upper flight have been laid out on
the ABC line and projected back to the center vanishing point. The
vertical measurements of all steps are thus laid out on the one facing
plane (TO ALL TRAINS) upon which there is no foreshortening to com-
plicate things. After points X and O have been foundby lines from
Z and A to VP cutting the verticals of the archway on the right we
draw a line from X through extending it upward until it intersects
the vanishing trace at OVP. From OVP to point Y we then have a line
that establishes points for the step corners at the left.

An analysis of David Hendrickson's drawing for the Travelers
Insurance Company represents some interesting points.

First note that the artist has used two vanishing points although
one of them is within the confines of the drawing. This "violation" of
the "rule book" improves the design of the picture by giving a slanting
direction to that top step instead of a horizontal one. Refer to Chapter
VI for a discussion of this point.

Note that the lines of the upper stairs converge to the vanishing
point with those of the lower flight. Of course they are parallel lines.

243

241

Ill
chapter xii

UP HILL AND DOWN

Do you have trouble getting up or down hill with your pencil? Does
the inclined street refuse to incline in spite of your graphic struggles?
Does perspective, which you profess to understand, somehow fail to
work in hilly country? If so, you are one of a large company.

The fact is that students who get along nicely on the level encounter
difficulty when the road descends before them or climbs up the side
of yonder hill They appear to know their perspective, yet when the
sketch has been completed according to the rules, the street looks as
level as a floor.

The perspective rules are simple enough, but they seem inadequate.
One soon discovers that the illusion of up and down is not secured
merely by correct perspective method. Science alone will not always
do the trick. Art, or rather artifice, must be combined with science ;
strategy must accompany mechanical skill.

For example, in the down street, illustrated, an auto van parked at

244 the curb becomes an important element in the illusion, because it con-
forms to the inclined plane upon which it rests instead of being ad-
justed to it as are the houses. The van thus presents several points of
difference: its top cannot be seen as can the horizontal roofs of
houses below the eye-level ; its uprights tip forward in contrast to the

245 verticals of the houses ; its converging side lines follow the curb lines

down, instead of going with the roof lines to the eye-level.

Again, emphasis is given to the horizontal lines below eye-level and
to the tops of .objects which the spectator looks down upon. Accenting
the sill lines of the buildings calls attention to that telltale angle with
the sloping street and creates a step-down impression which is impor-
tant.

The step-down effect is in fact nearly indispensable. When lines
which the observer knows are horizontal are shown at an angle with
the street, the illusion of an incline is assured. The greater the angle,
the more pronounced the sensation of incline. For this reason a steep
hill is more easily depicted than one with a gentler slope which de-
mands those subtle artifices suggested above.

The Yonkers Street (figs. 244 and 245) is especially interesting
because it involves four vanishing points. All horizontal, parallel build-
ing lines converge to VP 1 on the eye level. The street lines converge
downward to VP 3 directly underneath. But, it will be noted, the angle
of the street's principal incline changes at a point near the hydrant ;
from that point to the foreground it is less inclined. Hence we have
another vanishing point (VP 54 ).

Where the further truck is parked, the street obviously dips down
at an even greater incline; it is so steep that it cannot be seen. But
the top and bottom lines of the truck, converging downward, give
still another vanishing point (VP 4 ).

246

248

Figures 246, 247 and 248 suggest an experiment for demonstrating
the few perspective facts involved. A piece of cardboard with pencil
lines to suggest the curbs will represent the street. Cardboard boxes
or wood blocks will serve as models for houses when doors and win-
dows have been indicated.

When the street is horizontal as in fig. 246, of course its lines con-
verge with those of the buildings. But when it is tilted as in fig. 247,
its converging lines meet at a point directly below the eye-level vanish-
ing point. This new vanishing point is directly below the eye-level on
the vanishing trace.

The important fact to remember is that the tipping of the street
plane does not affect the perspective of the buildings: an obvious
enough truth, yet a frequent point of confusion for the beginner.

The inclined street (fig. 247) cuts across the doors and windows.
In order to reproduce the true effect of a street, the house models
should be adjusted in height to conform to the grade of the street
as shown in fig. 248. Notice the step effect produced by the sill lines
in fig. 248.

In the up-hill sketch a steep street in Assisi, Italy (fig. 249) the
inclined street lines naturally converge upward and the horizontal
building lines seek a point directly below. The spectator's eye is about
on a level with the curved tops of the doors of the building on the left.

113

"A Street in Assiai, Italy"
Pencil sketch bv the author.

New York University Law Center, Eggera and Higgins, Architects.

251

252
Oil painting by Walter Klett.

us
chapter xiii

Perspective books written a generation ago were not concerned with
problems discussed in this chapter. Until comparatively recent times
no one ever thought of rendering a vertical line other than vertical.
Until the advent of skyscrapers, people actually didn't have to tip
back their heads to take in the roofs of such structures as were com-
mon up to fifty or sixty years ago. To be sure, there were the great
temples of Greece and Rome, and towering cathedrals such as Rheims
and Cologne to make tourists crane their necks in viewing lofty cornices
and majestic spires.

But until the camera taught people that vertical as well as horizon-
tal lines converge when viewed from below or above, that phenomenon
was ignored by artists. We see no evidence of it in the old prints which
recorded artists' impressions of those far away days. And although
the early photographers discovered that their lens when pointed up-
ward produced converging uprights, they were careful to handle
their cameras so as to avoid the then unfamiliar effect.

As buildings reached upward to the sky, however, it became no
longer possible to overlook the importance of vertical convergence
which now is the concern of every photographer and illustrator. And
when the airplane provided man with wings, his familiar world, now
seen from on high, assumed new aspects that the illustrator had to
reckon with. Viewed from above, vertical lines were no longer vertical ;
the old reliable horizon line began to tilt and slant in alarming fashion.
To cope with this situation the old rules had to be revised and amended.

The camera and the cinema have long ago accustomed people to
the effects which at first seemed distortions. Close-ups taken with
tilted cameras opened up new and dramatic possibilties in picture-
making. The camera has made objects actually look different to us than
they did formerly.

These new facts of appearance do not involve new rules; the old
principles have only to be adapted to the new conditions.

The value of vertical foreshortening is convincingly demonstrated
by a comparison of the two pictures shown on the opposite page. The
first picture is an architect's typical rendering of a building designed
KLETT by his firm. Fig. 252 is a reproduction of a painting by illustrator
Walter Klett. Both buildings are viewed from approximately the
same height and the same angle. In the former, all vertical lines have
been drawn exactly vertical; in the latter they converge downward
and, if projected, would meet at a point far below the picture. Note
that the Law Center actually seems to be broader at the foundation
than at the eaves ; its upright lines appear to converge to a point above.
It is an unnatural effect.

253

Illustration by Al Parker for
a story in Good Housekeeping.

Now when we look down upon buildings from the air we adjust our
picture plane that imaginary transparent plane so that instead of
being a vertical plane it is at right angles to our downward direction
of sight. Not only will all vertical lines now appear to converge down-
ward ; the heights of the windows will diminish in the lower stories.
Observe this in Carl Bobertz's street scene on page 117.

We have become so habituated to the appearance of downward con-
vergence of verticals that three-point perspective is commonly used
even in the rendering of furniture and other low-lying objects. Close-
up camera shots from above will give this kind of effect to any object.

254

285 Drawing by the author of office <U*k and chair.

266

Anilluttrationby
Carl Bobtrt* for a
ftory m Collier's.

118

PARKER Yet, turning to Al Parker's picture The Amateur, on page 116, we
note that this famous illustrator ignored downward convergence in
this instance. Although all the upright lines of the building slant from
the vertical to give the downward-looking impressions, they are paral-
lel. It would be interesting for the student to experiment with this
picture in an effort to discover why the artist did not converge those
verticals downward. Leave the corner of the house as it is but converge
the lines of the window and blinds. Would the design be less pleasing?
MARINSKY Now let us analyze Harry Marinsky's painting for Shell Oil Com-
pany, on page 119, and see what kind of perspective layout it is based
on. Fig. 258, page 119, is a reproduction, greatly reduced in size, from
a mechanical analysis traced from the author's picture. Ignore the
dotted lines and point X in this diagram for the present ; we will refer
to them a little further on.

The first step in making such an analysis is to carry out the con-
verging lines of the roof-tops to their respective vanishing points
(A and B). A line connecting these points is, of course, the horizon
line on the level of the observer's eye.

Then extend the building's vertical lines until they meet at a point
below the picture. Next draw a vertical line from point C to the horizon
line a line at right angles to the horizon. This line, which is the center
line of vision, will be seen to pass through the vertical building lines
that are actually vertical in the picture ; that is, at right angles to the
horizontal bottom line of the picture.

Now the horizon line in Mr. Marinsky's picture is horizontal as it
would be if the spectator were looking down upon the scene from a
very high tower ; or if from an airplane, the plane were flying on an
even keel, that is, with its wings parallel to the earth's surface.

What if the airplane were to bank as it does when flying in the arc
of a circle instead of in a straight line? In that case the horizon line-
in a photograph taken from the banked plane-would be tilted at an
angle to the actual horizon.

Suppose Mr. Marinsky had chosen to give the effect of a view from
a banked plane-all he would have had to do, having first laid out his
perspective as described, would be to cut a mat and lay it over his
picture as indicated by the dotted line in fig. 260.

SIEBEL In most instances the illustrator would follow the plan employed by
Marinsky-a horizontal horizon, but there are times when it is effective
to use the tilted horizon. Such is the very dramatic picture that Fred
Siebel painted as an advertisement for the John Hancock Mutual Life
Insurance Company. In studying the analysis of this picture on page
121, it will be seen that it was first laid out with a horizontal horizon.
Siebel achieved a tilted camera effect merely by the way he has masked
his picture. Cut a rectangle the size of the photograph in the center
of a sheet of paper and lay it over the diagram of the secretary (fig.
262) with the vertical sides of the mask parallel with the center line
of vision. Your mask will coincide with the dotted line in fig. 262. Then
you will see how the drawing was laid out in the first place : the vertical
sides of the picture at right angles to the horizon line, the horizontal
sides parallel with it. The center line of vision, it will be seen, runs
through the secretary a little to the left of its right side and, of course,
is at right angles to the horizon line. Now turn your mask and you
will see how the effect of the picture was achieved.

Advertising painting

"Not the DROP but the STOP"

by Harry Marinsky for

Shell Oil Company, Inc.

257

258
>A HORIZON LINE POE ^Pi

O-C

Of course there is violent distortion in Siebel's drawing. All three
vanishing points are too close to the object to give a strictly natural
appearance. Angles X and Y are sharper even than right angles. The
study of similar situations in your own home will convince you that
such angles are impossible ; the X and Y angles would have to be wider
than right angles instead of narrower. However, no one would think
of criticizing the drawing, because the distortions are managed in such
a masterly way as to give a dramatic and satisfying design.

I think it wise at this point to call attention to erroneous instruction,
sometimes given, in locating the C-point in a three-point perspective
drawing. This is the notion that the ACB angle should invariably be
a right angle. (See fig. 262 A.)

The fallacy of this notion is easily proved by making analytical
studies of drawings and photographs as we have done with Marinsky's
painting. If Marinsky had obeyed this rule his C-point would have
been at point X (fig. 258) quite near the picture. In that case the
perspective of the vertical building lines would have been as violent as
those in fig. 262A.

Now the location of that C-point is a purely arbitrary matter. Put
it where it will give the most satisfactory effect to your picture.

261

Drawing by Frederick Siebel for an advertisement
for John Hancock Mutual Life Insurance Co.

Itl

P-OE

262 A

262

I M * ; ft O V M f NTS IN A N $ T H t $-J A

266 Courtesy Abbott Laboratories, North Chicago, Illinois.

f< O R I Z O N L I N E g_

It is appropriate here to point out again that what is proper in per-
spective drawing depends upon the use to which it is to be put. As has
already been explained, the painter thinks nothing: of violating: the
rules for the sake of better design in his pictures. The illustrator, who
usually aims at literal representation, has to come close to photographic
appearance ; he usually avoids obvious distortions. On the other hand
he finds distortions useful, even necessary, in certain types of demon-
stration drawings in which "normal vision" is inadequate. An example
of this is the Curare picture on page 122. In this we see the same acute
angle effect in the foreground as in the Siebel drawing. But we shall
see that no "correct" perspective rendering of this subject would per-
mit such a comprehensive illustration of the hospital's functioning as
is here made possible by distorted perspective.

Note first that the observer is brought very close to the corner of
the building, a factor that accounts for its acute angle. Of course the
eye could never see it like that, but the camera could.

However, it might be asked why that left vanishing point would not
as well have been pushed further to the left and the sharp corner
avoided. In that event the over-all horizontal dimension of the building
would have been considerably increased, necessitating, perhaps, a
reduction in the scale of the picture as a whole in order to get it on the
page. Furthermore, the left wall, in that case, would obscure much of
the interior rooms on the near corner. As it is we have an almost
unobstructed view of the operating room on the top floor.

Another good reason for the violent perspective is found in the very
pleasing layout of the page, due to that sharply pointed building sil-
houette (see the layout analysis).

Looking down into the first three floors we see how by establishing
another arbitrary vanishing point for the X-lines far to the left for
the end walls of the rooms, it was possible to give these rooms better
illustrative clarity than would have been possible had the X-lines been
made to converge with the building lines to A. As a matter of fact,
the artist did not bother actually to carry those X-lines to a single
point ; they merely take a general direction to a vanishing point.

Note that the C-point is far below the picture.

Thus far we have considered three-point perspective of objects seen
far above. Now let us get back to the ground and do some looking up.
This involves the exercise of even greater judgment and more subtle
strategy. Even though our eyes have, through photography, become
conditioned to great distortion in this kind of three-point perspective,
the illustrator cannot always "get away with" effects that are accept-
able as photographs ; because, after all, almost every one does recog-
nize the limitations of the camera through his own amateur experience
and subconsciously makes allowances for effects that will not be
accepted from an illustrator.

In photography it is often impossible for the camera man to view
his subject in such a way as to avoid distortions. He may be obliged,
when working in narrow or busy streets, to take positions which give
unavoidably distorted results and, for the sake of detail, get too close
to the subject for "normal" observation. The illustrator is not limited
by these conditions. And even though he is required to draw the subject
from a specified viewpoint which would give unpleasant distortion in
photography, he has devices in his bag of tricks that enable him to
come up with a rendering that does not offend the eye.

It will help the student to make a collection of pictures both photo-
graphs and drawings involving this upward-looking problem. Careful
study will help him to acquire a sense of what is acceptable to the eye.

its

270

Everyone is familiar with the distorted effect of buildings when
photographed with the camera tilted upward as in fig. 270, opposite.
That is an unsatisfactory and unnatural impression, one that would
never be seen by the human eye.

What about the picture of the skyscrapers, fig. 271? Do we not see
here exactly what a person would see when looking up as the building
lines converge skyward? The answer is yes. What is the condition that
makes this effect acceptable and at the same time makes that of fig. 270
unacceptable? We find the answer in fig. 269, where the spectator is
shown at three different observation points, A, B, and C. Stationed at
A, very close to the building, he has to tilt his head back and look sky-
ward in order to see the top of the building. When doing so, his picture
plane tips at an angle and through it he sees exactly what is illustrated
in fig. 271. While looking up he simply cannot see the base of the build-
ing. The camera has a much more extensive range of view, as illus-
trated in fig. 270.

At station point B (fig. 269), the spectator is in a more favorable
spot for viewing the building as a whole, but even here the situation
is similar to that of the A observer. Observer C is far enough away
to have a comfortable view of the entire structure; and his central
direction of sight indicates a picture plane that is less tilted from the
perpendicular. This means that there will be some upward convergence
of vertical lines, but not much. It is probable that normally the spec-
tator's range of vision does not exceed a 30-degree angle. C's range is
slightly less than 30 degrees.

271

The drawing of Radio City (fig. 272) is a good illustration of a
skyscraper's appearance from station C. Now in this drawing, when
we focus on the lower part of the building, we are not disturbed by
the slightly converging lines of the vertical. And in looking upward
there is enough convergence of verticals to create the normal perspec-
tive effect of towering height.

STAHL What Ben Stahl did in his picture (page 127) is very interesting. He
did here what we have just said could not be done satisfactorily. We
should have qualified our statement by saying that usually it should
not be done. A master illustrator like Stahl can and does do things that
are difficult for the less creative and less experienced. The eye-level
here is the foundation line of the church. Yet from the way in which
the whole picture is handled, especially the figures in the foreground,
we have the impression that the spectator's eye is perhaps on the level
of the extreme bottom of the picture. The question is, "Is the effect
better-more dramatic than if Stahl had kept the upright lines vertical,
which would be a more 'logical* thing to do?"

This brings us again to the axiom that the creative illustrator is
never the slave to rules or even to logic. He is a dramatist and he uses
his imagination and his skill to achieve his purpose, violating rules
when this serves his purpose. It would be a profitable experiment for
the student to copy this picture, "correcting" the drawing of the church
by making its upright lines vertical.

272

273 "The Lord Was Their Shepherd" painting by Ben Stahl'for John Hancock Mutual Life Insurance Co.

277

278

chapter xiv 1*9

To one who knows perspective, reflections present very little diffi-
culty. Indeed, it is only necessary to point out a few simple truths such
as can be demonstrated in a brief chapter upon the subject.

The whole matter may be summed up in a single statement: "The
reflection of every point is located directly underneath, as far below
the reflecting: surface as the point is above/* Thus the reflection prob-
lem may be considered as involving but three points, A, the point to
be reflected ; B, the point on the reflecting surface directly underneath ;
and, C, the reflection of the point. So we shall refer to A-point, B-point,
and C-point in describing the operations which are controlled by these
points.

The reflection of a post set vertically in the water, as in (W) fig.
274, is its exact image inverted. Likewise the post set at an angle in a
plane parallel to the picture plane (X) reproduces itself in the reflec-
tion, the reflection being the same length as the post itself. In ( Y) and
(Z) the conditions give different results. The posts inclining forward
(at Y) and backward (at Z) make reflections differing in length from
the posts. Such variations in length of objects and their reflections will
not confuse the student who remembers the relationship of points A,
B, and C. Point C is always as far below B as A is above. That is the
key to all puzzling situations. So long as one is content to find the
reflection of one point at a time, little perplexity will be experienced.

A building seen on the water's edge (fig. 275) reflects a perfect
image of itself in the water provided the spectator's eye is near the
'water line. Fig. 275 appears as a bisymmetric shape bisected by the
water line. Occasionally, the camera catches such effects so perfectly
that it is difficult to distinguish reflection from reality and the picture
seems as true upside-down as in its correct position. But when the
eye-level is considerably above water-level the object and its reflection
differ radically in effect, as illustrated in fig. 276.

This is more easily understood if one thinks of the reflection as a
part of a bisymmetric solid with its lower half submerged. The reflec-
tion appears exactly as the lower half of such a solid figure would
appear when looking down upon it, and its drawing is dictated by the
same rules of perspective which are associated with the appearance
of objects.

In the rule stated at the beginning of the chapter, we learn that "the
reflection of every point is located directly underneath, as far below
the reflecting surface as the point is above." When the object is above
the water line and set back from its edge (fig. 277), the student will
have no trouble in finding his C-points if he remembers that the B~
points must be on the water-level. The dotted lines underneath the
building indicate the plan projected down to water-level to locate B-
points.

Fig. 278 represents a familiar and interesting situation. Conceiving
the reflection as a submerged duplicate of the bridge, reflections and
bridge become a solid mass of masonry with cylindrical tubes or tun-
nels passing through it. When the tunnels have been constructed
according to the usual perspective method, the reflections have been
properly indicated.

130

284

Advertising drawing by I. W. Ferguson,
Advertising Manager for H. H. Robertson Company.

279

281

282

Now, referring to the powerhouse (fig. 284), we note an interesting:
violation of natural appearance. Had the rules been followed, the
smokestacks and the PWR sigrn would not have appeared in the -water ;
instead there would have been an uninteresting* reflection of the ver-
tical lines of the rectangular masses. Note that the illustrator chose
not to show reflections of the steel tower and the conveyor chute. A
good exercise for the student is to "correct" this drawing, making the
picture deep enough to accommodate the entire reflection. Eliminate
the boats in order to allow for the reflection of the steel towers.

Let us consider, next, reflections by vertical surfaces such as are
seen in a mirror on a bureau or dressing table. In fig. 279 -we have a
box that represents a jewel casket. It touches the mirror. (For the
sake of simplicity we will suppose that the mirror has no frame.)

Our procedure is the same as in water reflections, as is readily seen
when we tip the drawing up (fig. 280) so that the mirror is horizontal.
The mirror reflects the casket exactly as though it were water reflect-
ing a building at its edge. This simile will be especially helpful in visu-
alizing what happens when the mirror is tipped forward, as in fig. 281.

The bottom line of the mirror swings up as well as backward ; so
our first step is to project the glass downward until it meets the plane
of the dresser top, extended backward at the dotted line X. Then we
can project the lines of the casket back until they touch the glass.

Now in fig. 282 we tip the drawing up again so that the mirror is
horizontal. Following: the procedure already demonstrated, we find B-
points on the mirror vertically under A-points, on lines marked Y which
are parallel with the short lines of the mirror. The C-points are thus
easily located.

In fig. 282 where we liken the mirror to a sheet of -water, the AC
projection lines are vertical. They "pass through" the mirror at right
angles to it. That is what we always must remember about reflections :
the projection line always "aims" at the reflecting surface at right
angles to it. It is not as easy to judge its direction -when the reflecting
surface is tipped at an angle as in our present problem, but that is what
we have to do. It is not always practical to turn the drawing to get
the mirror in a horizontal plane as we did here. In fig. 283 we see the
problem's solution.

Innumerable other conditions might be illustrated here but they
would not introduce new principles. If the foregoing is thoroughly
assimilated and if the student has become structurally-minded enough
to work with projected lines and planes, there should be no difficulty
in solving any problem that is likely to be encountered.

290

chapter xv ***

In our study of reflections we concentrated upon finding: reflections
of points. The procedure with shadows is somewhat similar ; we look
for shadows of points that, when properly projected, provide direction
for lines that bound the shadows.

The method is illustrated in fig*. 285, which represents the line AB
casting: its shadow BC. In all of these examples the sun's rays are com-
ing: from the left in a direction parallel with the picture plane, at an
angle of 45 degrees, a direction arbitrarily assumed in all our demon-
strations wherein the sun's rays come directly from the left side. The
shadows of all verticals, on the ground, therefore are horizontal. When
the sun comes obliquely toward us, the method of locating: points and
finding: shadows is no different. It will be found, however, that the
shadows of verticals, instead of being: horizontal and parallel, will
converge to a vanishing 1 point on the horizon directly underneath the
sun. This is illustrated on page 136.

The shadow of point A is point C. So let us think of every point that
casts a shadow as the top point of a pole set in the ground. When the
point we are working: with is not connected with the g:round, we have
to drop a line from it to the ground. In fig:. 286, for example, we drop
a line from point A to point a, directly under it. We locate this point
by projecting: forward the base line of the box end, bx, which we know
will be directly under line AB, whatever the position the hinged box
flap happens to take, since the line AB swings in the same plane as
that of the box end (fig:. 287) . To find the direction of the shadow of
line AB on the gnround we have to locate the shadow of point B ; that
is, where it would be if the vertical line B& stood alone instead of being
the edge of the box. Thus we find the line Cc. From the point D, where
Cc cuts across the bottom of the box, the shadow of AB is BD.

It will be seen in fig:. 288 that all the other box flap points are simi-
larly found by projection of the planes in which they lie. Just take
each point, one at a time, and there should be no confusion. Finding:
the shadow within the box (fig:. 29O) presents no new problems. It is
only necessary to find the shadow of point A, just as though line Aa
stood alone instead of being: the box corner. We know that the shadow
of line AB is parallel with it, hence converges with it: so we do not
need to find the shadow of point B.

The only other question that might arise is whether or not the box
flap X is in shadow. We find the answer in fig:. 289, where, it is discov-
ered, the shadow of the line CD falls within the shadow line of AB,
which means that plane X is in full lig:ht and therefore it casts no
shadow that is visible in our drawing. If the X flap were in shadow,
the line CD would, of course, cast its shadow on the ground, and line
AB, then being: in shadow, would cast no shadow.

Let us now study shadows cast by a flight of steps, fig:. 291. First
we find the shadow CD of the line AB, which may be considered a wire
stretched taut between these points and touching: the corners of inter-
vening: steps. Actually, point B casts no shadow at all. But it would if
the wall went back a continuation of the side plane of the steps along:
the dotted line BX* The shadow of point B would then be point D. From
the steps 9 corners we project diagonal light rays to intersect CD. These
points are all we need, since we know that shadows of the treads are

291

parallel with the treads themselves and thus converge with them. The
shadows of the vertical risers of course are horizontal.

We see that the shadow of point N falls close (point Q) to the base
line of the wall. Hence the shadow of the top tread NE is very short
on the ground. From the point where it cuts across the base line of
the wall it goes up the wall to point E.

Going to the other end of the steps-to find the shadow cast upon
them by the balustrade we start with the shadow of GH. It crosses
the first step horizontally and vertically up the second riser, proceed-
ing horizontally again on the second tread until cut by the light ray
from G at point K.

From this point on, the shadow lines on the treads will not be hori-
zontal ; we have to find the direction of lines cast by the balustrade's
inclined line GL. We locate the shadow of point M on the plane of
the second tread extended back under step 3. A line connecting this
point and point K, shadows of points M and G, respectively, estab-
Jjshes the direction^ of all shadow lines cast by the inclined line GL on
the horizontal treads. They will all be parallel and will converge to a
vanishing point at the right.

To ascertain the direction of the shadow from point P on the riser
of step 3, it will help to imagine the third riser extended upward as
high as R on the balustrade (fig. 292) .

Now if we draw lines ST and PU parallel with AB and HW-con-
sequently converging upward with themwe have points for our shad-
ows on the upper treads.

We need, at this time, to find Z the shadow of point L on the plat-
form. That is where the shadow of the sloping balustrade ends. From
point Z the shadow parallels the line of the horizontal balustrade.

135

In fig. 294 we simplify the procedure of finding the shadow of the
desk-top's overhang by imagining that the drawer compartment X
extends to the floor. Here we see the shadow of the imagined line AB
rising vertically on the box side until cut off at C by the sun's ray
from A ; the shadow of a vertical upon a vertical jjlane being always
vertical.

The diagram in fig. 296 carries us one step further, giving the shad-
ows of points A and R on the floor. The actual shadow of point A, as
was seen in fig. 294, is point C. However we need point as well as
point P to give us the width of the desk-top's shadow.

In fig. 297 we develop the shadow of the X unit. It will now help
us to imagine the right unit (fig. 295) as a simple box-like object rest-
ing on the floor instead of being raised on legs. Then when the con-
verging shadow lines from P and meet the base line of the plane
Y at H and K, they streak upward across the Y plane to M and N,
though of course they also continue on into the shadow of the right
unit and merge with it on line S.

293

294

295

186

298

In fig. 298 we are facing the sun, whose position has been arbitrarily
placed at the right of VP 1 . Its rays, which approach the earth in par-
allel lines, are subject to the same laws of convergence as any other
parallel lines. Probably every one has observed the phenomenon which
is a common sight in great railway terminals when the rays of sun-
light, broken up into streamers by the mullions of the big windows,
are made visible by the hazy atmosphere of the interior. When viewed
from the side, the rays are parallel. When one faces the window, they
converge perceptibly.

So in fig. 298 we see the sun's rays striking the corners of the posts
and cutting off the shadows, which converge, not to VP 1 , but to a point
(VP 2 ) on the eye-level, directly under the sun. Note however that the
shadows of the retreating top side lines of the two left posts (marked
with arrows) cast shadows that converge with them to VP 1 .

Note that in order to find the shadow of the "Road Closed" sign, we
first have to find our ground points as previously demonstrated.

In fig. 299 similar posts are illuminated by an artificial light whose
rays come from nearly the same direction as those from the sun in
fig. 298. There is an important difference : to find the shadows we drop
a vertical from the light source to a point on the groundit is in a
horizontal line that passes through the pole's base-instead of to the
eye-level as we do when the source is the sun. All shadows, we note,
converge to this point (VP 2 ) on the ground under the light.

Let us next consider shadow problems in an artificially lighted
interior. Instead of using a logical interior for this demonstration,
simple objects which provide greater clarity than conventional fur-
niture have been chosen (fig. 300). In this diagram, in order to avoid
confusion of many lines, we have omitted vanishing points and con-
verging lines of the objects in the room.

The light (X) here is in the ceiling a little to the left of the center.

Our first step is to find on the floor the point directly under it. Carry-
ing a horizontal line to point W, thence down the wall to the floor
line (V), we next run a horizontal line along the floor until it cuts a
vertical from X at point Y We now have a vertical plane XWVY par-
allel with the rear wall and of course Y is directly under X.

The procedure for finding shadows by artificial light has already
been explained. What we always have to keep in mind to avoid confu-
sion is to find one point at a time.

To find the shadow of the top of the cabinet on the middle shelf,
we project a horizontal from point Z on the shelf's level, in the plane
XWVY. We erect a vertical through A, the point where the line from
Z crosses the shelf line. This gives us point B on the top shelf and we
find its shadow C. A line through C, the length of the shelf, to VP
is the shadow line we are after. The shadow of the shelf on the bottom
of the cabinet is found by a light ray through A to D on the VY line.

290

137

It will be noted that the box is not set parallel with the floor lines.
Its edges have vanishing points not shown in the drawing. We need
only to project one light ray through point O to find the shadow of
the box on the floor because the shadows of both edges of the box will
be parallel to those edges themselves, hence converging with them.

To find the shadow of the stick on the box, we have to find the point
on the floor directly under one of its ends; it doesn't matter which.
We do this by dropping a vertical to the floor from the point where
the stick crosses the box corner, then draw a line along the floor
parallel with the stick. Where it meets a vertical dropped from the
end of the stick, we have the point we need.

All shadows of vertical lines are vertical when they fall on vertical
surfaces, as does the shadow of the front vertical edge of the cabinet
when it strikes the wall.

The student is advised to experiment with the light in different posi-
tions in the room. Place the light on each of the three walls.

Ordinarily, cast shadows are darker than the shaded sides of objects
which cast them. The reason for this is that light is reflected upon the
objects from lighted areas of floor or wall. This is not always the case.
All depends upon the conditions in the room, the colors of objects and
reflecting surfaces, and the position of the light. Although this relation-
ship is generally observed in our demonstration drawing, the shadow
effects are only approximate, realism being sacrificed here to clarity
of procedure.

300

188

VE. 1 .

302

306

301

Now for the arched entrance (fig. 301). Although a complete
description of its construction repeats some instruction given else-
where, the problem is sufficiently interesting to justify a step-by-step
demonstration.

The side elevation (fig. 302) gives the needed structural facts. In
fig. 303 we have constructed the grid in perspective. On line CE we
have measured the 15 equal horizontal dimensions. These could have
been a little more or a little less ; all that matters is that they be equal.
From E a line is projected through D to the horizon, giving us a van-
ishing point for all lines from the points on CE. These lines, cutting
across CD, mark off perspectively equal spaces on that line.

Having stepped-off the seven vertical measurements on AC, we now
have all needed points for constructing the grid.

In fig. 305 we concentrate upon the shadow of the structure without
reference to the arched opening, the shadow contour of which is
developed in fig. 304. In fig. 305 we see horizontal lines carried out
from each point on line CD underneath points 1, 2, 3, 4, 5, and 6 and
corresponding points on the far side of the structure. From points
1, 2, 3, 4, 5, and 6 sun rays are projected to the ground at a 30 angle.
Where these rays cut corresponding horizontals on the ground we
have the shadow points 7, 8, 9, 10, 11, and 12.

It is not necessary to project the sun rays from points on the far
side of the arch corresponding with 1, 2, 3, 4, 5, and 6 ; their shadow
points are found by the crossings of the parallels from 7, 8, 9, 10, 11,
and 12 which converge to VP 1 .

The inside of the arch that faces us received some of the sun's rays.
However, there would be a shadow cast upon it by itself see fig. 301 ;
that entire area is arbitrarily shaded in fig. 304. This shadow can be
developed by rather complicated mechanical procedures, but no illus-
trator need go to that extreme. Simply hold a strip of stiff paper
(curved to simulate the arch) up to a bright light so that its light rays
approximate the direction of the sun in the drawing. As a matter of
fact, a great many of the problems carried out mechanically in this
book can be more naturally solved by simple observation with the use
of makeshift models.

In finding the curved shadow edge in fig. 304, we first set off an
indefinite number of points on the arch and drop verticals to line AB
underneath. From the points on AB, horizontals are projected. These
are cut off by light rays passing through the points on the arch, giving
the desired curved shadow line.

Any number of points can be used on the arch for this procedure.
They can be located at random; it is not necessary to have them
mechanically spaced.

307

308

809

310

141

chapter xvi

FURNITURE

There is nothing difficult in the drawing of furniture for the student
who has acquired the habit of analysis and structural thinking. The
drawings in this chapter are self-explanatory.

Wherever we have several pieces of furniture placed in relation to
each other, we begin our drawing with the floor plan, as illustrated
on the opposite page, where chairs are drawn up against a table. In
drawing an entire room all the furniture would, of course, be laid out
in plan in this way.

Throughout the book we have emphasized the importance of acquir-
ing the ability to draw the various geometric figures in perspective
with great facility and to know how to draw one figure in proper rela-
tion to the others. Thus in the office chair, below, it is important that
the ellipse, which we use to locate the four legs, be correctly propor-
tioned to the square seat. Turning to page 143, we see the triangle,
the square, and the circle in essential relationships.

Most furniture is based upon relatively simple geometric forms. In
our drawing we first reduce the object to these forms, ignoring until
later the character variations. If the basic structure is right, the details
readily fall into place.

In addition to drawing directly from furniture in the home, the stu-
dent is advised to do a great deal of drawing from photographs in fur-
niture advertisements. Make analytical studies of them as we have
done on these pages. Try turning the tables on page 143 so that the
triangle and square will have a different relationship to the circles in
which they are inscribed.

Tracing paper is very useful in studying photographs of furniture.
Lay it over the piece being studied and make the analysis with the
pencil.

313

Courtesy Hey wood-Wake field Company.
314

315

316

Courtesy Knoll Associates.

317

Courtesy Knoll Associates.
319

324

323

322

Courtesy The McGuire Company.

325

326

327

Courtesy Mason-Art Furniture Company.
328

330

149

332

"Still Life with Fruit Basket"
by Cezanne
(French, 1839-1906).

Perspective analysis
of Ctzanne's still life by
Earle Loran from his book
C6zanne's Composition,
published by the
University of California Press.

chapter xvii 14r

UNIVERSAL PERSPECTIVE

The notion that objects and nature ought always to be drawn and
painted as they appear to the photographic eye is of relatively recent
origin. For thousands of years artists had been chiefly concerned with
expressing their ideas without regard to imitative accuracy. They did
not hesitate to depict a man bigger than his horse or even his house.
After all, wasn't a man more important than either? In a company of
people, those furthest away were apt to be as large as those in the
foreground. That permitted the artist to portray all with impartiality.

If the artist wished to illustrate more of an object or an episode than
could be seen in a single view, there was no reason why he should not
combine several views in the same picture. And he often did.

When we compare present-day illustration with that of pre-per-
spective days, trying to free our minds from the prejudice of tradi-
tional ways of thinking, we are forced to admit that the old boys had
rather the better of it. When it comes to the expression of ideas, an
artist who is not bound to make things look "natural" can say a whole
lot more in a picture than contemporary illustrators who are limited
by the restrictions of the camera eye.

It was easier for the early artist to paint better pictures because,
unchained by the necessity of composing his subject so that it would
meet the test of photographic accuracy, he had a freer hand with his
design. He could arrange the elements of his subject as they would
look best as design.

So-called modern art has adopted many of the ideals and the methods
of the ancient masters. Modern artistswe refer now to painters have
revolted against the concept of photographic reality. They ask why
the painter should attempt to compete with the camera which produces
theoretically accurate imitations of nature. Since the perfection of
color photography their argument seems even sounder.

So they distort perspective or ignore it altogether. They arrange
their subjects with utter disregard of natural effect, if they so desire.
Their emphasis is upon design and the expression of a mood or an
emotion.

C&ZANNE One of the first "moderns" to revolt against the academic ideal of
naturalism was Cezanne (1839-1906) . He adopted the practice of what
has been called universal perspective, that is, the combination of several
views in a single picture. His method is so clearly demonstrated in Erie
Loran's exciting book, Cezanne's Composition,* that I have asked Mr.
Loran's permission to reprint his analysis of Cezanne's Still Life with
Fruit Basket. He has kindly consented. The diagram and the following
explanatory text are taken directly from the book.

"The diagram reveals sources for many of the devices of Abstract
painting, principally the incorporation of several eye-levels in one pic-
ture. The first eye-level, marked I, takes in, roughly, the front plane
of the fruit basket, the sugar bowl, and the small pitcher (the last two
objects are seen at slightly higher eye-levels). The second eye-level,
much higher, marked II, looks down at the opening of the ginger jar
and the top of the basket, as well as other objects, including the table
top.
* University of California Press.

14*

"The result of these distortions is a greater sense of three-dimen-
sionality, but at the same time, paradoxically, these top planes of the
ginger jar and basket, being tipped forward, also relate clearly to the
flat plane of the picture. The endless tensions between planes seen at
different levels but related also to the picture plane are the basis of the
mystery and power of this still life. An emotional, nonrealistic illusion
of space created by the changing of eye levels has been the point of
departure for Abstract art as well as for a revived interest by Byzan-
tine icon painting. This device, mentioned elsewhere, is sometimes
called 'universal perspective*. . . .

"Another distortion shifts the artist's viewpoint from the left side
to the right side of his motif, increasing the illusion of space, of 'seeing
around' the object. The change may be traced from the vertical arrow
at la, which indicates the straight front or slightly left-hand view
from which the table and most of the objects in the picture are seen.
But the handle of the basket is turned, as if seen from a position far
to the right, lib. Picasso's familiar device of incorporating front and
side views in a single portrait head is perhaps traced here to one of its
sources.

"An extraordinary distortion may be observed in the splitting of the
table top. The dotted line from A to B indicates the tension that
develops because the table plane fails to unite under the cloth. The
arrow at C emphasizes the tension, the pushing back into space, that
results from this splitting of the table plane. Abstract artists have
resorted to the breaking up of planes and objects in a highly intellec-
tual and conscious spirit, sometimes dividing the picture plane into a
dark and a light area, sometimes even sharply dividing an object, as
in the familiar table pictures of Braque. Many examples of split table
planes exist in Cezanne's still lif es. ... It should be pointed out, how-
ever, that the two sides of the table in this still life tend to converge
in a more or less normal kind of perspective. In fact, so far as I have
observed, there are no table tops in Cezanne's still lifes that actually
expand in direct reversal of mechanical perspective; his lines tend,
instead, to be parallel. . . .

"The last distortion explained in the diagram recalls Cezanne's habit
of tipping the vertical axes of nature to the right or left. The sugar
bowl and pitcher, marked D and E, are falling definitely to the left,
while the ginger jar, F, remains vertical. The play and tension between
axes continues throughout the entire painting, with the strongest axial
variations occurring in the pears.

"The conflict and dualism of static and dynamic axes, the plane ten-
sions resulting from the shifting of eye-levels, the action of three-
dimensional space forced to maintain its relation to the picture plane
these are the elements of the inner life of C6zanne's art."

GAY DOS We frequently encounter instances of universal perspective in con-
temporary illustration. In the advertisement by Gaydos, fig. 334, for
example, there are three distinct eye-levels ; one for the goblet, gloves
and candy, another for the teacup, and the third indicated by the hori-
zon line.

149

Advertising design by Gaydoa
for Niagara Alkali Company.

334

Alexander F. Yaworski in his watercolor of Galena Station (fig.
335) has employed two eye-levels for a very interesting reason. Fig.
336 is a view as it would appear when seen from above. This sketch
was made to show that neither the boards of the platform nor its edge
are parallel with any of the building lines.

YAWORSKI In fig. 337 we see the boards of the platform converging to a point
far above the eye-level used for the building. The importance of this
may not appear in the small reproduction of his large painting, but if
the vanishing points for the boards had been put on the eye-level,
the design effect would have been unsatisfactory. We have taken the
liberty of inking some of the board edges in the photograph because
they do not show up in the reproduction as in the original

A watercolor by Alexander F. Yaworski. The black board lines were added by the author for purposes of demonstration.
336

335

150

151

chapter xviii

FIGURES IN PERSPECTIVE

This subject is dealt with in Chapter XI and on page 59. In those
demonstrations we see lines converging to the horizon line from the
feet and heads of foreground figures. Naturally, all verticals extending
between those horizontals are of equal height. That, to be sure, is a
simple procedure, but another that is often used by layout men and
illustrators is demonstrated here.

Note that in fig. 338 the horizon line passes through the centers of
the two foreground figures ; there is as much of the figures above as
below the line.

Now what is true of the foreground figures is also true of any others
on the same horizontal plane. So all we have to do, having established
the foot position of any figure anywhere, is to place the head as far
above the horizon as the feet are below.

338

15S

339

Drawing of the foreground horseman
by Constantin Guys (French, 1805-1892).

GUYS In fig. 339, see above, the eye-level is lowered to the level of the
horse's kneesabout one-quarter the height of horse and man. Thus all
other horsemen would be one-quarter below the line and three quarters
above.

Suppose we wish to draw a man in the middle distance. We cannot
use the one-to-three ratio. Assume that the man's head comes about
up to the horse's mouth. That gives a one-to-two ratio the man's
head will be twice as far above the horizon as his feet are below.

In fig. 340 the eye-level is considerably above the foreground figures,
whose height is approximately two-thirds the distance from their feet
to the eye-level. The height of other figures on the floor therefore is
two-thirds the distance from their feet to the horizon, regardless of
their position on the floor.

340

Drawing of the foreground group by Constantin Guys.

163

When we have a situation similar to that in fig. 341, the procedure
is different, though the principle is the same. Usually, though, the
illustrator, in a composition like this, would begin with the foreground
figure and scale others to it, just as when there are full figures in the
foreground. Then he would establish an eye-level.

In this case we have conveniently located the eye-level one head's
height above the head. The ratio, naturally would apply to all heads
in any part of the room. This is a very simple method, one that can
be applied in most situations, though not in all. The eye-level can
be lowered or raised as desired. We merely have to apply the ratio!
of the foreground head to eye-level distance above it.

341

O&SEK-/&K s

154

342

Advertising drawing by Fred Freeman for
Combustion Engineering-Superheater, Inc.

343

156

FREEMAN

Here is a superb drawing by a distinguished American illustrator,
Fred Freeman.

The excellence of this drawing derives from many factors not
directly related to perspective : thorough knowledge of horses, authen-
ticity of the fire engine, and fine rendering in the black-and-white
medium. Over and above these is the masterly manner in which the
scene is dramatized ; in this, perspective strategy plays an all-impor-
tant part.

It certainly would not occur to anyone lacking a prying, analytical
attitude that Freeman had solved an unusual perspective problem
here. Perhaps you the reader are not aware of such a problem. As a
matter of fact there are two striking violations of scientific perspec-
tive.

First, observe that the horses are traveling in a different direction
than the fire engine : they are heading more directly toward the spec-
tator than is the vehicle. The diagram in fig. 344 illustrates this. In
order to "correct" this discrepancy, the vehicle would have to be drawn
somewhat as it is in our "reconstructed" rough drawing (fig. 343).
Either that, or the horses would have to be shown more in sideview
in which case much of the drama would be lost.

In fig. 345 we have indicated another liberty that Freeman took
with reality an amazing liberty it is and a daring one! The three
horses are not really running parallel ; although they appear to be
parallel to each other, they take positions roughly like those indicated
in fig. 345.

Now what is accomplished by this? Obviously that relative position
of the horses gives us a head-on view of all of them a most important
factor in the smashing success of the drawing.

This drawing, almost more than any other in the book, demonstrates
the importance of knowing how to violate perspective.

344

186

Pencil drawing by the author
for an Eldorado Pencil advertisement.

349 L

EYE LEVEL

chapter xix

PROBLEM OF THE BRIDGE TRUSS

The jacket picture of a bridge structure was made by the author
after a pencil drawing used as an advertisement for Eldorado Pencils.
The model from which the drawing was made was a paper construc-
tion, one of a series demonstrating various uses of the pencil.

While no principle or method not covered elsewhere in the book is
involved, the procedure as here applied is interesting enough for dem-
onstration.

In a problem of this kind it is useful to make a diagrammatic analysis
that records essential facts needed for the perspective rendering. Thus
in fig. 346 we draw a side view of the bridge truss.

Note that the base line CD is divided into ten equal divisions which
locate the points where the triangular members touch both CD and AB.

Having decided upon the placing of the eye-level (fig. 347), we
establish the desired direction of line CD and draw AB converging
with it as shown in fig. 348. We find the ten divisions on line CD by
the method already demonstrated on page 96. From point D we draw
an indefinite horizontal line (DE) which will be our measuring line.
From point X, arbitrarily established on the eye-levelit could have
been farther to the left or to the rightwe draw a line through C to G
on the DE line. We now divide line DG into ten equal parts and from
the division points carry lines to X, dividing line CD into the same
divisions perspectively.

When the structural lines of the truss are drawn on the framework
thus developed and the converging lines are carried out to their vanish-
ing point, we have the diagram reproduced in fig. 349 on a small scale.

157

158

INDEX

Abbott Laboratories 57, 122

Advertising 8, IS, 20-1, 80-3, 44-5, 55, 58-63, 66-7,

72, 76, 80-7, 90, 93, 118-23, 130-1, 141, 149, 154-5,

157

Air views 115-6, 118
American Locomotive Co. 54
American Rolex Watch Corp. 13
Angles 11, 22-3, 26-7, 36-7, 39, 41-2, 44, 47, 51-2, 67,

70-2, 77-8, 82, 84, 89, 93, 96, 107, 111, 115-16, 118,

120, 123, 125, 131
Appearance 9-14, 17, 23, 25, 64, 72-3, 75, 99, 115, 129

(see also Realism)
Arches 80-1, 84-5, 138-9
Architectural renderings 16, 86, 39, 55, 90-1, 114-5

(see also Buildings)
Arcs 18-20, 27, 72, 82, 84, 118
Art 9-12, 111, 147-8
Artists 9-10, 12, 16-17, 41, 47, 70, 115, 147-8 (see also

Illustrators)
Assisi street 112-13
Association of American Railroads 55
Associated Press 76
Atherton, John 00-7
Axton-Fisher Tobacco Co. 86-7

Bobertz, Carl 116-17
Bobri, V. 58-60

Boxes 12-14, 27, 30, 130-3, 136-7
Braque, Georges 148
Bridges 70, 72, 75, 80-2, 156-7
British Commonwealth Pacific Airlines, Ltd. 72
Buildings 31-7, 39-43 f 58-60, 90-1, 94-7, 110-89
(see also Interiors)

Cameras 9-11, 17, 20, 41-3, 47, 52, 55, 57, 70-1, '78,

115-16, 120, 123-5, 129, 147
Center of vision (see Station point)
C6zanne, Paul 146-8
Chance, Fred 52, 54
Chapin, R. M., Jr. 75
Chest of drawers 32
Childs 44
Chinese 10

Chesapeake & Ohio Railroad 77
Church, country 35-7
Circles 22-3, 27, 30, 47, 68-87, 89-93, 103, 118, 141

Concentric 74-6
City Safety Council 26
Clocks 71, 75
Collier's 15, 64-5, 117
Column magazine 12

Combustion Engineering-Superheater, Inc. 154
Compasses 17-19, 69
Cones 23-5, 88-93
Convergence of lines 13-14, 17-21, 26, 36-7, 40-4, 47,

50-67, 71, 84, 91-3, 95-7, 99, 105, 107, 109, 111-12,

115-16, 118, 123, 125-6, 133-4, 136-7, 148-9, 151,

156-7

Coolerator Co. 99, 102
Coutances Cathedral 34
Coty, Inc. 66-7

Cubes 23-5, 37-8, 46-50, 78-9
Curare 42, 122-3
Cylinders 23-7, 30, 68-72, 84-5, 87-9, 129

De Hooch, Pieter 100

Depth 11 (see also Distance)

Design 9, 11-12, SO, 57, 59, 61, 64, 67, 109, 118, 123,

147, 149
Dimensions 9, 31, 36, 42-3, 57, 76, 96, 99, 105, 109,

123, 139, 152-3 (see also Measuring)
Direction 10, 14, 18-19, 26, 36, 41, 47, 51-5, 59, 69,

77-8, 89, 109, 116, 125, 131, 184, 155, 157
Distance 9, 13, 39, 51, 71, 75, 78, 103
Distortion 9,11, 42, 54, 57, 59, 61, 64, 67, 70, 84-5,

99, 115, 120, 123-5, 131, 147-8, 155
Dividers 17, 96, 99
Dome, Albert 15, 24, 86-7

Draftsmen 14, 25, 31, 59, 92 (see also Artists; Illus-
trators)
Drawing: Freehand 9, 14, 17, 19, 27, 31, 36, 39, 47,

49,99

Mechanical 14, 16, 19, 25-7, 31, 90, 92, 133, 139

(see also Instruments, drawing)
Drawing boards 17-21

Eggers & Higgins 114

Ellipses 23, 30, 69-78, 84-7, 89-90, 92-3, 103, 141

Eldorado Pencils 8, 30-3, 157

Elevations 35, 43, 139 (see also Views)

159

Engineering sense (see Structure)

Enlarging 20-1

Equipment 17-24

Erdoes, Richard 11-12

Eye 9-10, 18, 23, 24, 41, 55, 70, 12S, 125 (see also
Seeing)

Eye-level 19, 42-4, 49, 51-2, 55-7, 59, 69, 72, 76, 81-2,
84-5, 89, 99, 103, 111-12, 126, 136, 148-9, 152-3,
156-7 (see also Horizon; Station point)

Fawcett, Robert 44, 55, 64-5

Ferguson, I. W. ISO

Figures 58-9, 67, 103-9, 150-5

Foreshortening IS, 31, 35-7, 43, 49, 51-67, 75-6, 93,

96,99,109,115
Fortune 54

Four-point perspective 64-5
Flag-tiles 98-103
Fraser, Eric 13
Freehand (see Drawing)
Freeman, Fred 15-4-5
Freight cars 20-1
Furniture 67, 116, 134, 136-7, 140-5

Galena Station 149

Gardenhouse 82-3

Gate 32

Gaydos 149

Geometric forms 13-14, 21-38, 46-50, 54, 59, 68-96,

98-105, 107, 129, 141
Giusti, George 55, 61-3

Glasses, measuring or reducing 32-7, 39, 43, 47
Globes 73-6, 86-7 (see also Spheres)
Good Housekeeping 118
Great Bear Lake 73, 76
Gruen Watch Co. 55, 59, 62-3
Guys, Constantin 152

Hanes Hosiery, Inc. 58-9

Helck, Peter 16, 72, 78-85

Hendrickson, David 109

Hexagons 90, 103

Heywood-Wakefield Co. 142

Hills 110-13

Hinged box covers 27

Horizon 43-4, 50-1, 57, 61, 69, 94-5, 115, 118, 133, 139,

149, 151-2 (see also Eye-level)
Hudson, W. N. 29-30

92-3, 109, 115-24, 126-7, 130-1, 139, 149, 151, 153
Inclines 110-13
Industrial scenes 80-5

Instruments, drawing 16-17, 31, 36, 39, 41, 49, 95
Interiors 16, 44-5, 55-7, 98-109, 123, 136-7, 141
Italian building S3

Japanese 10

John Hancock Mutual Life Insurance Co. 118, 120-1,

127
Joseph Dixon Crucible Co. SS

Kitchen range 44-5, 55-7
Klett, Walter 114-15
Knoll Associates 142-3

Ladder 26

Lawnsweeper 28-9

Layout 30, 32, 57, 59, 61, 118, 120, 12S, 151

Levy, Julian 11

Lines (see Convergence of lines)

"Listening ears" 92-3

Locomotives 77-5, 80-5

Loran, Erie 146-8

Ludekens, Fred 14

Mantel 32

Marinsky, Harry 118-20

Massachusetts Normal Art School 12

Mason-Art Furniture Co. 144-5

Materials 17-24

McGuire Co., The 143

Measuring 25, 29, 31-9, 42-3, 49, 57, 76, 96, 105, 107,

157 (see also Glasses, measuring or reducing)
Models 20-1, 23, SO, 47, 49, 69, 73, 82-3, 87, 89, 92,

112, 139, 157

Flat 21-3, 73
Morocco, street scene 12
Museum of Modern Art 42

National Gallery, London 100

Naturalism 11, 17, 147 (see also Realism)

New England Mutual Life Insurance Co. 93

New York Central System 80-5

New York Times 76

New York University Law Center 114-15

Niagara Alkali Co. 149

Illustration 11, 20, 147 (see also Advertising; Illus-
trators)

Illustrators 9,11-12, 14, 16-17, 19-20, 23-5, 27, SO,
36-7, 39, 44, 54. 57, 59, 61, 64, 67, 74-5, 80-7. 90.

Observatory, Palomar 72-3
Observer (see Station point)
One-point perspective 51, 55-7, 61, 99, 105
Open door 27

160

Painting 10-12, 16, 52, 80-5, 114-15, 119, 123, 127,

147-9

Papers, drawing 17, 20-1, 23-4
Parallel perspective (see One-point perspective)
Parker, Al 116, US

Pencils 17, 20, 24, 81, 90-1, 95, 113, 141, 157
Peninsular Grinding Wheel Co. 70
Pennsylvania Railroad 20-1
Photography 10, 14, 17, 20-1, 24, 41-S, 47, 51, 57,

69-72, 78, 90, 92, 115, 118, 120, 124-5, 141, 147
Picasso 148
Picture plane 10-11, 13, 36, 39-45, 47, 52, 57, 59, 70,

77-8, 82, 91-2, 95, 97, 111-12, 116, 125, 181, 133-4,

148, 151

Pratt Institute 13-14
Procedures 17-24
Projecting 14, 18-19, 41-3, 49, 59, 71, 82, 90-1, 93,

96-7, 99, 108, 105, 109, 129, 131, 133-4, 186-7,

139, 157

Projection machines 20
Proportion 31-5, 47, 69. 71, 77-8, 141

Radio City 126

Railroad tracks 39, 51-5, 61-3, 77-85

Realism 10-12, 16, 59, 61, 123, 129,137,147,155

Rectangles 13, 23-4, 28-30, S3, 37, 40-2, 44, 48-9, 54,
57, 71, 82-3, 94-5, 107, 120

Reducing glasses (see Glasses, measuring or reduc-
ing)

Reflections 72, 128-81

Reilly, Prank J. 20-1

Renaissance 10

Retina (see Eye)

Riggs, Robert 92-3

Robertson, H. H., Co. ISO

Rowlandson, Thomas 27

Rulers 17, 23, 25, 47, 49, 96, 99, 107

Rules 9-12, 16-17, 39, 51, 54-5, 57, 70, 84, 109, 111,
115, 123, 126

Scotch tape 17, 28, 27

Seeing 9-10, 41, 48 (see also Eye)

Shadows 16, 132-9

Shell Oil Co., Inc. 118-19

Siebel, Fred 118, 120-1, 128

Simmons, A. L. 11

Skyscrapers 115, 125-6

Solar system 75

Spheres 25 (see also Globes)

Squares 22-4, 28-9, 31-8, 75, 77, 98-105, 107, 141

Stahl, Ben 126-7

Stairs 104-9, 134-5

Station point 10, 41-2, 51-2, 57, 75, 99, 112, 118, 123,

125 f 129 (see also Eye-level)
Step-down 111

Straightedges 18-19 (see also Rulers)

Structure 14, 24-30, 71, 81, 90-1, 95, 97, 103, 129, 13

133, 189, 141, 157
Students 9, 12-14, 16, 21, 28, 25, 27, 31, 37, 47, 4

54-5, 61, 69, 73, 78, 87, 89-90, 92, 95, 99, 111, 11<

124, 126, 129, 131, 141
Sydney Harbour, Australia 72

Tanks, oil 68-9

Templates 18-19, 21

Thomas Register 29-30

Thompson, Bradbury 55, 61, 62

Three-point perspective 21, 43, 51, 114-27, 129

Time 75

Towers 38-4, 90-1

Tracing 17, 23-4, 85, 39, 47, 49, 54, 59, 64, 67-90, 75

84, 87, 92-3, 141
Transparencies 32, 37, 47
Travelers Insurance Co., The 109
Triangles 17, 21-2, 26, 28-9, 47, 87, 92-3, 141
Triangular prisms 26, 28-9, 94-5
T-squares 17-21, 47
Two-point perspective 51, 54, 59, 99

Uccello, Paolo 16
Units of measure 31-8
Universal perspective 146-9
University of California Press 147-8
Up and down: Hills 110-13
Stairs 104-9

Vanishing points 14, 17-21, 26, 40-5, 47, 50-2, 54, 57,
59, 61, 64, 67, 71, 80-5, 94-7, 98-9, 103-7, 109-13,
118, 123, 133-4, 186-9, 157

Vanishing traces 71, 81-2, 95, 97-9, 107, 109, 118, 120

Vasari, Giorgio 16

Views 16, 25-6, 29-30, 35, 147, 157

Visitors' Information Center, Portland, Ore. 57

Walker, Hiram, whiskey 14

Watson, Aldren A. 2 , 53

Watson, Ernest W. 8, 80-3, 90-1, 113, 116, 157

Weir, Maurice 101

Westvaco Inspirations 59, 61, 62

Wheels 23-4, 27, 29, 70-1, 77-85

Windows 33

Woodcut, 14th century 10

Worms Cathedral 89-91

Yaworski, Alexander F. 149
Yonkers street 110-11

143 298