cannot be done if the atten- tion is frequentlydiverted by drawing, light,and shade,
and color. Through these the painter should express himself,as unconscious.
FR EE HAN D DRAWI N G -
LI G HT AN D SHADE
C TIVE FREE HAN D PERSPE -
FO R
A rt Stu dents
N ST R U C T
O
R
O F
a nd
K
A N SO N I
U SE
TH E
OF
Teac bers
C R O SS
.
O
OO
M A SS A C H U SE T T S N R M A L A RT SC H L A N D m T H E SC H D R A W I N G A N D PA I N T I N G , M U SE U M O F FI N E A R T S B S T N m
TH E
,
FO U R T H
I ll
us
E D IT IO N
tr a t e d b y
A 33 g .
C RO AR T
M A L N OR a
32 Pl
.
a
te s
S S !
SCHO O L
O O
OO
L
FR I EN D AN D FI RST T EAC HER
m
R ab a t I
N SC IN
HIS
R I
Hannah
.
BE T H I S
BO O K
R EC O G N IT I O N
E FFO R T S
TO
A DV A N C E
SER I O U S AN D C O N SC I E N T I O U S ST U DY
OF
N AT U R E
PR E FA C E
.
T HE
book
,
n ot e s
w ere
prepared
for
N orm al Art
s ac h u s e t t s
ou t
M odel D ra wing
on
School
.
,
of
forming
the body of this
M as
the use of the students of the
illustrations as explanations
the course
,
They of
w e re
printed
w ith
th e draw ings given in
lectures on this subj ect and ,
w ill
be
of
little assista n ce to those not takin g the lectures H aving been requested for the book by persons n ot students of .
the school and realizing that draw ing is o ften poorly ,
taught esp ecially in our public sch ools and being unable ,
,
to recom mend a book
w hich
and presents artistic methods
treats the subj ect simply of w
ork
,
I
concluded to
re w rite th e notes adapti n g them to general ,
meeting
,
as
far
as pos sible th e demand ,
on the principles
of
fre e
-
hand dra w ing
The book is intended especially
u se ,
and
a text book
for
-
.
for
teachers
,
an d
at
fi rst glance the artist may think it co n siders more theory than is vi nc e d
n
ecessary
than I
,
No
.
th e
of
upon theory alo n e
.
I
one can be mo re stro ngl y folly
of
c on
teaching and depending
believe that theory
is
'
of
use only
PR E FA CE
vi to th e artis t
wh o
can draw
.
w ithout
it
To such a per
.
son and to th e teacher theory may be ,
ance
instead and
of
w ould
w ork
wh o
Th e artist
.
upon his eyes
should
great assist
depend upon theory
w ould Certainly
,
of
be ve ry un w ise
probably produce unsatis factory
consisted simply in draw ing from
w ork
N ature
,
If
.
w ould
,
of
have little need
his
and from
subj ects be fore him exactly as they are to be sented h e
,
r e p re
theory and could ,
sa fely de p end u pon his eyes 5 bu t the a rtist o ften has to design and dra w w ithout a subj ect be fore him and ,
for
this
w ork
he must depend upon his kno w ledge
this has b een arranged und er a he has d iscovere d dra w
w ith
far
these h elps
simple rules
fro m
draw ing
more freedom and
w hen w ithout
If
w hile
fe w
N ature
,
.
If
w hich
he
w ill
greater accuracy than
.
his mind is so constructe d that h e canno t discover
and apply the
fe w
rules n ecessary
quite like ly that his time in some other direction
w ill r f o ;
for
be more
this
w or
k
p rofitably
th e rules
of
,
it i s spent
perspective
artis t re quires are so simple as to be easily given in a fe w sentences Fro m the s t and point of th e
w hich t he
.
artist then the re may be more th eory than is needed ,
,
but the teache r tru e
of
much experience
w ill
,
not find this
.
E very wh o
teacher has found the bright thoug h t ful student ,
has aske d qu estions
thought
.
N early
of w
hich
th e
teacher
h as
never
all the points considered in t hes e notes
PREFA CE
vii
.
have be en suggested by such questions re ferred to me
,
w hich
have been ,
It is impossible to furnish ans w ers to
.
the teacher is likely to be a sked but the main poi n ts can be covered and these u n der all th e questions
w hich
,
,
st ood oth er questions depending upon the m can be ,
readily met
.
Though intended
for
the teacher and student the ,
subj ect matter is to a greater or less extent interesting to -
the artist the illustrator and others ,
,
the kno w ledge
of
Proj ection
follo w
necessary to
some
of
who
may not have
and Scientific
Perspective
the problems considered
.
The problems requiring this kno w ledge are more impor tant to th e teacher than to the artist and it is hoped ,
that the average art s tudent may find the simpler prob lems suited to
h is
capacity and his needs
,
not interes ted in the scientific discussions parts intended
for
them
th a t thos e
a nd
w ill
study the
.
The teacher may feel inclined to criticise the w hich
the fre e hand p a rt -
may d esire a rule as to second etc ,
He
.
of
th e subj ect i s presented
w hich
may not
w ay
w ish
line to draw first
,
.
.
He
He
w hich
to cultivate his feeli ng to
such an extent as to cast aside conventio n al methods w orking
in
of
may upon consideration ackno w ledge the
methods advised to be more artistic but he may say ,
that they are harder to teach th at artistic
feeling
.
There is no question but
and correct taste are di fficult to
obtain but surely this is no reason ,
w hy w e
should not
PRE PA CE
viii
.
l
cultivate
the
for
may po ssess no reason ,
m echanical methods
An
of
small amount
taste
w hich
the students
choosing conventional and
must destroy artistic feeling
w hich
artistic method is di fficult
to
teach to students
,
but
I
-
a
struggle on th e part
of
w rong ,
and the obj ections
have to change old methods they re fuse to change
I
.
w ill
the mind h as not been
nearly all the duties w hich
of
,
w ould
spend many years
of
is in th e begi nn ing
If
.
there
u n til the training
of
for
the mind concerning
Art
facts ,
of
is
but
of
the
is l ong
w ith ,
th e training
the art student
w ill
in
.
for
postponing this traini ng
until th e student de cides to make it
N ature ;
”
There is no good reason w hen
w ay
the student to
the mind to accept the story ,
truth find that
any
severe labo r to enable himsel f to
eye is made as compl ete as and begins of
w ere
the thi n gs see n could be
and not to reason th e appearance
se e ,
,
develop ed as to per form
be unnecessa ry
of
wh o
those
last only as lo ng as
se e
so
the eye
less kno w ledge
aw akened it
of
believe that the easiest and the
best time to train the eye to
by
both pupil and teach er
do not admit that it is more di fficult to start right
than to start
w hen
w ho
Change w i l l
have be en taught an inartistic one and the involve
.
Art
h is
pro fession
realized that the teacher in charge
of
,
an
d
art edu
cation in the public schools has a most important posi tion th e first step in advance ,
A bility
to tal k
w ell
w ill
and intelligently
have been made of
general matters
.
,
PR E PA CE and
even
of
lx
.
art as presented by various
w riters ,
does
n ot
constitute this special fitness ; neither does the ability to draw pretty things upon the blackboard nor to explain ,
s e t of
the course as arranged in a the faculty
of
text books
planning and carrying out a course of
to produce an interesting exhibition w ork ,
and eve n
-
manual traini n g etc ,
th ings are important but
.
dra w in gs
is not enough
,
of
so a s
fancy
,
these
Al l
.
greater importance is per
sonal artistic feeli n g and practical ability in art invol v ing ,
more study than m ost
who
are teaching in the public
schools have been able to give w hich
.
Without this trai n ing
alone can enable one to j ustly realize the end
his teaching and thus to
w ork fro m
th e first
the instruction given must be unnecessary illogical and harm ful ,
I
do not
wi sh
,
of
this end
for
,
,
m echanical ,
.
to dis parage the valuable results
w hich
have been accomplished nor to criticise the teachers ,
who
have
w orked
so faith fully in this fi eld
ply to encourage those artistic qualities
as
n ow
in the
w ork
.
I Wish
to look
m si
for
its
much as p ossible and to advise those ,
intendi ngto take up the study to obtain good art training and not to accept certain
w ay
done thus of
a good reason
for
the fact that all authorities The influence
.
is being felt instead
as
.
those
other people
,
wh o
depended upon others and the time ,
of
in
a
the past have
the honest impressio n ist
of
We are beginning to of
proceedi ng
,
u se
our
ow n
eyes
in like manner have is
at han d
w hen in
PREFA CE spite
of
the
p resent
ridicule
of
learned to see the honest student ,
ap preciated and those ,
wh o
.
those
have never
appearances
of
ridicule
study or to step into th e background
who
.
w ill
w ill
be
be forced to
FR EE
2
-
HAND DRA WL VG
.
have been edu cate d prevent even consideration
we
the opinions
of
other p eople
of
.
Th e ability to think and act independently is possess ed fe w w h o
by the
w ork of
h as
he
lead
.
Thus it is that
an artist the techniqu e
of
recognize in the
we
the teacher
w ith w hom
studied and find him frequently unable to se e ,
merit except in his favorite school
and so me are unable
to separate the result from the
by
du c e d ,
result
of
the method b eing
w ay
w hich
it
w as
pro
greater i mportance than the
.
The te ndency
1n
this direction increases
decreases and is strongest among thos e ,
instruction in th e public sch ools teachers
,
methods
w ho of
to teach art
as
the ability
who
direct art
This is th e result
.
of
have given great atte n tion to th e best
teaching the ordinary branches attempti ng ,
w hen
they kno w nothing
of
it and naturall y arises from th e necessity w hich exists in most places for ,
th e regular teachers giving the lessons in dra w ing w ill
consider this
w ork
by itsel f but ,
express the impossibility
of
formulating
schemes arbitrarily fixing details by
w hich
I
of
teachers
who
that all methods but a certain medium these
of
art
w ere
w ays
out
w e re
attempt to produce
of
n ow
I
to
systematized
w ork ,
it is to b e j udged as good or bad
have kno w n
w ish
I
.
and rule s
.
have told th eir students
w ay of w orking
or using a
date and that dra w i n gs made in ,
nece ssarily bad w ork
.
I
in accordance
have seen the w ith
so me such
OF THE
TR A I N L V G
l a n p
AR T
S T UD E ZVT
result in atrociously bad draw i ngs
,
w hich
.
nevertheless
to be admired b ecause done accordi ng to the latest
w ere
method
and only approved
Some
.
,
for
instance
that a charcoal draw i n g must be made entirely point
of
,
bl ending it ,
from
is
good
n ot
the ig n ora n ce
coal instead ing is
if
th e charcoal and that
of
the
the draw ing sho w s any
S u ch a stateme n t results o n ly
.
w hich
inte n ded to convey
— it is dr aw ing
w ith
looks at the paper
and
char
th e e ffect or the impression the draw
for
for
The problem
n ow s a y
,
.
the art student to master is dra w i n g
w hether
h e u ses the p e n cil in
an
,
outli n e
sketch the charcoal in a shaded sketch o r the brush ,
,
and color
Though
.
ne w
proble m is practically ’
years duri n g ,
w hich
colors may be discovered the ,
w hat
it has been
time almost all
hu ndreds
of
and means
of
for
w ays
producing a dra wi n g have been tried and used success fully of
by those
have practised art
wh o
The stro n g artists
th e past did not confine themselves to one medium or
to on e
w a y of
pen and
in k ,
usi n g it chalk
,
.
They
w ater
aim
w as
pression
not the of
w ay o f
w orked w ith
color
appare n tly o ften u si n g that
of
.
,
l, oi
pencil crayon
,
and other mediums
,
w hich w as
,
handiest
usi ng the medium but th e ex ,
an idea and this must be th e o n ly end ,
the best e ffort
of
Their
.
the artist
w orthy
.
To o mu ch importance is laid on technique an d the way the story is told It is eve n said that in looki ng at a .
picture
,
we
sho u ld first see
h ow
it
is
painted
,
as
if
the
FR EE HAND
D EA
-
of
kind h ow
canvas the thickne ss or thinness ,
it is applied concerns the pu blic ,
say that ‘
no
WING
.
of
th e paint and ,
As w ell
.
if
d ecide
th e color
the sentences
of
of
its skin is agre eable
an orator be fore
to be moved by his eloquence
.
we
of
;
can permit ourselves
,
be good w hether
of
The question
deserves and it d ese rves very little w ell ,
color to
or analyze
nique should b e accorded th e imp ortance story
we
must analyze the peach to decide wheth er or
we
like its flavor ; or formulate a theory
we
might
If
.
tech
w hich
it
a picture tells its
and is ple asing in color and sentiment it must ,
w h ether
painted
w ith
m uch labor or quickly
the paint is thick or thin rough or smooth ,
,
.
When th e pu b lic realizes t hat it is not methods but results w hich
mad e
constitute art a great advance
w ill
,
have been
.
The question
of
h ow
the picture is painted should con
cern only the artist and the advanced stud ent .
for
,
they
are intere sted in its practical construction as a builder is intereste d in that
of
the houses
To th e student a study ,
w hich
of
the
he sees
w ays
in
.
w hi ch
othe r
painters have secured results serves as a guide and cor re c
«
ti ve
w ork
.
But it is i mpo rtant to observe that strong painters
in many di fferent
w ays ,
and pictures even by th e
same artist are entirely di ffer ent in their handling of
t
the technique of others
hat there
18
w ill
more than on e
S t u dy
.
soon convince the student
w ay
’
to paint
.
The artist should unde rstand all the details
of
his Work
TRA INING OF as fully as
t he w
d e rs t a n d s
the use
w ork ‘
orkman in any
‘
h is
w hich
very
ra m e e p
study
fe w
be
N ature
.
the i n dustrial arts
,
p ersonality
ow n
for
the stude n t is to be
,
of
for
this temperament he must ,
N ature
as sh e appears in order ,
positions and imaginative subj ects
N ature
the poetic tem
it the artist can simply
to exercise his higher facultie s in the sent
.
truly and this is a point beyond
w ithout
able to represent
un
tools but to produce th e bes t
I f possessed
.
ST UDENT
can expect to pass
nt i s rare , and
N ature
of
the first requisite
able to represent
still
of
he must express his
U ndoubtedly
AR T
TH E
'
a i n i n t p
g
The ability to
.
truth fully is the first step
for
com
of
r e p re
the student and ,
he should be satisfied to study her seriously until he has attained a hi gh d egree of per fection It is so o ften said that the aim of art should be not reproductio n b ut ideali .
z ati on ,
that the student
is
likely to be deceived and to ,
attemp t to produce th e ideal be fore he can truth fully
N ature
represent
It cannot be co n tr adicted that the
.
higher is possible only through the lo wer and the student ,
must be satisfied to study until he can give easily and truth fully form color and values ,
produce a great e nt i re l y
tion is
'
to
.
.
w ords
.
,
To
This cannot be done
if
the atte n
diverted by dra w ing light and shade ,
Through these
himsel f as unco nscious ,
,
.
art the mind must be g iven
w ork of
the result
fre q u e n t l v
and color
,
in short e ffects
of
the
.
r a i n t e p
,
,
sh ould express '
m eans as the orator through
FR E E
6
H A zV!) D l t A ’
-
It is not meant that th e final aim of
be the po wer
WING of
.
the student shoul d
photographically delineating
that care ful study
of
N ature
-
but
,
dra w ing values and color should be ,
considered necessary to th e advanced and more valuable the artist is free to express
w ork w here
R eproduction is i mpossible th e si m plest obj ect
We can n ot
.
We can only paint
.
a more or less truth ful impression e ffects are
far
of
art must be ackno wledged to be in
artist is thus j ustified
N ature
r st
of w
from 2d
ps
c om m on s te
flat copy Light
.
and still li fe d 3
.
w hat
in
of
,
reproduction
hat h e se es but ,
in outline
f
o
th e
.
Th e
means may best
of
of
the ideas
w ork
w hat
it is a
he feels
.
a r t s t u de n t a r e
N ature
fro m
may create
the palette and
his highest
in th e w or k
even
M any of N ature s
.
w hatever
and so metimes
.
and shad e in charco al fro m casts the anti q ue ,
.
Study fro m li fe in charcoal
.
h t 4
n ot
“paint
creating an impression ,
D raw ing
.
of
using
creates in him and
question not only Tb e
it
.
’
beyond th e possibilities
ans w er his purpose
h is feeling
C olor
.
study fro m still li fe li fe and ,
N ature
.
There is no question but that the color sense is the mos t di fficult to cultivate and ,
is
very rare at th e present time
.
The deficiency in color perception is probably due to ‘
la ck
of
training in this direction
color sens e
w ere
.
If
the education
of
the
begun earlier undoubtedly much good ,
TRA
INING '
w ould
that
THE
OF a
it m a y b e
resu lt and ,
the first instruc tion
if
greater progress
w ould
AR T
ST UDEN T
7
.
true as some have suggested ,
w ere
be mad e
in the use
of
color
,
,
far
.
The great di fficulty is th at b efore art instruction is ‘
give n the stude n ts have obtained a very practical k no w l ,
ed g e of both the actual form and its absolute color of
kno wledge
the
for m
Th e
.
it s
of
prevents th e acceptance
appearance and the mind is traine d to accept the imag e ,
of
the eye only a fte r long continued e fforts -
is absolute and ,
if
.
The fo rm
the e fforts are continued almost
any
of
the
as
w ell
,
one can lea rn to draw
fairly w ell
.
The color
obj ect is absolute and the mind kno w s this color ,
as the absolute form ; but the color appears to change in
a much greater degree 1than
t he
form
.
Th e
form
d
appears to change according t o c e rt a in fixed a n d simple l a w s b ut th e col or ch a n ge s according to la w s much more ,
co mpl ex ; for th e s am e local color m ay appe ar a n i n fi n i t e num b er of di fferent colors according to light and sur roundings and it is ,
fa r
more di fficult to prove that a yello w
ap pe ars blue or gree n or some color not yello w to a w ho
s t udent z on t a
l
,
line belo w the eye appears to incline up w ard
retreats Th e
cannot se e it than it is to prove that a hori it
.
tendency
of
the student
who
kno w s th eories
a n atomy or perspective or color is too frequently to ,
by theory instead if
as
,
of
in many cases he
by obse rvation and it
w ould
,
is
of
w ork
a qu estion
not be b etter off withou t a care
FRE E—H 4 ND
8
fully
arrange d th eory
for
DRA W[ I VG
all condi tions
.
C er t ainly
.
this
is
so unless he can be m ade to realize that theory should come last and care ful study
of
N ature
first
.
Though color is so di ffi cult to realize it is more impor ,
tant to the artist than any other quality
We may not realize the appearance recognize the mass by the color through previous observation
,
We see color fi rst
.
the color but
of
,
.
we
is familiar to u s
w hich
Form may be al most
.
obliterate d by distance or other conditions but the color ,
is
seen and through it
of
light and shade are second in importance
c
,
orrect the e ffect
of
,
detail is faulty
kno w the obj e ct
N ature
is given even
The masses
.
if
.
if t h e dra wing
are o fte n arranged and according to
w hich
,
ing s are criticised
these are
Thi s reverses th e order in w hich th ese
-
factors
of
we
dra w
.
M ost instruction in draw ing has for its end form It m ay b e a s s o me cl aim th at it i s of no u s e to l o o k for .
,
,
color th at th e s tude n t h im s el f w ill acquire t h e color o f r ense this certainly is no t t ue values the rela u t s b ( ; ,
r w a light and dark hich e more of ) necess ary to the e ffect of a picture than absolute form
tions
the masses
of
.
ff hat students do not appreciate th e masses or the e ect T ,
of
N ature
,
is proven by the numbers
of
c t u re s w h i ch i p ‘
are so cut up by e xaggerated detail that the e ffect can This criticism n ot be realize d at a proper distance more frequently th an a ny other may b e made of th e p ic .
,
,
ures in our e hibition s x t
.
T h e fau l t
is due in part to
t he
FREE—H A I VD
10
is
Wh en h e s
D RA
WING
.
not likely to have a long course .
study I
of
,
hould advise that draw ing and values be considered in
this fro
w ay in
mli fe
,
there is This
not all
his
of
an d
its prop er value excuse
no
w ay
if
w ork
is
of
not making a study
for
much m ore value tha n that
When h e
.
h a s form ed
sible to break aw ay
so
ence to th e
and
N ature
w hole ,
of
this habit it
w hich
,
is
se e
re fer
look at
th e masses
th e greatest importance ,
scho ols
w ill
in their
n ow
be removed
w ay w h en
they leave the
.
The advanced stud ent may sometimes study vantage form or local values his first study
h as
w ithout
enab l ed him to
ad
w ith
a background
If
.
relative values h e
se e
,
may n ot need fart her s tudy in this direction as much special study
,
for
,
of
hen our stud ents start by observing them one
the chie f di fficulties
.
im p os
w ith
n ever
h e can certai n ly of
e ffects
p ermits
almost
as to consider the parts
The masses are
.
of
only one thi n g at a
as he should until h e i s able to
and e ffects an d w
the dra w i ng i s
in draw i n g fro m still li fe
the stud ent in beginning to think time
If
.
very little time is required to indicate th e back
of
grou n d
most
instanc e
of
th e figure
.
as
In th e public
schools evening draw ing schoo l s industrial schools and ,
,
,
all el ementary and preparatory schoo l s values should be ,
c
onsid ered as important as form and all ,
represent the obj ect and its background .
Another ods
of
fact w hich
w ork
w ork
shoul d
.
does much to continue bad meth
is that many art students even in advanced ,
OF
TR A I N I I VG
THE
ST UDEN T
AR T
sch ools are either advised or permitted to ,
part to the
w hole
Thus in a figure
.
11
.
we
w ork from
th e
find them paint
ing the first day the head the second , the shoulders and s o on getti ng on the last day to the feet or possibly not ,
,
,
as
as thi s the canvas be ing covered part by part
fa r
such
,
w ork
it is not p ossible to obtain a harmonious
In the first place it ,
l u nt i
the
is
entire canvas is covered
.
second the l ight and ,
w arm
,
first day cool the second and so ,
,
on
the
wa y of
Such a
.
does not consider the e ffect and it is a
w onder
,
that students trained thus produce as good do
w hole
impossible to determine the e ffect
color are constantly cha n ging the e ffect being w orking
By
.
w ork
as
they
.
The e n deavor pleasi ng e ffect
of
of
th e artist should b e to produce a
color light and S hade and true values ,
,
in short a satis factory resu lt ,
ing
of
Why should not the train
.
the student look to these points !
If
it
is
“
this the student must try to express the e ffect ,
as possible so that h e ,
m ay
,
as
to do
quickly
be able to change and bring
all the detail into its proper relations
.
All
parts
of
the
draw ing should b e begun at once and should be carried ,
along together works ,
or
of
w ith
d raw i n g , vas
It is
of
little importance h ow the student
so long as h e has as his aim the quickest possible
suggestion coal
.
the
w hole
e ffect
.
He
may draw
w ith
char
the brush or he may make no preliminary ,
as som e recom mend but he must get the can
Covered
,
and
th e masses placed
in
a short space
of
F R E E LH A N D
12
BR A
time and in doing this he is ,
WING
.
w orking
upon the most
i mportant part Of the draw i ng all th e tim e until the e ffect ,
is fairly obtained
H ow of
.
shall th e student
wh o
is
c omm e n c m
g
th e stu d y
art best spend his time ! What shall he draw
w hat
mediums shall h e use !
As
and
has been stated no one ,
method shoul d be permanently adopted to the exclusion of
all others
There is valu e in all and in his late r “
.
,
w ork
h e may find it necessary to use many di fferent means expression
I f we
.
the schools
,
we
acc ept as
w ell found ed
of
th e p ractice
shall postpone color and begin ,
w ith
of
the
pencil or charcoal making outline or shaded draw i n gs ,
from
.
casts or from geometric obj ects
stud e n ts begin by copying fro m the flat may be derived from this
w ork ,
In so me cases
.
,
Some benefit
.
but it cannot be
re c o m
m ended w ing made fro m The simplest d ra value than th e most elaborate copy
N ature
is
of
more
.
C opying
portions
of
for
outlines cannot a ssist one to se e the pro
original draw i ngs
.
C opy ing
ums can only assist in the matter
of
,
w hich
other medi
technique and this
should not concern the student at first drawing and the medium
in
,
.
H is
problem i s
allo w s him to think
of
th e dra wing and doe s not require thought about its ,
T R A I N I A’ G
handli ng
fairly w ell
charcoal
THE
for
him to us e until he can draw
the best
is
,
OF
AR T
ST UDEN T
The pencil or charcoal in outli n e
.
in
light and shade are means ,
w hich
to give his entire thought to the dra wi ng be used until form
He T he
h as
13
.
be en master ed
,
w ork ,
and
enabl e
and
h im
they should
.
may work fro m the cast or fro m geometric obj ects
geometric solids can be obtained in complete sets
exactly made and e mbodying all the type forms
.
,
My
l .
experience has led m e to believe that study fro m these obj ects in
for
a
fe
ww eeks
w ill
than a similar amount g
The li n es
of
give greater ability in draw
of
time spe n t in any other w a y
a cast or a figure are very fine and it is ,
more di fficult to se e the m correctly tha n those metric forms in
w hich foreshorteni n g
,
are illustrated in the simplest of
can see the errors
drawing
w ay
m uch
for
testing the appearance
more easily in a cube
of
M oreover
.
of
his draw ing
and
,
the
the geometric forms
are so simple that a child can apply them th e errors
the geo
u n trained eye
An
.
of
and convergence
or plinth than in th e more di fficult cast means
.
w hen
,
disco v er
an d
several obj ects are
arranged together every point is se e n in relation to so ,
many other points that this relation cannot be neglected
.
Thus th e dra w i ng involves so many problems that the training it gives is most valuable This
w ork w ill
also give a practical kno w ledge
T h e y m a y b e ob ta in d of c op i e d fro m t h e a n c i e n t G re e k 1
.
e
.
a rt
de a
l
l
e rs , a s o a
se t
of
v
of
ase
per fo m s r
,
— FREE HAND sp e c t i ve ,
all
h is
w hich w ill
later
w ork
.
be
of
DRA
WING
.
great val u e to the student in .
,
These subj ects see m best
reasons but the strongest one is that the ,
many
for
'
u se
.
o f the
thread to cov e r the various edges and continue the m to of
intersect the opposite edges
the group (s e e page provides a test so simple that all can appl y i t a n d ,
so
sure that it discovers at once all ser 1ous errors in th e dra wing
It makes the student his
.
teacher and
own
,
if
he carries on the dra w ing properly uses fi rst his eyes ,
then tests and changes ne w
lines he ,
w ill
w ithout
erasing
quickly attain ability
d ra w with fre edom from
him to
b ut
by d ra w ing
w hich w ill
any subj ect
.
,
enable
.
Frequently the student is first required to dra w in outline
.
Som etimes this
m ay
be necessary ; but as cor
rect values are second in importance to color and out ,
lines are
of
least i mportance it seems that ,
of
h e should combine the study lig h t and shade draw ing
.
If
for
be given to one medium
form
way
is an altern ation
as explained on page
22
at first the attention is to
any length
of
for
a nd
Sh a de
w ork ,
w ith
but the outline
,
the draw i ng to
be
.
a co mplete study
,
.
,
light and shade
value s the subj ect must be represented ground
time charcoal
.
Li h t g
In order
of
possible
and values in a
in light and shad e is pre ferable to outline best
w hen
It is not m eant that
w h en
w ith
of
it s b aCk
a grou p
is
seen
OF
T R A L VI A G ’
agai n st other obj ects
THE
AR T
of
these
all
,
draw n but that the general value w ith
t
so
be care fully
m u st
the background
the gro u p should be given
first to place the obj ects
15
.
of
,
compared
ST UDEN T
It is
.
as
w ell
at
that they are seen agai n st
simple backgrounds as a sheet of gray paper or an y m aterial of on e color Th e gro u p s ho u ld h ave a s tro n g light comi ng pre ferably from the le ft and from above ,
.
.
When dra w ing from the models
w h ich
,
are
w hite ,
some
dark obj ect should al w ays be placed in the group this is not done the student ,
stro n g
,
for
very dark The
by contrast
w hen
w it
w ill
If
.
make th e shades too
h the lights the shades seem
the obj ects are strongly lighted
.
dra w i ng may be made as follo w s
The s i ze and p osition of th e draw i ng should first be determined b y suggesti ng w ith ligh t a n d ra pid St rOk e s the “
general e ffect
of
the mass
of
todra w i n g th e rough outli n e .
obj ect as sho w n by Figs ,
.
5
the group
the group se e n
of
and
Th is amounts
.
8
.
on e
as
This dra w i ng
as
,
all
,
should be made by the eye unaided by tests or measure ments (page When made it may be tested by measuring t h e apparent w idth a n d height of the group ,
w ith
the pencil as explai n ed on page ,
lines the inner lines and th e s s
hould
n
m asses
ext be su ggested the dra w i n g ,
hade progressing at the same time
to draw the outli n es and the n b etter
to allo w the li ght
and
p
ut
in
.
68
Within these
.
of
light
and
an d
the light
dark and
Th e tendency the shade
,
b ut
shade to help in the
it
is is
d ra w
FRE E
16
HAND
-
ing
,
for
the mass e s
than the edges
are o ften almost invisible in th e
light or lost in the shad e of
ve ry important and ,
no account the shapes
Then th e cast shado ws
.
of
th ese the outline dra w ing take s
the cast shado w s and thus the mind is ,
eye and the student ,
w ithout
w ill
together form masses
of
prejudice the image
one value
,
in
of t h e
find that the shade and shado w dark
,
w hich
and placed than any other features of
a re
There is n o preconceived ide a co n cernin g
.
a condition to accept
indicated
.
light and dark are m ore easily see n
of
w hich
,
WING
DRA
it
.
are more easily see n Th ese ma sses being
is easy to strengthen the darker
part and thus bring out th e separation or edge
,
w hos e
direction is o fte n place d much more truly by re ferrin git to the shado w than it
w ould
,
l ines and then the sh ado ws of
Th e masses
be by dra w ing first the Ou t
.
dark should be lightly indicated at first
,
in order that they may be m oved about until they are rightly placed on s se n t at i
of
W hatever lines may be dra w n
.
ne w
r e p re
edges should be very lightly sketched
the same reason ing a
as
'
.
It
,
for
is much bette r to change by dra w
line slightly st ronger than the first and to thus ,
continu e until th e corre ct position .
is
secured than to ,
dra w a line and erase as soon as it is found incorrect
A lthough w orking
the student in this
on the value
w a y,
of
m ay
not see the importance
.
of
too much stress cannot be placed
the training obtained by bringing th e
drawin g into place
w ithout
erasing
.
FREE—H A I VD
18
The e ffect
DRA WING
be realized only
c an
w hen
.
the entire group
is seen at a glance and to do this the vision must be ,
blurred until all part s are s een equally and necessarily indistinctly
This e ffe ct may be obtained -
.
for
in focus
w ith
the eyes
a shorter or longe r distance than that
of
the group and i s the same as that given by looking ,
through a lens ing
t welve or fi ftee n inches focus
of
the eyes is better than nearly closing them
cuts
off
most
of
th e light and loses the color of
and shade this is a matter
.
O pen
.
for
,
this
In light
not much consequ ence b u t ,
it is better to study in light and shad e so as not to be oblige d to change
for
advanc ed
w ork
.
Th e struggle comes in se eing for th e first time A l en s of fi ftee n i n ch e s focu s h a s b ee n of gre at a s s i s tan ce to many By it s aid they have been enabled to s e e the .
.
masses and to realize their errors
w hen
explanation or assertion on the part be en
of
the least value
th e teach er has
mirror but ,
t
he blur glass is
th e only means tha t I have been able to use of
degre e ci at e d
success
A fter
.
th e masses and ,
h as
det ail in these masses h e ,
little practice w ithout
w ill
w h ole ,
only
w ay
w ith
the student has once seen
w ill
h ow
any
a p p re
unimportant is the
ne ed no artificial help
.
A
enable him to see th e entire group in fact to see naturally the group
special e ffort
as a
of
Some reco mmend the reducing
.
C laude Lorraine
glass or a
of
no amount
,
and it mus t not be forgotten that th is is th e
to se e e ffects
.
of
When a number masses
of
THE
OF
T R A I N L VG
AR T
draw ings
S T UDEN T
w hich
light and dark as Fig ,
give simply the
have been made the
2,
.
19
.
,
student should try to get all the values being care fu l th a t ,
the grays and detail in the lights an d the reflected lights ,
in the shade are not made too prominent ,
He
.
should
understand that the first dra wings made express the most i mportant truth that ,
contrast
of w
w ith
strong light there is al w ays the
ell defined masses
of
light and dark
tendency is to look upon the draw ing Fig ,
stage and to study the detail ,
,
w hich
2,
.
The
.
as simply a ,
can al w ays be found
upon close exa m ination so care fully as to los e all general ,
e ffect
There i s al ways a tendency to exaggerate the
.
slight di fferences
,
w hich
appear greater than they really
are and the student must struggle to ,
simple
d r a w ing w ith th e
the draw i n g
p a r is on f r om a dis ta nce of til e up i ss a r o s n e c e w n the dra ing bei g g y
Fr e qu e n t
.
k eep
c om
"
,
r
,
placed beside the group
If
.
the
th e e ffect being realized by use
t wo of
are thus compared
the blur
lass g
if
,
th e
student has not yet learned to us e h is eyes it is thou ght ,
that
if
he
w orks
earnestly he ,
w ill
in a short time be
to produce fairly truth ful representations Figure
of
the e ffect
represents the group already studied 3
the gradations
.
It
w ill
.
w ith
al l
be noticed that there is al w ays
some point in the group that th e high light on a
ab l e
w hite
is
lighter than any other
vase or sphere
.
,
as
These poi n ts
should be care fully considered and it is evide n t that the ,
rest
of
the ma sses
of
light must be slightly gray
.
There
— FRE E HAND DRA
20
WING
.
also in every group some spot th at appears dark er
is
.
than any othe r w ith
All
.
the oth er darks ,
this and to be sure
truth
of
,
must also the grays in the light
m ust b e '
w ith
compared
each other as ,
.
The tendency is to make th e dra w ing too black may be avoided by w ith
c om
of c
a large piece
,
p
ari ng
This
.
darks in th e group
th e
harcoal held in front
of
th em and ,
.
shaded by the h and so as to appear black ‘
of t h é
the darks Th ere
group see m quite gray
if a n ot h e r
point
of
colors
do
for,
sees a colored Obj ect in front w hite
im mediately thinks
of a ,
of
,
an d
this
is
in
as already explained
not app ear th eir real colors -
.
great di ffi culty
regard to th e colored obj ects
This m akes
.
The student
.
cas t
w hich
,
who
is grayish
th e actual color
of
the
obj ect in comparison with th e actual color of t h e cast The color may be darker than th e cast This being s o ,
.
it
is frequ ently
n early imp ossibl e
the color eve n ,
if
for
.
,
him to realize th at
quite dark may be so lighten ed by ,
direct light as to appear even lighter than th e gray ,
of
a s hado w upon it The statem ent is o ften mad e that th e sur face receiving
the cast
w ithout
.
of
the most di rect rays not
es t
light appears lightest
.
Thi s is
The h igh lights are the surfaces th at reflect the light most
true even
for
obj ects
of
the sam e color
.
directly to th e eyes not those that receive the m ost ,
direct rays
of
light
.
Th e di fficulty incr e ases
if
the colored obj ects ha ve
smooth
or
‘
THE
OF
TR A I I VI N G
AR T
,
21
.
fre quently
surfaces and
i h e o l s d p
ST UDEN T
very dark
colors may app ear much lighter than the light obj ects of
the group through their reflecting more light to the ,
-
eye than the lighter obj ects student is not to
work
The only sa fe rule
.
by t heory or to think ,
for
ought to see the colors but to look ,
for
the
h ow
he
the actual impres
sion reme mbering that this is very likely to contradict ,
A fter op p osite
‘
w hat
h e thinks
.
dra wing exactly
having frequently made his from w hat
i t should be the ,
student should have no di fficul ty in trans ferring '
dependence upon his ideas to his eyes step has been taken book to be studied ,
,
N ature
w hen
he
w ishes ,
and
i t is no longer a
,
w ork
w hich
t he
is
must be
When this
.
is be fore him as an open
question of seeing but of the best w ay to do
A point
c are fu l l y
n g
w hat
arded
in all ,
on e
time
,
so
,
edges and separations are
b rough t
ou t
is
seen
that the e ffect
cannot be given by a draw ing in ‘
The eye
.
This point
.
clearly all other points indistinctly
w hich
of
all the
by hard line s
.
In
obj ects throug h con color and light and shade and w e do not s e e
there are no lines
t ra s t s of
.
hardness that comes from definite lin e s and
sees but a point at any
N ature
he feels
aga m s t
sharp separations bet ween the di fferent parts
N ature
his
.
We
se e
,
sharp definitions bet we en th e di fferent colors straight edges
of
E ven
the
the models are not s een as sharp lines
,
the atmosphere and the action to blur and so ften
.
.
of
the eye
ng c au s i
the m
.
FREE
22
HAND
-
The
DRA
WING
draw ing mu st be definite
w ith out
Frequently th e outlines are entirely lost of
th e shado w s or in th e mass is it true
of
d etail i n casts
.
.
being hard
.
This occurs in
.
the light and particularly ,
— G e nerally
th e outlin es dis
a short distance on ly The stude n t k no w ing th e form is very apt to supply th e missing part and draw appear
“
for
‘
.
,
,
w hat
,
h e does not see and thus his draw ing becomes hard ,
and cut up what
If
.
he
w ill
study the e ffect and dra w only
he s ees avoiding sharp edges and hard se p arations ,
h e cannot fail to make a good dra wing I have descri b ed th e w or
k
but
way in w hich th e s t udent should ,
not advise him to spend all hi s time in this
w ork , for of
.
to produce the finished light and shade draw ing
do
,
I thin k great benefit
outline simply
I t is
.
w ill
result from t h e study
b e t t e r from '
the start
for
him to
I say pencil in f re erence to ch arcoal because erasures should not be p give part
of
this time to pencil outlin e
.
,
mad e until th e correct outline is secured is
u
se d it is i mpossible to ,
out erasing
.
With
s t re ngt h e n e d e ac h
w ithout
valuabl e
p ositions
I
w ould
many changes
w ith
,
the last line being slightly
time and th e corre c t result obtai ned “
,
erasing a line .
ke
charcoal
m ediu m pencil th e lines may be
a
given many di fferent
ma
If
.
.
The
t ra1n1ng thus
given is very
h ave dra win gs mad e in this
the m od els until groups ,
of
five or six
cult on es can be correctly draw n in
an
of
w ay from
d iffi
the m ost
hour
Or t w o
.
finishing the dra w ings the li nes should be accented ,
explai ned on page
44
.
In as
TRA IN ING In connection the making pencil
,
of
TIIE
OF
w ith
this
AR T
w ork
S T UDEN T
the student
quick sketches in a note book -
shade and values and
and
if
simple o bj ects he ,
w ell
,
find that
w ith
greatly assist to freedom and accuracy
w ill
Sketches may be made complete studies w ith
w ill
a group
of
23
of
a so ft These
.
light and
one is made each day beginning ,
w ill
soon be able to dra w freely
several obj ects
I have said little about tests
.
He
.
wh o
intends to
study art as a pro fession or even as an accomplishment ,
,
should be able to depend upon his eyes and should use ,
The follo wing tests are su fficient
fe w
tests
for
measuring proportions
.
and h eld in
,
The pencil
!
front
of
lines for
to give their angles or held horizontal or vertical ,
comparisons and in beginning the ,
,
l ater ,
the passing
of
u s e of
i t r i o p
the pencil
the thread and ,
over the lines or the ,
draw ing in th e air time
w ill
If
.
he cannot succeed
be better spent in other w ork
ing of tests in the latter part
of
,
means
for
have to teach those m ay
such aids n ot
for
w ithout
be necessary
At
first the ma tter ,
of
,
the head
,
the
tests correctly
public school teachers in
,
,
.
s r e a l t M a i f
.
techniqu e and handling is ,
who
these cases they should
o
importa nce to the student
,
ability and though
sp e C 1al
be required by the art s t udent Us e
U nder
.
th ese his
this book are given several
assisting th e pupil to apply
but these are intended
w ith
w hose
of
no
only aim should beito
FR EE—HAND
Z4
D RA WING
obtain good drawing and correc t values not m ean that i t i s w or
ks
,
for
h e may
ends in vie w duction
of
in bad
w ays
By this
.
h ow
no i mportance
w ork
.
and
we
do
the student
w ith
un worthy
We m ean that having as a result the pro
.
,
of
drawi ngs true in e ffect in as direct a m anner as possible h e is not likely to w aste time over a w ay of ,
,
handling w hich does not tend to this result and hone st student is thin k ing of
the execution
the draw ing
of
,
for the
earnest
the e ffect rathe r than
It is interesting to see
.
clever handling and brilliant execu tion and they ,
ar e
to
f be d m w é ggdy fb u t the student should not try for them f ss An d style w ill come of themselves in time C l e ve r rm If ’
.
.
’
the a
stu
de ht t rie s for these he may secure them but prob ,
bl y at the expense
of
,
,
the substantial qualities
which
m ake a str ong picture H e sh ould be s atisfied to study N a t u r e ; and w ork earn estly until a true representation of .
is qb t a in e d This dra w ing is much more v aluable even th ough the labor s p en t upon it is evid ent th an th e
h er
.
,
,
m ost
th e
clever study
kno wledge
wh ic h
directly ,and thus
N ot
w ith
H onest
study g i ves in tim e enables one to express
w hich
is untru e
.
an interesting handling .
only does t h is honest s t ud y
,
of
N ature
a nd a
p p ear
a u ces produce th e mos t valu able results but from the ,
sta rt it is
m ost
interesting to th e student
that h e discovers a an
new
inves tigat or in a
h e p re sse s
,
'
on w
fact ,
ne w
e xp e r1e nc e s
field and ,
ith ren ew ed vigo r
.
w ith
w h o,
each tim e
th e pleasure each
ne w
of
ide a
,
FREE
26
HAND DRA WIN G
-
.
even beginners in the public schools are oblige d to render light and sh ade by a hatching
A dherence for
to any such rules
sometime s one
w ay
lines as in a lith ograph
of
w ill
cause much loss
of
,
is the most di fficult and slo w es t student
is
advised to de fer all ,
for
w ay
of
wh en
w ork
w hich
handling
are
h e may pursue these
training simply in their handling and not as
for
for
lines
,
.
,
“
mediums
.
imaginable and th e
w ays of
di fficult and slo w to the time m ethods
time
is quic k est and sometimes another
But to make a light and shade dra w ing by means
.
the study
of
e ffects until he
light and shade
He
.
s h ould
render the m truly and
c an
‘
,
should not allo w himsel f to be trammelled by arbitrary rules or di fficult
w ays of w orking
.
He
sh ould aim to get
go od dra wing and valu es in the shortest time and all ,
m e ans w hich
accompli s h this should be legitimate u s e of
Some teachers advise the
the stump the char ,
coal being ru bbed by it to an even tint to
stumping
.
Th e obj ection
.
is that the pupils see m
to
th i nk that
smoothness is a virtue and all that is n eces sa ry is t o move ,
the stump about vigorously ,and in som e stu mp w ill make the dra w ing Such u se .
w ay of
o r other the
the s t ump not
only quickly spoils th e paper but tends to create th e
‘
,
idea
tha t th e dra w ing cannot be made directly
stump may b e u se d in parts too small but th e te ndency rubbing
w ith
w ith
for to
.
The
advantag e to plac e th e charc oa l -
,
the finger and ,
for
li fting th e lights
use improperly is so strong that
the stump should be allo wed
.
,
no
TRA I NING O F
AR T
“
TH E
In order to get atmosphere it ,
of t he
sary to fill in th e gram
S T UDEN T
27
.
w ill frequ ently
be
ne c e s
paper by movi ng the ch ar
coal about until the depressions of the p a p er have received a tint
finge r over the paper been filled in this
the paper
h as
the dra wing should be finished
w ith
,
of
When the grain
.
w a y,
directly as possible of
th e
Th is may be don e by very lightly passing
.
the point
of
,
as
the charcoal a tint ,
the proper st rength being placed by care ful dra w i ng
j ust
w here
it
is
w anted
If
.
a small part has been m ad e
too da rk it may be lightened by touchi ng .
,
w ith
the finge r
a large part by blo wing off th e charcoal
or stump
,
lights may be draw n
w ith
an eraser
Fa b e r
.
’
The
.
s
erase r
made in pencil form is g ood f or this work and the
fi ne
,
line s
of
called
i " N i ri i v r n e o , g
w ide
l ight
may be t aken out w hich
enough to be strong
a pencil is th e best eraser
w ith
shou l d be c ut to a thin edge '
‘
Bread rolled into
.
It
.
w ill
of
the paper
.
is
w ill
w ithou
t injury
to the
,
t o form
a
p plied wit h
great care
w ith .
If
on the paper they will float the
cha rcoal and spoil th e draw ing the dra w ing
“
finish ed it mus t be sprayed
This should be
drops are allo w ed
'
.
Wh e n the dra wing fi xat if
r m of t h e fo '
q uickly remove almost
all the charc oal fro m a large sur face texture
the h ard eraser
,
If
.
too much is appl ied
shine and lose its li fe
.
,
It should be
a
ppli ed a little at a tim e and allo wed to dry bet w een the
a
ppl ications
coal
,
on
.
It
account
18
well
of
to avoid
‘
the di fficulty
t oo of
much sur face char fixin g the dra wing
— FR EE HAND DRA WIN G
28
t
t fl o t n g t h e ch arcoa l S poiling t h e dra w ing
Wi h o u
.
and
the
p aper
require more
fi x at if
ov e r
a 1
thu s
.
The darkest parts light parts
of
H aving
th e
w ith
a p a per in needing
l ac e p
described th e
w hich
fi xat if
and
can dra w
a hole is made
of
.
w ays
in
w hich
the student may
w ish
,
to
say
that he
rend er values in charcoal is ready to
in any m edium and a fter th e first experiments
w ork
,
necessary to a
ne w
success
if
the m edium the problem
is
m edium he
w ill
,
h e understands that
t he
the
1
study to obtain facility in dra w ing I who
than
It can be placed upon these parts by cover
.
ing the d ra w ing th e size
w ill
w hatever
d o so
w ith
,
same and is simply and al w ays dra w ing and va l ue s ,
and color
.
Th ere are
t oo
many
who
paint by rec eipt but the re ,
a w a f s o h ould no such thing as a rule or a doing e b s y many se em to think w h en they as k h ow to repre s en t ,
,
tree s or grass or drapery etc ,
,
,
w h o w ould b e
To all
.
serious the proble m is simply obse rvation ,
N ature
is al w ays d ifferent th ere
c an
,
and since
;
be no receipt s
representing her infinite variety So me students see m to think t h a t they are
for
.
ing a 1
The
ne w
Fixa t if
subj e ct
m
m ay b e s ou d
l h l h l o
a co
mp
for t h e i
l
of a c e a r a s t r on g
,
d il
t ie s u ri
mb
u te d
w hen ad e
st an d ,
to se tt
l
e r c o or. so
h
t at a
l
e
taking up a
c om m e n c
m edium
ne w
This
p u re a l c oh ol s s olv e d l on g e n o u gh a ft e r t h e gu m h a s b e e n d i T h e u pp e r p a rt w ill t h e n b e a t t h e b ot t o m b y d is s o
lvi g w h i h ll
.
te
n
s
e
ac
in
.
,
.
I t m a y b e t u rn e d in t o a not d ro w i e a ora t e e a in
p
ll v
p
,
l v
h b tt l er
o
g j u st a
e , a nd
if t oo
t ra c e o f gu m
.
TRA INING OF THE is not so
for
,
AR T
ST UDEN T
29
.
the subj ect is al ways the same and the ,
treatment should be the same in striving first masses and the e ffect
for
the
.
The most frequent error of all is the atte mpt to finish a part be fore the e ffect is indicated
M uch
.
time is spent
in care fully dra w ing and finishing a part only to find when ,
the rest is in in values
l c a e p
that it is out
of
dra wing or incorrect ‘
The dra wing should begin and progress all
.
at once and equally until the desired e ffect is attained
,
quickly the
w hen
w hite
of
the detail may be studied
.
th e masses Th e more
pap er or the canvas is covered the ,
better and until the value s and masses are nearly cor ,
rect nothi ng else should be considered
.
There are so many draw ings and paintings
wh ich
are
merely conventional p retty thi ngs that th e student may have di fficulty in realizing that they are not true and that ,
,
his
w ork
should be serious and honest
.
It is hoped that
soon a higher standard may be placed be fore the art
st u
dent that h e may understand that not all his problem is ,
in the
d raw m g,
but that value s and color are equally and
eve n more important than absolute may acquire the po w er to represent trut hfully
.
form ,
and that he
N ature
easily and
C HA PT E R O UT LI N E IT
In a
.
D RAWI NG
.
is o ften said t hat there are no outlines in way
N ature unders t ood to
this is t rue but it canno t be
.
mis unnecessary or that it may be slighted ,
m ean that for T he
II
.
student canno t l earn to paint or to make pictures
in any m edium
w ithout
,
T he
d efining
of
bits
of
w hich
color
draw ing th e forms
of
the obj ects
.
the lights and sh ades and the v a rious are seen
in
N ature
is n ec essary to
give solidity and character to a picture and it i s useless ,
to think th at anything can be a cco mplished
light and shade c
annot be made E very
if
approximate representations
color or of
form
.
obj ect has definite form and size and th ough ,
it may not be outlin ed it h as bou ndaries ,
representat ion c
w ith
of
ten as even
th e
obj ects in out l in e only is at best a ,
onventional and imper fect
of
A lthough
.
form
m eans
of
expression so ,
is concern ed th e student ,
c an
far
be
taught to observe e ffects and may o ften succeed in con ,
v e yi ng
and
of
a fair impression varieties
that th e study 30
of
of
of
the character
sur face and texture
appearances
a nd
.
t h e ir
of
the obj ect
He
w ill
,
find
representation
,
O U TLINE
DRA WING
as fully as possible even in so simple a ,
dra w ing
w ill
,
in
re a t
g
'
m e a su re
31
.
w ay
prepare the
as outline
w ay for w ork
in lig ht and shade and col o r The w hole q uestion is simply one of seeing and the student should not trouble .
,
himsel f over techniqu e as his only aim should be a tru e ,
N ature impo rtant p oints
representation The most freedom ,
.
,
w hich w ill
the production of
of
.
,
prevent all from
w ill
I t is d iffi c u l t to give ‘
produce these results as individu w orking of
handling and technique are is
in free hand draw ing are -
directness and accuracy
directions ality
of
in a uni form
w ay,
little importance
truth ful draw ings
is
th e
e nd
and
Since
.
desired it ,
no consequence that such dra w ings are produce d
by di ffere n t persons in di fferent fe w
to give a
general directions
w ays ,
but it may be
w ell
.
It is most important that the pencil should be h eld lightly and the first lines ,
and rapidly
of
the draw ing
es te d s ug g
fre ely
Th e paper should be not less than eleven
.
by fi fteen inche s and the draw ings should be large as sm all dra wings w ill produce a mech anical w ay of w ork ,
,
ing .
A
long pencil
may be h eld and first \
as
t wo
,
w ill
a stick
assist to freedom of
of
motion
charcoal bet w een the thumb
fingers and as ,
far
as possible
from
Th e paper should be fastened upon the board
its edge s parallel to those
It
.
of
the board
.
If
the w ith
the edge
of
the paper is not straight a horizontal line may be draw n ,
'
FRE E
32 n
HAND DRA WI I VG
-
.
ear its lo w er edge so that directions may b e re ferre d ,
to this line
atte mpting to dra w any obj ect th e
B e fore
.
,
student should ac q uire the freedom necessary to good tions
C urve d
.
p encil
from
w ork ,
of
w hi ch
m otion
by draw ing lines in all
is
d ire c
lines may b e produced by s w inging th e
the
w rist ,
lines by a motion
of
elbo w or shoulder ; and straight ,
th e entire arm
These move men t s
.
should be practised until li n es can be dra w n instantly across the paper in any direction for
most important
This fre e m otion
.
is
all sketching but in finishing or ,
accenting a draw ing
,
w hose
thus sketched more pressure ,
propo rtions w ill
have
be en
be required and th e ,
pencil m ay be held more fi rmly and n earer th e point
.
Th e first subj ects may be th e ge ometric solids or any ,
co mmon obj ects
I
.
w ill
explain the
th ese may be studied by making a s k etch ,
it s
cover thro w n back
.
in
w ay
;
of
w hich
b ox w ith
a
i See F g ( .
First nearly close the eyes and try to se e the box not ,
,
as a solid but as a silhou ette th e outline
of
,
,
the box against the background being care fu lly studied
A
.
little practice
w h at
w ith
In
Of
sh ould fi rst be
the eyes n e a rl y
closed w ill enable one to se e th e mass in this -
the mass
Fig ( 5 o r der to realize th e directions w hich the e d ges
appear to have lines may be dra w n ,
ing the
w ay
.
.
nthe air by m ov
i
,
pencil p oint so that it appears to cover the edges
.
When this is done care should be ta k en not to move the ,
p encil
a w ay from the eyes that is in the actual '
,
,
d ire c
FREE HAND DRA WING
34
-
be en changed to agre e w hole
w ith
.
the measurements
‘
of
the
h eight and width and tested by moving the pen cil ,
poi n t t o cover th e edge s it
w ill
,
be
w ell
to te s t b y me a n s
of
vertical an d h orizontal l i n e s take n th rough th e di ffe r ent angles of th e box Thus drop the pencil point verti ,
.
cally from point
and
i,
w here it
se e
cuts th e lo w er e d ge
and carry the point horizontally from point its intersection
th e front edge
w ith
.
and
2,
A
,
B
,
etc until th e points
C,
.
,
ote
The p e n cil may
n ow
of
the
be made to continu e the apparent directions edge s
n
,
w here
the continued
lines appear to intersect the opposite outlines are noted
.
These tests may also be applied by the pencil used as a straight edge and h eld horizontal and vertical appear to coincid e made
,
w ill
w ith
lines
produce a dra w ing
and should be d epended upon of
height and
D istances
s h ou l d
w idth
w hich
are
n
Th ese tests
.
'
w hich
,
if
,
and to care fully
is practical l y true
,
The fi rst m eas u re ments
.
very care fully taken
be
EF
early equal as ,
also be com p ared but as a rule ,
,
fe w
.
and FG may ,
measurements
of
.
proportion should be made as short distances or shor t ,
w ith a
long distances cannot be compared ,
ccuracy to be
as e xplained ,
of
Fig ( thread may be used instead
T he
line
,
w ho se
on
any value
a e p g
74
.
intersectio n s
.
w ith
su ffici e nt
.
T he w ith
of
th e p encil
for
tests
,
thread app ears a fine
the edges may be easily
placed so that until th e eye can be depended upon the ,
t hread
is pre ferable to
th e
p encil
.
O U TLINE
DRA WING
35
.
It is mo st importa n t that all changes be made not by erasing but by draw i ng
ne w
,
b ut
li n e from fi rst to las t
on e
and i nacc u rate draw i ng ; made to agree spirit
lines
w ith
,
for
w ill
h e avin e s s, b u t
thro w the dra w i n g be secured
can
most students to draw
aw a
h as
,
n and start a e until the result w y
w ithout
havi ng lines
blac k that they
so
.
for w orking ,
a nd
too
,
student to depend as e rases
w ithout
it is better rather than to erase to
can n ot be easily erased The reason
eepi ng
still be lacki ng in
lightly enough to secure th e correct lines great
k
although it may fi n ally be
'
’
and
surely produce a hard
tests it
I t i s di fficult at first
.
w ill
and
the
all
E rasing
.
fa r
in this
w ay
is that
w e w ish
as p ossible on his eyes ,
.
the
If
he
one line from th e start un n ecessary tim e is ,
giv en to th e draw ing and h e ,
w ill h és it a t e
to erase his lines .
.
light li n es are dra w n and not erased but others draw n
If
,
as soon as there is doubt about th e fi rst being rightly placed th e student is much more fre e to cha nge as each ,
suggestio n occurs and to w ard the last he h as his choice ,
the var ious li n es already dra w n This is by prepares at first cal
for
for
w a y of
have
to
far
a n d c an
experiment freely
th e quickest and most accurate
rapid and truth ful sketchi ng
the student
who
.
It
w a y,
is
has been taught the ,
able to produce truth ful sketches u nnecessary lines
.
w ay
be fore h e
w ithout
.
and
di fficult
m e c h an i
dra w ing one line at a time but h e
draw very long in this
of
w ill
w ill
not be
dra w ing many
FRE E
36
-
H A I VD
DRA I VING
There is not much choice the
w ork , of
nature
but it is the
we l l
,
.
pencils
for
this part
of
to use al w ays as so ft a one as th e per m it
w ork w ill
be used the lead
of
.
m aking
As
.
no pressure should
at first as ligh t a line as can be
seen and as all li n es except the correct ones must be ,
is
erased there ,
wh y
no reason
the student
wh o
has diffi
culty in usi n g a so ft pencil should not use a hard on e u n til the dra w ing is ready to accent
.
When the correct outline has been found it is
ne c e s
,
sary to finish the dra w ing
The paper must first be
.
cleaned all the lines exc ept th e last being erased ,
easiest
to rese rve these lines is to make them
w ay
stronger than the others so that they w hen
The
.
w ill
sho w faintly
the e raser has been passed over th e paper
ing all but an indication The draw ing may
n ow
of
the result
,
r e m ov
,
.
be accented
w ith
a so ft pencil
.
The pencil may be h eld more firmly and th e lines dra w n ,
of
their proper strength by one touch the attempt be ing ,
not to produce a fine even line in imitation of a ruled one but rather a lin e of medium strength w hich w ill con '
,
vey the idea better
for
of
straigh t edge s
the lines to be mad e
For the present it is
.
of
uni form strength
,
w ith
no attemp t at gradation o r the frequent conventio n al ,
acc enting point
w ill
of
th e nearer edges by hea v ier li nes
b e considered later but
the stud ent
,
,
if
w e w ish n ow
h e is already familiar
as quickly as possible and ,
to
strength or as explained on page
w ith
44
This
to advis e
it to forget it ,
finish in lines .
.
of
one
.
O U TL INE
DRA l VI A G '
37
.
The student sh o u ld dra w from various obj ects in positions until he is able to
fe re nt
,
correctly at first w holly
them very n early
for
The time required
.
upon the pupil and the care
are f ollo w ed
se e
wi
d if
this
w ill
depend
th w hich directions
.
A fter
the practice fro m single obj ects several shoul d be arranged in a group The student will probably ,
.
attempt to draw the obj ects one at a time taki n g first the ,
A
pris m
,
Fig
.
7,
C,
next the vase B then th e cylinder ,
and last t he frame D The obj ection to this w ay of pro c e e di ng is that as the obj ects are dra w n one at a time .
'
,
'
until the last is completed the proportion of the wI1ol e — group that is its greatest height in comparison w ith its — great est w idth cannot be seen Indeed this is o ften not ,
,
.
,
even considered th e student taking ,
it for
granted that
since he measured and tested each obj ect as it .
w as
draw n the single obj ects are correct and there fore the ,
group
,
But
.
frOm w hat
has been said it
w ill
each obj ect is likely to be a little out indeed
,
we
may
s ay
is sure to be
th e errors are multiplied
and
if
so
.
proportion
This being the case
the height
compared the proportion is found to be ,
of
be see n that
and
w idth
far from
; ,
a re
correct
.
It is a principle generally ackno wl edged that in all teach ing the c
w hole
should be presented be fore its parts and it ,
annot be contradicted that adding one obj ect to another
FRE E
38
-
HAND
I G
DR A IV N
.
until finally th e patch w o rk is co mplete is an w ay of
on al ti
proceeding w it h
unsatis factory as ,
crease
,
and
dra wings
at
w here
Practically
.
each
it is also m ost
the di ffi cult ies
o bj ect
last it become s impos sibl e to th ey belong
The only logical
.
u n e du c a
l c h a e t e p .
,
p ro p ortions
pr incipal points Fig ,
8
.
.
is
wa y
dra w the group all at once fi rst co nsid ering it as a and blocking in its
in
to
m ass
by lines passing from the
When th es e lines have been
dra wn and considered they may be tested by measuring ,
w hole
t he
by
u se of
height and the
w idth ,
thread or p encil as
A
the directions ex p lained
and
teste d
.
good plan is as soon as the proportions have b een determined to drawhorizontal and vertical lines forming ,
,
a
re ct angle enclosing the d rawing
,
the
w hole
group
m easu rements s
an d
w ithin th ese lines
the drawing is kept of
,
b eing
.
to be care ful that The proportions
t h us determined as nearly as
can determine the obj ects may
be
n ow
,
ketch ed by eye the m ost important lines being draw n
first
,
These are the line s
.
w hose
p ositions
and directions
i They a re th e longest lines lines one obj ect w hich are nearly continuations of those are most easily
se e n
,
some other obj e ct and lines ,
ti nc t l y
w ay
by shade or shado w of
the dra w ings
at the sam e time
,
.
w hich
of
of
d is
are bro u ght out
I t is evident that in this
the di fferent obj ects are proceeding
an
d the shorte r and le ss prominent -
li b es bei ng dra w n last th e group may be said to be draw n ,
all at once or as ,
if
a S ingle obj ect having many p arts
.
O U TL INE DRA WING
39
.
While draw ing th e student must think
the tests
,
horizontal and vertical li n es
,
,
applied by the thread and
,
continued lines
of
of
of
and draw ing in th e air by passi n g
the pe n cil point to hid e th e edges to be represented
w ill
,
Th e obj ect S ho uld be studied in this
w ay
and changed as o ften as found incorrect until the
e ye
help greatly
.
,
can do no more
It is
.
n ow
time to apply systematical ly
_
the tests explained by the dra w ing
the box
of
.
The first test is to compare the height and of t h e
each obj ect dimensions
w ith
group and also to compare t h es e ,
those
th e most important Slight inaccuracy
,
an d
c an
th e
of
w hole
group
,
c an
w ith
w ill
by adding lin es and ,
w ithout
m ade ,
not
,
for
for
.
for
by erasing but ,
the tests
the continuing
of of
.
Th e thread may
horizontal and vertical all the edges and third
co v ering points in the group opposite
that
t he
m eas
other m easurements u n til
th e eye can see no more to be done lines second
be
generally change the draw ing through
The changes should be
then be u sed , first
c an
of
th ese measure
By this time the student should be able to
These tests .
case
,
ure as accurately as these draw ings require out
the
are nearly equal and the best th at
done is to make the draw ing agree .
be compared in
,
me n ts
.
hardly be avoided but these dim e n
more accurately than any oth ers especially w hich
This test is
.
should be very care fully take n
sions are the longest measurements, an d those
w idth of
intersections
of
,
on e
these diagonal li n es
anoth e r w ith
,
the
FREE
40
-
edges
m ay
be noted
DRA WING
[I AND
.
The thread used thus
.
w ill
disco ve r
e very discrepancy except th e slight deviations only the accurate eye can detect w hich
A fter
.
w hich
the training
is given by these dra w ings made entirely by eye
be fore any tests are a pp lied this accuracy ,
secured
w ill
soon be
.
found ,
Wh en the correct lines have been are to be erased as explained on page ,
ing is to be accented of
to think
But
.
n ow
the others
and
6 3 ,
the student
the
w ill
draw
do
w ell
e ffect and to see if more interest and expres ,
sion cannot be given to the drawing than is given by uni form
lines
The student has perhaps be en taught that
.
th e nearest obj ects are seen most strongly and that the ,
strength diminishes true in a general
w ith
w ay
of
,
of
Thus
a
r ow of
course is r c e s e p p
of
a nu mbe r
appe ar t h e darkest
w ill of
.
appear th e
dark obj e cts
the
n
t he
distance appears dark er and th e dark one lighter
and
w ill
a erial
of
light obj ects the nearest ,
of
color by intervening atmosph e re
lightest and brighte st and earest
This
.
It is th e e ffect
.
tive or the changing
th e distance
The light obj ect in
.
1
,
in
,
a sketch representing considerable distance this
principle
w ill
be
of
assistance
But it mus t be stated so
.
as not to convey th e idea that there can be
ng i n n ot h i
the distance as strong or stronger than the unimportant features
of
the foreground
,
for w e
do no t s ee obj ects
more or less distinctly according to their distance 1
l h bj
V e ry ig t
o
e c ts
m ay
c
h g an
e
l l
b u t itt
e.
in fac t
,
FREE
42
-
for
th e outline
farther
of
HAND DRA WIN G
th e nearer is barely visible
is distinct against the blackboard
In color
.
,
.
of
certainly should not think
we
l e t he whi '
representing
the nearer as darker than the farther or in any other ,
w ay
than as
shade w ith
it app ears and th e sam e is true ,
Why should
.
No
outline !
not do the same
,
reason to th e contrary can be given
,
li n es are seen is the result no t ,
t r a s t s of
light and possible
we
the di fference in clearness
for
of
w hen
w ith w hich of
th e various
distance but ,
colo r and light and shade
Of
.
,
course
of
con
e
shal l
we
ex p ect to find th e strongest lines among the nearest ones but farther than this
cannot go and
we
,
if w e
adopt
conventional accenting recommend ed by text books -
are
w orking
w ill
the we ,
by rule and not by observation and the resul t ,
be th e production
C haracter
,
,
of
hard mechanical draw ings ,
appears in outli n es
An
.
.
obj ect as a cast ,
,
having a smooth hard sur face sho w s these qualities in ,
its outlines
A
cube
w ill
,
w ith
w h ich w ill
be represented by smoot h lines
smooth faces has sharp straight edges ,
be represented
b y straight lines
rough boards has broken edges
,
.
w hose
A
breaks into th e other
.
A
box made w hich
,
of
w hich
light or a gro w th Light
of
of
one sur
draw ing from the figure
can express the variations in the appearance li n es parts
w hich
c h aracter m ay be
given by draw ing the irregular outline in face
,
.
of
the out
are sharp other parts blurred by
hair
,
.
a ffects the appearance
of
the outline s strongly
,
‘
O U TL INE
I VA/VG
+3
.
in some place s making th e m distinct in other places ,
indistinct
An
.
of
these variations of
var iation
for
even line
everything disregards all
e ffect ; so also does any conventional
strength
If
.
gard e ffects in outline
th e student is allo w ed to
w ork ,
in seeing them in later
he
w ork
.
w ill
d isre
have great di fficulty
There is no more labor
involved in representing e ffects than in disregarding th em
for
,
one line is as easy to make as another
t ion only ée ing
r ed r e qu i
pe rf or m and as
l Ong
,
Tb e
.
The
N ature
ca n
found
.
conventional accenting taught in th e p ublic schools
sketches .
s ee
he can learn to correct
,
pr o duces the most mechanical out
zo/zo c a n
as any di fference s can be
bet w een his draw ing and the errors
s t u de n t
,
oé s e r oa
when t h e
U ndirected
student he
,
w orks fr
w ould
hard
and unnatural
mN ature ind o ors or o ,
,
never produce such childish
and ridiculous e ffects but a fter his instruction in draw ing ,
from
the obj ect
represented
,
w ith
w here
he has learned that lines must be
a degree
of
strength corresponding to
their distance he naturally does not think ,
of
observing
and d raw ing w hat he sees but simply mechanically grades the strength of line as he has been taught ; He ,
makes the heaviest lines
should be the where
faintest
no lines at all
of
th e draw ing
indicatio n s
w ould
of
w here
there
lines and o ften ,
be b etter than fai n t lines
.
I t is almost impossible to get a student from the pub “
lic schools to make sketches in
w hich
the unim p ortan t
FREE—H AI VD
44
detail w ith
,
w hich
h eavy black lines
.
,
is
This
.
WING
the e ffect is not brought out
of
is no part
DRA
not surprising
,
he
for
sees this detail and it is near him there fore according to ,
his instruction it must be stro ngly accented In outline as in other mediums ,
can to express
we
w hat
why ,
advance rapidly and
N
,
outline
make dra w ings
of
,
wh a t
as its form
w ell
th e
of
There
.
once started rightly h e
N ature
be true and artistic
o r a te c a n
simply
if
w ill
they are representations w ill
The e ffect
.
the student should not be taught to
observe the e ffect and
e ffe ct
should do th e best
we
is be fore us
subj ect sh ould be considered as is no reason
,
.
t e give n ,
,
since
h ave variety
of
.
other than to study and represent fa r
is seen as
w ill
w hich ,
w ill
as possible as it appears ,
In
any light and shade it i s im possible to al w ays ac c ent th e lines j ust as they appear For instan c e ,
w ithout
.
,
.
of
som e edges to be
might
w holly
be
imp r es s ion
,
the obj ect m ay be so lost in th e shade as invisible but ,
w ithout
the m the dra w ing
incomplete and unsatis factory
a c t s f
f lin e can be o mitted even o
ti re
m a s t be
if
c onvey e d
No
.
fe w
of
accent the lines
,
as
w ill
im p ortant
,
th e ge ometric solids
lines in nature it
c or r ec t
no t seen but other w ise th e
lines should be represented as they appear In dra w ings
A
.
,
.
w here
th ere are
sometimes be impossible to
th ey appear
important ones may b e invisibl e
,
,
to represent them as th ey appear
for or
-
some
of
the
m ost
seen so faintly t h at
w ould
make th e draw
O U TLINE ing give a false impression
DRA WING
.
Fr equently w hen the obj ects
.
are strongly light ed their outlines on the light side
of t he
group i n ters ect one anoth er
of
mass is composed Of parts
that the outli n e
so
,
of
t h ose
This outli n e is very prominent
,
of
w hile
We must accent
as
of
ligh t
.
cannot accent as
we
w e feel
several obj ects
.
th e edges inside
the outli n e are almost lost in the mass evident that in this case
the
the group and
we
,
ing as the li n es are seen is unsatis factory
we
,
is
se e
.
accent
w hen
,
It
must
u se
our j udgme n t and make the accenting express the facts in a satis factory manner
.
When dra w ing from furniture or from any subj ect hav ing many lines the e ffect ,
w hen
w ill
generally be satis factory
the lines are accented as they
are s e e n
.
H ere
there are s o many lines and so many changes in directi on that the parts
w hich
a re
not se en
w ill
and the student can represent more nearly But it must be unders t ood that it is feeli n g for w hich
At
no rule can be given
first most students
di fference in the
w ay
in
w ill
be
missed
w hat
he sees
rarely
w holly
a matter
,
.
of
.
have di ffi culty in seeing any
w hich
the various edges appear
.
This is due to the fact that but a single point can be clearly seen at over the '
parts
.
an
y
w hole of
one tim e
.
The eye gla n ces rapidly
an obj ect care fully observing all
We are unconscious
,
of
this
m otio n
.
All
parts
it s of
the o bject are seen distinctly and the variety of e ffect is All the parts w ill conti nue to give the n ot realized ,
.
FREE—H AN D
46 of
im pression
DRA
WIN G
equal strength until the
a
.
bility to see the
w hole of
an obj ect at once has been acquired as explained
on page
18
,
I t is not possible other wise to se e simply
.
to realiz e e ffects and masses
,
and
the student must
tise until he can thus see be fore he thinks any m edium ar a i e t v p
,
o all
f
r
strength
Although no
of
rule
of
d eman d equally a study detail for
,
ac r p
success in
of
th e co m
.
accen t ing can be given the e ffect ,
is found to con form to th e princip l e th at
a ny
cl z zo/zi
de t a il
‘
c om es
is a
in
po r ta n t
u ni m
t/ze m a ss of
ei ttze r
.
re ti r a o ti h t o t h t f g
th e
s tra de
Thus an edge defining a light sur face
gainst another sur face also light is not
p rominent
,
and
an edge separating a sur face in th e shade fro m anoth er shade sur face is se en faintly are those
w hich
.
The impor t an t
come bet we en the ligh t and
fea t ure s
the
shade
.
FREE
48
-
HAND
D RA
WING
.
of
n early as possible the actual appearance of
We obtain the dim e n sions w hich
fi nd that the sur face
we
,
of
appearance is that ,
draw j ust sketch
a sphere
w hat w e
w hich
se e ,
impression and
see
gives th e
cannot b e d evel ca nn ot al w ays '
and it is impossible to m ake a
shall include an extended ran ge
of '
sp a c e
w hich
w hich
why w e
,
and give th e exact a p pearance T he
,
w hich
This th en is the reason
.
w hich w e
Carryi ng out this principle and extending
.
the subj ect op ed
.
this appearance on a plane
is p erpendicular to the dire ction in
th e obj e ct
everything
the
visio n
,
2 pages ( 9 9 can be included in a mod el ,
may be represented on a plane
d raw m g,
w ithout
notice
abl e distortion should not include an angle at the eye ,
over t w enty eight degrees
If
-
the questions
of
,
each part and a correct
of
w hole
w h ic h
of
.
the curvature
this is much exce ed ed
of
horizontal and vertical di s t ances
of
parallel lines w ill
for
arise but a
s
,
both most
draw ings require a larger angle the question must be con si d e re d
.
The mind kno w ing lines to be straight ,
,
w ill
hesitate to
accept their representation by curved lines or kno w ing ,
the m to be vertical on s e nt a t i
,
w ill
not readily accept their
by incline d lines
the impression
of
N ature
,
.
as
Th e draw ing should give fa r
as possible even
the eye is not at the proper distance of
,
.
,
.
w hen
The impression
vertical line s is given by vertical lines and
lines by straight lines
r e p re
of
straight
For this reaso n it seems be st ,
IN TERIOR S
that the student should represent as possible
i n accordance
w hat
w ith
'
49
.
he sees as nearly ,
the perspect ive prin
tha t stra ight line s shall be represented by straight
ci
l e p
lines
,
but
WORK
AND GENERAL
Th is
.
w h ich
w ill
cause him to represent horizontal li n es
extend on both sides by parallel horizontal lines
and to substitute angles
w ith
the curved lines foun d in obj ects at
p icture
the
vanishi n g points
for
,
Th is
-
.
,
little as sho w n on plate ,
straight lines extending to w ill 28
t wo
change th e draw ing very
.
When the subj ect is extended or comes very near th e draughts ma
n,
causi g visual a gles
of
n
n
fro m forty fi v e -
to
one hundred degre es either horizo n tally or vertically it ,
is evident that the di fference bet w een the appearance and any dra w i n g made on one plane and some parts fro m
w ill
be very marked
,
the dra wing must be quite di fferent
of
the actual visual a n gle s formed in the eye
This
.
may prevent th e draw ing fro m bei n g truth fully blocked in as a
w hole
at first
.
in
It can ho w ever and m u st ,
,
beginning be placed as a
w hole
approximately
the The
.
central part or th e most important portion can then be draw n as it appears
.
The proportions
of
the outer parts
can be re ferred to the central and the distortion ,
is inevitable some w here d uc e d of
,
w hich
an exte n ded s ubj ect be
in
,
re
to the smallest degre e by making the perspective
these outer and less importan t parts agree
w ith
that
of
the ce n tral a rid importa n t mass The di fferent parts o f a n e x t e n d e d s u bj ect can n ot be .
e
— FR EE HAND DRA
50
WING
.
measured or compared by the ordinary use its distance from the eye cha n ges
for
tion
If
.
w ith
of
th e pencil
,
every n e w posi
it is desired to compare the visual proportions
,
the pen c il must be held at one dista n ce from t he eye by means
of
a thread attached to it and held at the bro w by
th e le ft ha n d
.
Wh en it becomes neces sary to make a p erspective draw ing throughout as som etimes h app ens ,
w alls of
w hen
thre e
of
a room are to be sh o w n the pro portions ,
this
dra wing may be very exactly fou n d by holdi n g th e pencil in a plane parallel t o the end of the room This draw ing should be avoided w h en possible on .
account w ill
its outer parts
to avoid representing on both sides
of
it '
a
the spectator
.
is to be represented it is better to dra w from
of
the room than from the centre as the line s
,
,
vanish and the distortion be less marked
walls
,
sid e
on e
of
an d
w all
one end w ill
w ell
w hich e xtends fa r
one
of
the serious distortion
also b e
room If
of
are repres ented the lin es ,
of
When
.
two
both must va n ish
.
When three are s ho w n th e middle one must have no van ,
ish in g .
Figure
9
sh ow s that
if
its lines va n ish the ,
both vanishing p Oin t s
of
the le ft
of
the dra w ing and thus ve ry unpleasantly d is torted
w all w ill
be outside
of
w hol e
,
d r a w ing s h ou l d
A very slight
e
n e v r ex te n d
é ey on d ttt e wa n ts /Z ing
.
p oin ts
distance may be represented to the le ft
the le ft poi n t in Fig
.
9,
w hen
A
of
the draw ing r epresents a
Court or
any
interior
w here
ortion p
unimportan t
of
WORK
GENERAL
I I VT E R I O R S A I VD
the part at the le ft is a ver y
the draw ing but it is
D istortion taken
with
such
that in Fig
as
of w
a le n s
e erally n g
,
sa fer to end the drawing at the vanishi n g point ‘
51
.
.
is seen in ph otograph s
9,
ide angle
.
and
,
photographs the ,
most common p erspective dra wi n gs exert a strong ,
in flu
e n ce to p erpetuate the serious distortions in the dra wings of
an d
our illustrators
artists
.
In draw ings of street scenes etc the lines are long .
,
,
an d
broken and their appare n t curvature may not be noticed ,
if
each part is draw n as it appears
does not kno w the conditions in
N at ur e H e n ce there I
.
bet w een the appeara n ce
is of
edge co n cer n ing the fact s
.
such subj ects one
In
.
The li n es
m ay
be curved
not the instan t co n tradic t ion
of
the k n owl
and
the dr aw ing
the things represented
.
If
the artist chooses sometimes to represent straight li n es by curved lines he ,
of
h as
N ature
as authority and the example
noted predecessors and no ,
on e
his dra w i n g is not good o r that it plane perspective
w ould w ish w ould
be improved by
.
In interiors and in street scenes there is ,
questio n
of
b u t also that
to say that
n ot
o nly the
horizontal foreshortening to be considered of
vertical
foreshortening
this foreshorte n ing shall be g iven
18
.
Whether or
a question
which
,
no
can
be a n s w ered o nly as it arises and decided according to ,
the co n ditions
of t h e
I t is a question
of
subj ect and the aim
of
the less importan t giving
the
d raw m g
w ay
.
to the
FREE
52
HAND
-
more importan t and is ,
dent
,
wh o
for
DRA
a
f
o
.
the artis t rather than the
stu
should until h e has attai n ed by long practice ,
ability to j udge proportions c o rrectly never be p ermitted ,
to draw other than those he sees
.
The unnumbered plates follo w ing are from students
N atu re
dra w ings from draw i n g in
.
Such
w ork
public schools
the
obse rve and to do
w hat
advance in this direction
Fine
Arts
,
f
l i s p p , u
taught to
th ey se e may make a great ,
of
th e perspective classes
D raw ing and Painting of at the N ormal A t School
of
and
of
.
the b e ginning and th e end s w hich i
w hose
,
The sketches are by students at the School
should be the aim
’
r
of
.
th e
M useum
of
The y illustrate
a course in model draw ing
the only pe rspective n ece ss ary to the artist
.
,
CHAPT E R
D RAWING I N T HE
value
.
PUBLI C
T HE
of a c ou rse
iv
in drawing
S C HOO LS w hen
.
the subj ect is
properly presented can hardly be overestimated but it must h e con fessed that much of the instruction given is ,
it s
such that
At
benefit is a matter
the beginni n g
be taught to l i h d s e , p
se e
of
correctly
When this has been
.
and he is able to represent truly
w hat is
be fore ,
,
an d
his personality may be
But as the first point to b e gained is ability truly it follo w s that w e should from the very start
cultivated
.
,
demand truth truth ,
and truth
of
color
In begi nning I ,
of
outline truth ,
w ish
the pupils can observe until they
‘
c an
of
for
d raw from
any value u n til
of
themselves
n i ;
obj ects instead
have not materials
models and
,
to say that draw in gin the public
This is impossible in many places
t eachers
light and shad e
.
schools can never acco mplish results
.
a c c om
he thinks he sees it then
as
he is in a position to advance
ings
.
,
,
se e
do ubt
his art education the p upil S hould
him as it appears and not
to
of
.
other
of
n ow
from
w ords ,
draw
because the
The schools must have
all necessary materials or the ,
.
w ork w ill
53
be
FREE
54
-
simply the copying
of
HAND DRA WI I VG dra w ings in the books or ,
of
are not used th e copying ,
board
w ell
enough in
grades should have the purpose
for
theory dra w ings
these the
011
In the elementary grades the instruction can be
.
given
if
th e
l
o v i d r e p
'
z
d for ‘
D rawing
.
but the advanced
c a ssroom ,
_
the m a room arranged
cannot be taught
w ithout
materials any more than manual training can be t aught w ithout
tools
,
and
a part
of
the necessary materials can
be used in one no more than in the other
N o committe e w ould w ork of
the
w ood ,
.
expect a boy to use a gouge to do
a chisel or to learn to use his tools ,
o r that a class should ge t along
w ith
w ithout
for
tools
one
st udent ; yet th e committee or superintendent o ften ex c e t s p
dra w ing to be taught
t e rial s for
part
of
the class
w ithou t
mate rials or ,
.
ma
.
In most public schools attention is ing
w ith
n ow
given to draw
In cities this instruction is g enerally in charge
special teacher but this special teacher ,
than to direct the regular teachers l ara i e v t p
y
n e w,
.
d raw m g,
and
fe w
a
do little more
The subj ect
these teachers have had
lar instruction in
c an
of
p erhaps
is
com
no regu
k i ng w or k o
have had the
li
r th e subj ect necessary to interest the m in th e to cause them to obtain the knowl edge t he y a re expected
for
,
e
to impart and ,
w ith
all the stress
of w
o rk upon them it ,
is
‘
surprising that
the y
h ave
ac c omplishe d as much as has
been d one in some pl a ce s
.
In many c ases the spec ial
teachers have had but little trainin g
,
an
d
frequently
thi s
FREE
56
-
I I AN D
DRA WING
ing should have an hour by itsel f
.
C utting
.
paper
w hit
,
tling paper knives se wing p en w ipers etc can neve r give -
-
,
.
,
the least abili ty in draw ing
neither can this
'
many carry it on give any kno w ledge
of w
,
ings
Th e making
.
of
obj ects can be
and s h ould naturally go
w ith
,
as
orking draw
great assistance
of
of w
the study
w ork ,
,
orking draw
ings but th e Obj ects shou l d be made fro m the dra w ings ,
must S ho w all the construction
w hich
I do not s
chool
s
ubj ect
a s!
se e
w ithout of
h ow
th e ma k ing
obj ects can be done in
,
sp ecial time b eing given to it and the ,
d raw m g
proper not su ffer ; and it se ems that
the result in many places
f avor
of
.
of
the present agitation in
m anual training th is su bj ect take s the place
of
,
d ra w in g .
M any
dra w ing teachers are unconsciously
p lacing
e ffecting th is by
of
in their course paper cutting -
'
and th e m aking
of
obj e cts that have
on n o c onn e c t i
either th e fre e hand or th e instrumental draw ing -
In many cities draw ing books are used -
contain example s
of
,
of w
of
w hich
models and com ,
are given as illustrations In many places most
of
possible app earances if not all of the w ork in obj ect .
of
draw ing is thus copyi n g and so little ,
from the obj ects is done that ,
found
w ith
actual draw ing
the obj ects be fore
copying th e
and the draw ings s tudent in front ,
These books
hich are to be copied and others
”
the m students are
.
historic ornament and design
are to be copied ,and also draw ings mon obj ects so me
.
w ith
of
of
the
r ow
are
d r aw m g
a
w hole
.
D RA
alike
WING IN THE
;
where
.
.
We have even kno w n
of
case s
the pupil has turned to som e text book as a geom -
,
in
w hich
h e has tried to find the appearance
obj ect be fore him from
S CHO OL S
or copying the draw ing made upon the board to
illustrate the principles e t ry,
PUBLI C
.
It is easier but such
for t h e
w ork
is
of
w hic h
Such are the results
copying draw ings
of
th e
come
.
teacher to allo w the pupil to copy no value and the copi es even ,
,
,
if
neatly done d eserve only censure Th e fe w teachers w h o have had the courage to dispense w ith copies deserve .
,
for
praise
sho w ing that dra w ing can be taught from the
obj ects and their example should result in a general ,
change from books to
N ature
In many places it is pos
.
sible that nothing could be done iii draw ingwer e it not for t h e
b ut
books
th e
.
Rightly used they ,
m ay
of
be
assistance
,
pictorial dra w i n g s ho ul d b e by its el f upo n b la n k
p ag es and e ach dra w ing S ho uld b e m ade f ro m th e obj ect The change from copying to draw ing fro m the ob ie c t .
,
w ill
require hard
both pupil and teacher and at first th e draw in gs w ill be very unsatis factory in t he m selves
w ork from
but a fter a short time
,
,
w hen
the pupils have been
started rightly in the lo w er grades they ,
and
w ith
N ature
,
greater freedom and
w hich
,
w ill
w ill
dra w readily
be able to draw
they ne v er are under the present systems
that allo w the m to copy from a book or th e board We have advised that art students dra w an d
frorri
in light and shade at once
.
w ith
C harcoal is
.
charcoal
not suited
FR EE
58
HAND DRA WING
-
to public school w here
At
w or
k
,
at least not in the lo w er grades of
it becomes a question t he
present it is
ai m of
k no wledge
ive a thorough g
outline in
of
the facts is
to
w h o is
course
of
represent the m
p encil
,
.
most courses in drawing to
t he
of
actual
attem p ting t o represent its appearance of
.
form
be fore
The kno w ledge
.
some assistance to the person
A
.
t h e ob j e c t
glance at
and it
is recognized and the mind supplies the in formati on ,
it migh t ta k e th e eye some tim e to discover
w hich
But
.
this kno w ledge is more a p t to do harm tha n good the pupil uses i t inste ad a d vi Sr
should facts ,
.
w ith
of
the facts
of
p ractice of
in representi ngthe
the appearance begin
.
p er fectly
Th e facts can be taught b ut
,
,
or at least that the study
the study
Fo r this reason I
.
by most teachers be postpone d until
th e pupils have had so me facts ,
his eyes
,
that the continue d and th orough study
follo w ed
n ow
of
for
in a very short time
,
to attain pe r fection in their representation is a prob
le m requiring much more study and l ong continued e ffort , and
for
this reason it should be given earlier and more
serious attention Th e study
begin
.
ap p earances in th e lo w er grades may
of
‘
plane figure s cut from cardboard or p aper as
w ith
,
l
the square circle triangle ,
,
,
h e xagon ,
etc
.
Th ese may be
placed horizontal up on the desk and their appearances studied in g,
.
This involves the use
of
th e p encil in
m e a su r
and it must also b e held horizontal to assist th e
p up il
WING IN THE
D RA
f o
to see the angles
PUBLIC
the lines
S CHO OL S
59
.
In beginning this
.
,
w ork
may be made easy by placing the card in the centre the de sk
w hen
"
,
comparison
of
the lines
the des k serve
for
of
horizontal
.
The cards may b e
of
such dimensions that the draw '
the
ings can be made of
ment
e nd of
height
w ill
”
size
of t h e c ard s
T he
~
.
measure
th en be obtained by placing the lo w er
th e pencil at the nearest point or side
of
th e card
and the thumb nail to cover the farther angle or edge -
the card
This gives the exact height
.
u s e of
It is th ought that this
p roportions of
w ill
of
th e draw ing
.
th e p encil in determining
be readily understood
The pencil
.
course be about vertic al but to be exact it
s
hould
s
hould tip back slightly Wh en a card h as it s n e are s t edge
,
.
l in e
th i s edg e
,
Wh en th e
n
w ill
be is
e are s t edge
p e n cil horizont al
th e
f ro m
edge
,
e nd
it s
the edge
and
li n e
.
the
de s k
its
p arallel to t h e de s k li n e
n ot
e nd
f ollo w s
again s t
th e
!
P l ace th e n
e arer end
me as ure th e di s ta n ce upo n th e pe n cil
to a point
just
u n der th e f arther en d
of
th e li n e
Th i s
w ay
of
w ill
set
,
off
me as uri n g
re s ults b ut b e fore me as uri n g
an
y
th e w ill
f arther
,
w ill
,
of
e n d of
give very good
except th e
n
e a re s t
edge th e dra w i n g S ho u l d b e m ade b y th e eye alo n e It
.
Th e n a vertical l i n e th i s dis tan ce f ro m the
.
n earer en d the
,
w ith
arall el t o p
repre s ente d it s re al le n gth
its len gth m ay b e determine d a s of
of
,
be
w ell
to
.
dra w th e card s at di ffere n t l evel s
Thi s m ay b e do n e b y pl aci n g the m o n b oxe s or books
.
.
FR EE
60
-
HAND DRA WING
.
By holding them horizontal and on th e level
of
the eye
,
see that they all appear h orizontal lines
,
‘
t he
pupil
w ill
and that their forms are se en only or belo w this level
w hen
they are above
.
I should not attempt to teach much perspective the ory U ntil
the
upils are older practice alone is p ,
w hat
.
they
need .
They can se e that th e apparent heights of the figure s d ecre as e as th e card s a re b ro ugh t to w ard t h e level of th e eye at w hich all appear lines They can .
,
also discover that parallel retreating edges ap pear to converge This may be seen by placing t wo pencils .
together and then s eparating the m until each app ears ,
to coincid e
w ith
an edge
Th e pencils must
.
be held at righ t angles to the direction in ‘
obj ect is seen
of
course
w hich
the
.
The cards may b e held in a vertical position by a s m all of w
block
ood to ,
w hich
th ey may be fastened by a tack
In this position the height
w ill
but the propo r tions
b e obtained as be fore
positions
of
w ill
be the great e st dimension
the cards be ing changed
a short time th e pupils
w ill
for
,
The
each lesson in ,
learn to use their eye s and
draw th e cards fairl y w ell Bo th horizontal and vertical posi t ions
w ill
.
be stu died in card
.
.
so
z on t al
t he
of
the cards may
sam e lesson by folding a rec t angul a r
tha t a right angle is formed one part being hori ,
and th e other vertical and held at right angl es
being tacked to a small
,
p iece
m ay be s t udied in th e sam e
w ay
of w .
ood
.
bv
O ther form s
DR A
N WING “ I
Whe n able to dra w
B L PU
1n
“
t h e c ard s fro m s
61
.
the position directly at th e right
.
,
.
To do this eac h pupil may draw from a card ,
.
placed n ear the corner sid e
s ex / oO LS
d ra w t h e m w h e n
in front the next step is to or le ft
IC
his desk or on the desk at his
of
This is much more di fficult th an to draw from t h e
.
.
den e y
w ill
be to t hink
ing horizontal For this
,
w ork
h orizontal ,
desk
ow n
this case it appears to va n ish
and at ri g ht a ngles .
AS
to
the d ire ction in
t his position
of
of
,
po n e th e
w hich
the card involves
besid e this di fficult test the com parison on the
.
the pupil mu st learn to hold the pencil
h e sees the card w idth
The ten
.
the li n e of the desk as appear
of
w hen in
h is
of
c ard placed on the centre
,
height and
encil it may be f ound n ecessary to post p ,
w ork
until the pupil has had practice
ing from obj ects placed in front to adv ance the
w ork
of
him
It
.
as rapidly as possible
.
should have little trouble in sho w ing that the essary and the b e ginning
of
properly presented the pupils ,
-
in
w ill
-
draw
be
w ell
The teacher w ork
is nec
pictorial draw ing and ,
w ill
be interested
if
The
.
more the draw ing seems in itsel f a picture and not a dia gram the ,
A from
m ore
interested
simple preparation
w ill
for
th ey be
.
of
the subj ect
model dra wing
th e solid blocks may be given by draw i n g from
planes ,
so
l ac d e p
various prisms
.
as to represent the bas s or ends e
Thus
t wo
represents th e axis
of
the
squares may be fastened by a
tack through their centres to a small cylinder w hich
two
of
the pris m
.
of w
ood
,
The prism thus
FREE
62
-
DRA W N
I G
HAN D
.
repres en t ed may be placed vert ical or hori zo nt al the edges
of
the pupil
w hen
each card are seen this practice
edges are not seen
A better
arrangemen t is a skeleton frame in
tical
fro m
th e
of
the bases
D raw ing
,
w hich
all the
.
edges are re p resented by ne c t
solid in
a
all
hel p
w ill
,
h e draw s from
As
.
w ires ,
obj ec t
th ese obj e cts
,
or in
w hich
w ill b e in
w hich
w hich w ires
ar e sheets
t eresting
th e con
t in
of
and
i
.
r c a p
.
A fter
this
k bes t
w or
o rder seems
th e solids may be s t udied in If
.
w hatever
to
the pupil has learned
u se
his
eyes th ere is little ch oice as to the order and by the ,
,
t ime he is ready
for
the high school he should be able
to dra w th e com mon forms quickly and truth fully not ,
only singly but in group s ,
Th e best and cheapest
.
w ay
to teach
m od el
draw ing is
by the use of a S late of gl ass on w h ich the d raw m g 15 1 m ade w ith a p e n cil prep are d for th e p urpo s e an d era s ed ,
when
fin i sh e d
dra w i n g s are m ade
If
.
in
th i s
w a y,
th ey
can be instan tly tested by holding the slate in front the obj ect
of
that th e lines upon th e slate app ear to
so
-
cover the edges
of
the obj ect the dra w ing being ,
of
such
size that th e S late may be h eld in the hand to apply the test
.
If
the
ob i c t s e
are large they S hould be p l aced ,
enough aw ay to have the draw ing upon the slate come th e right size
.
The easi est
w ay
draw fro m small obj ects on their 1
l
T h e C ros s Pe n c i,
so
far of
is to have the pupils des ks
ow n
ld b y Gi
na
When the
.
Co
.
FREE
64
-
HAN D
corrected bu t I thin k the glass
w ill
,
especially ‘
wh en
of
be
.
very grea t valu e
p repared
teachers are not thoroughly
It is thought that this
esting to th e
WIN G
DRA
of
if
it is
,
apply themselves to th e
w or
k
,
fou nd
that they do not
thinking that a sl ate i s too
child ish it may b e used at first as in th e later ,
connection
w ith
u s e of
the
.
the slate will prove inter
Use
u p ils but p
,
pape r
.
w ork ,
in
Th e draw ing m ay be
.
mad e by eye alone first on the sla t e or on the pap er as ,
is pre ferred
In
.
,
w hatever w ay
th e
w ork
is carried
the use o f the slate gives an eas y and sure test .
1rac y of ac c i
the proportions and ,
for
of t h e
p urpose
this
slate m ay be used to great advantage t hrough the of a ll
th e grades and th e high school
An i m prove ment
at each side
of w
on,
t he
wo rk
.
on the simple frame is the attachmen t
ires fitting in the frame so as to be drawn
out to any len gth the desk having t wo holes made to receive the w ires By means of these w ires th e sl at e ,
.
w ith
the draw ing may be held
al lo wing t h e exac t co mparison obj ect
Of
.
all the
th e
course the eye must be held in one place
for
of
p ractice
in drawing and ,
of
steady, thus w ith
this c om p arison By means
’
p er fectly
the dra wing
.
this slate any teacher can quic k ly obtain ,
necessary to ma k e up if
the slate
is
for
lac k
of
t raining
pro p erly used the draw ing ,
alw ays being made by eye be fore holding the glass slate in front wh o
of
the obj ect it ,
will
wish to learn to draw
.
be
of
grea t assistanc e
to
all
D R A WING IN
THE
PUBLIC
S CHOOL S
65
.
'
Wh en the p upil c an draw t h e simple obj ects t h ere is no fe as on w h y t he light and shade may not be r epres ented ,
by pencil tints put
on
with the s ide
Of
the pencil
advanced grades charcoal can s o metime s b e The high school ing and ,
models
.
c orn e rs of
A g rad uate
r oo m ,
of
.
wi t h m Or e
s
of
the less impor t ant
may impro v e
M uch
w ork
w ill
that
may give
each teacher
1t l ay oi
a nd
c an
zines and papers rep roduction s
,
that this
w ay
l ed a c p
w here
good
.
With
procure from maga
,
of
of
illustrators
an d
p e n cil p en ,
and shaded drawings by the best a rtists a re
as
necessary
if
,
fa r
importa nce
b e obtained from examples
draw ings by advanced students
d u c t ions
of
.
h elp
ve ry small
and
,
truth so
t h at t h e
I t is hop ed
.
this s ubj ect may be r ealized
ome
di ffic u lt groups
w ith
,
.
of
.
this school should certainly have
the ability to sk etch indoors and out roportion is concerned p
sed
u
sh ould inclu de furniture dra w
w ork
the
in the
they can
If
.
seen
be
.
ink
,
these repro al l
the time
,
interest th e pupi l s and g ive th e m j an id e a of expression such as they can never obtain fro m the mecha n
they
w ill
ical cuts t
,
.
of
most draw ing books -
.
C are
should be taken
osecure some draw ings S imple in character
serve to interest the pupil in
h is
,
w hich
elementary
own
These draw i n gs should not be copied
,
for if
may
w ork
.
copying is
begu n it is almost certain to be done to excess and as ,
,
has been said the elementary w ork ,
of
cannot properly consider technique
.
the public schools It is hop ed that
FREE
66
-
soon th e t e ache rs etc
.
HA ND DR A WIN G
who
are
talking
n ow
.
a
bout m e t hod s
,
may give their attention to the simple study
,
N ature
r th ful draw ings
of t u
and the making
,
Some have atte mpted to state th eories esthe tics
a
taste
,
w hich
of
w hich
schools and
,
wh o
.
p resent
are at the
p ractical ,
s olution
wh o
in one
of
p ersp ective
fro m
of
w or
k
.
of
of
the be auti fu l
N ature
the p eo p le w ill
i nv olv e d
.
of
good examples The
t i me
be much b e t t e r in t h e
s
.
of
Salem
,
,
the bes t ar t
of
cannot fail to cul t ivate the tast e and raise standard
”
by good artists pho t o
,
The influence
many
th e obj ect
the schools
graphs casts and oth er r eproductions ,
of
p rin
this proble m has bee n
p ictures
has j ust arranged
,
of
time making the fear ful
productions labelled
given by an artist
M ass
color and
have be en drilled into the students
w o nder ful
Th e mo st
of
this theory may b e illustrated by
re ferring to the num e rous state ments l ci e s p
.
the student may study to improve his
The value
.
of
this natur e
t he
a
rtis t ic
giv e n t o theories
of
s t udy
of
'
in t h e
sp e n t
g
im p le st drawing
.
C
HAPTE R T EST S
P IN
a ragr a p
h
s
m a rk e d
(T ) a re for .
V
‘
.
.
t h e u s e of t e a c
e rs on
l
y
.
beginning the student should understand that his ,
dra wings are
of
no valu e in themselves but are of use only ,
as they tra in the eye to see correctly taught or rather the ,
image
of
mind
The eye can be
.
can be made to accept the
the eye only by depending upon it and ,
él e to d r a w
ttze
,
zns by m e a s u r i ng a n d te s ting l ze w i ll éeg
s t u de n t d
h
oth e r w i se
.
This is undesirable
n e ve r
ée
for m any
reasons the most important b eing that no me asurem ents ,
can be applied c e p ti on ,
w hich w ill
take the place
of
or begin to equal the trained eye
correct per It is thus
.
important that the student from the beginning depend ,
,
entirely
for
his first dra w ing upon his eye s
The best possible training use
of
w ishes
all young or old
the glass explained on page ,
62
.
Any
,
d raw m g w it h t h especial
by eye alone his ,
tions
one
the wh o
1m
n s of e ssi o r p ‘
pencil upon this slate
the fo rm and then testing ,
edraw ing by ho ldi ng it in front of the obj ec t Th e
is
to train his eyes to correct s eeing can do so most
quickly by th
for
.
re a diest
of
w ay of
.
determining the apparent propor
an obj e ct is by th e
u s e of
a pencil or any straight 67
,
FREE—H A ND
68
D RA
WING
.
slender rod held at arm s length an d to a p pear to cover ’
,
th e lines to be compared
Thus the
.
may be held so as to appear to obj ect
w hose
,
of
the pe n c il
over th e top
c
an
of
apparent height may be measured on th e
pencil by m eans
of
the thumb nail p l aced -
to cover the bottom turned into a
e nd
of
th e obj ect
h orl z on t al
If
.
as to appear
so
th e pencil is
n ow
position th e app arent height ,
th e obj ect m ay b e compared
w ith
its appare nt
w idth
.
of i
If
th e m e asuremen t cove ring the h eight is one hal f th e dis -
tance on t he p enc il w hich covers th e appears t w ice as w ide as high I n this .
proportions It
is
of
mine simply th e proportion be
trans ferred to t he p aper
di fferent positions tak en and
if
,
of
of
w hen
,
for
th e draw ing and not its
curacy pencil fe c t l y
.
as
t he
pencil must
n ot
the eye and hand are in
the various m easure ments are
be incorrect in proportion
The slightest change in distance w hen
.
they are trans ferred to the p aper th e dra w
ing re su l t ing w ill
eye
the apparent
the pencil shall d eter
The measurements on
.
w ay
the group
any obj ect or group may be found
important th at t h is use
actual size
w idth ,
of
proporti ons are compared The only far from
w ay
th e w ill
.
p encil
from
the
occasion inac
to be at all correct is to hold the
the eye as p ossible the arm being per ,
strai ght and th e pencil being turned by t w isting the
ntire arm e
.
pencil m ust be at right angles to the direct ion in N early all students think the w hich the obj ect is s een .
T he
,
.
TE S TS
69
pe ncil should be parallel to the side bench up on
w hich
the obj ect rests
w holly false , for t he
of n o
to its surrou n di ngs is be consid ered is desired
w hen
If
.
must look at it
of
position
w hen
,
the obj ect
l
w ith
,
an
re ference the obj ect
a cube is to be represented the st u dent ,
a nd
,
the plane
gives its real appear
w hich
w hich
,
When thus held its
.
,
distance from the eye
A good
,
is
d m u st not
of
ppearance
a
measuri n g the pencil must al w ays
this position
w hich
,
This ho w ever
.
ance is perpendicular to the direction in and
the room or the
consequence
ac tua
the
of
e nds
he looks
be
held in
are the same
.
plan is to find some position in the fi ngers in
the pencil is p erpendicular to
w hen
t he
arm
,
w hich
outstr etched bri ngs the p encil into pract icall y the correct position Fig 1 0 ,
,
T (
.
)
I
n
tne
p
ma y fi n d
some
angles to it is hel d
so
.
.
o w hen
u t /r e s e /zo
the subj ect is beg u n
that a pin pushed into the p e n cil at right
w ill
help to place the pencil
that only the head
of
th e
.
i n p
cil is p e rp en dicular to the direction in looks of
.
so ft
A better device may be wire (a hair pin ) about -
sho wn in Fig
.
12
.
O ne
angles to the n eedle
,
end
an d
of
made by
When the p e n cil is se e n th e
re c t l y
.
e nd
The
e n p
,
w hich
the pupil
b e n d ing a
piece
a large k n itti ng n eedle a s th e w ire proj ects at ri ght -
the other exte n ds back
proj ects a short distance perpendic u lar to The lo n ger
.
the
a nd
fi rst end
.
serves as a sight to place the needle cor
w ire
should press the needle enough to
70
FREE
keep in pl ac e
u
-
HA ND DRA WING
pon it
.
I t may be moved b y t he fi nge r
.
or thumb, and th e measurement taken by sighting over th e short end
This slide
.
w ill
assist greatly
and
,
as it is
important that measurements should be correct it is ,
st ud e nt
advised that every
p roperly slide
It
.
p rovided
be w ill
.
pared third
w ho
also as sist
w ith of -
the larger
meas urement is not an
the other
If
.
Se e p age
.
2
3 .
the former is one hal f or one ,
,
of
or four ninths -
taken in such a
w ay
if
the first
th e second the proportion
,
be
c om
-
the latter this is easily determined but fi ft h s
il
an d
this measuring needle
no t so easy to determine and
c an
c
-
w hen one
of
p en
cannot hold the
The s m aller me asurement should al w ays be )
is three is
u
w ith
easily determined part T (
'
,
if
the
t wo
measure ments
that th ey may be c om p ared
at leisure the p roportion may be more surely determin ed ,
.
This may b e done by taking the smaller by the sliding -
w ire
and the larger by the thumb Th e b e s t an d s i m p le s t me a s uri ng ro d .
-
e
n e d p e n c il
ray s s
w he n
ur fac e
.
,
it
w h ich w il l b e
is
so
S t ud e n t s
m e a s ur e m e n
ts
th at
s h ou
ld
an u n s h arp
perpendicul ar t o
t h e v i s ual
~
n e ith er en d u se
su c h
is
vi s ible
p e ncil
a
f or
of
I
the
fro m
needle or pencil
the
proportions are compared must be the same
distance is so apt to made several times chance
of
as
a
al l
.
The distance w hen
h el d
is
v
.
e ye
Th e
ary that u n less each comparison is
w ith
the same result th ere is little ,
the m easure ments being correct
to think tha t tests no t care fully ta k en
are
.
I t is useless
w orth t h e
tim e
F
R EE
72
When possible
HAND D I
-
WING
.
comparisons should be made
al l
,
/I
G
by
s w in ging the pencil from a vertical into a horizontal posi tion by motion ,
of
the
arm from th e shoulder
w hole
avoiding change in distance by re volving of
about one
e nd
height and
w idth of
of
measuri ng th e
h and
the first measurem ent
along the top and d ropping th e
w idth w ith
th e height or measuri ng ,
make the comparison by tak ing the s w m gm g
th e top and ,
or by taki n g the
w idth
T (
.
a lo n g
,
w ith
.
1
of
distance may
a degree
along
M easuri ng in
3
.
assist greatly to correct results
A short )
w idth
th e
at the botto m and s w ingi n g the ,
w a y w ill
w ith
the p encil d o w n about the thumb
encil up about the thumb as in Fig p this
th e
,
the height and then li fting the hand to compare w idth ,
if
a table are to be compared inste a d
w idth
to compare th e
,
p encil
the
Thu s
.
an d
of
.
course be compare d
w ith
accuracy varying w ith the stud en t
but such measurements are not recommended and are un
necessary
Another
as other tests
,
w ill
give
bet ter results
.
by which distances may be compared i s by marking upon the edge o f a ruler o r piece of cardboard
w ith
w ay
‘
a p encil
leisure
.
T he
dista n ces
m ay
be co mpared at ‘
.
The above are the dire ct tests
for
proportion and
care fully take n should give the correct mass ,
ing,
b ut
f or
s
h or t di s t a n ce s
oth e r te s t s are b etter
an
d
,
of
di rectio n s
if
the dra w of
l ine s
.
Th e l in e s w ith w h ich it
is
n
atural to comp are directio n s
TE STS
73
.
are
vertical and horizontal lines
A
.
horizontal line
w hose
e nds are equi distant from the eye appears hori
z ont a l
and
c al
-
is
represe n ted by a horizontal line is
line appears vertical and
verti
A
.
al w ays represented by
a
ve rtical li n e I f a ruler is held h orizontal w ith its end s e qually dis tan t from th e e y e th e appea ra n ce of it s edg e .
,
,
I
S repre s ented b y a hori z o n tal li n e ,
in
th e draw i n g
By
.
looki ng over the rul er thu s held the apparent direc t ions ‘
,
of
of
lines
the obj ect may be compared
w ith
the horizon
~
tal A t h re ad w ith
li n e
a
w eight
attached serves as a plumb
By holding it in front
.
be compared
w ith
th e vertical
ter th an the ruler or p encil hides none h old
of
of
the obj ect
.
the obj ect its li n es may The thread is o fte n be t
.
for
C are
h or 1zon t a l
the
must al w ays b
the thre ad p erpendicular to the line
p osition is easiest
ne d ob t a i
b y
of
li n e e
the eye
.
T
his ,
t w o feet
ends are then equally distant from
care must be exercised to have the thread hori This positio n can be obtai n ed o n ly by seei n g
hg but
n ot h i
.
.
M ore z on t a l
,
w hose
,
it
directly facing the group
,
the thread
as
taken to
sight
extending the arms equall y and holding about of
~
the th read until it is levelled
de n t may look behind
it
If
.
the
s tu
the student sees the group
be fore th e thread is level its li n es ,
,
w hen
w ill
probably
m ak e t h e
thread seem horizo n tal w he n it is n ot I f there are hori zo n t a l li n e s in th e subj ect w hich are parallel to the pic .
— FREE HAND
74
t ure
no t foreshortened
an d
w ill of
lin es
p lace
ING
D R A IV
they
w ill
the thread correctly
.
appear horizonta l
but
if
the horizontal
the subj ect are not thus situated they
w ill
not
cause the thread to be
ou t
,
app ear horizontal and so
w ill
,
of l e ve L
It may see m that unnecessary s p ace has been given to .
these di re ctions but it has been found almost impossible ,
to mak e many students understand the matter and hold ,
t he
thread co rrectly even a fter repeated explanati ons ,
illustrations
and
found te n
So me
.
a fter months
,
holding th e t h r e ad or
p e ncil
of
study
at an angle
to thirty degrees aw a y from the co rrect
are
,
of
from
i t i a n s n o o d , p '
it is thought that no explanation can be too care ful T he su
so
simple that any student
cceed should have no di ffi c ulty
hat h e
t
is
problem w ill
never learn
over his mistakes ; and
to
'
c
m ost
the
He
.
u nti l
h e is able to
of t he
u se
,
,
.
14,
t h re a d horiz ontal to c over point
d is is
a
.
h aving been dra w n ,
may be tested by the thread as follo w s
t
thread
,
obj ect as the cube Fig
to
may be sure
impo rtan t test it should be correctly applied
Any r
as
d raw ’
w h o w ishes
.
H old
!
the
and note its apparent 5 — — inter se c t io ns w ith the edges r 6 and 6 7 H old the thread vertical in fro n t of p oint 3 an d s e e w h ere it “
,
.
,
t e rse c t s n
1
— H old it in fron t of 6 7
5
,
an d
— H old the t hre ad t o in tersection w ith 2 3 and c om p a re the d ir e ctio n s also 2 and 4 5 .
“
,
,
z on t al
line
.
C ontinu e t h e
e dge
— a y
notice its '
c ove r r
w ith
t o int e rs e c t
and
a hori
6 5 , -
and
TES TS
75
.
— t o intersec t 4 7
C over
'
-
n d a 6 4 , 3, 3
and
t h read appears to his
T of
fi rst m e t h od
and
etc and notice
1,
.
edges betw een
of
lines in the air the ,
fi nd
the use
of
w hich
,
If
.
t h re a d
p
.
re f
can be made to
the obj ect, and its m ore
a line formed by a pencil or rule the obj ect
th e
of
th e edges can be seen much
si d e rab l e of
t he
,
exactly cover the edges that
the
course the simpler is all that is needed
as it gives a fine li n e
w ith
r
.
Wh en the eye is trai n ed
.
But most student s w ill
tion
w here
,
d ra w m g
angles than
w hich is of
e ra b l e ,
any opposite poi n ts as
in t e rs e c t t h e
explained
~
,
.
the thread is simply a more exact metho d
u s e of
d iscovering
first
r
2
'
these tests
,
in t e rs e c
readily than
w hich
w ith
hides con the thread
are applied th ey cannot fail to d iscover every error importance
of
,
.
T (
.
A last )
test may be applied by holding
together at righ t angles to the direction o bj ect is seen
an d
,
be see n in
,
of
an d
lines e ac h
.
p
This way
5
’
If
.
w ith
is
—3
2
great care is take n the ,
re ference to each other may
.
of
measuri n g the apparent an gle betw een of
paper and holdi ng it so that
appears to coincid e
igh t
r s t a g r
o g
—6
by foldi n g a piece
a rt
the
the draw ing tested by continuing these lines
n a e w O ) y
is
in w hich
separati g the m until one covers
these lines
the draw ing T (
pencils
n
and the other covers directions
t wo
w ith
one
of
the
two
lines
.
easie st ap pl ied by the use of a hi nged rule I cannot recomme n d e d ge o f t w o parts '
.
FREE HAND DRA WING
76
-
this test
there are
for
,
.
straight edges to
t wo
right angles to the direction in
w hich
do not kno w
I
Those
.
held at
the student looks
and it is so di fficult to do this that many students w h o have succeeded
be
wh o
an d
,
w ith
them
T (
l ine
.
w ithout
ge t
many mechanical tests than
.
A noth er )
of
testi n g the direction
w ay of
to hold a straight edge upon the line
18
of
can hold
the rules correctly may depend upon their eye s the draw ing better
,
of
a long
the draw
ing and then li ft the board and straight edge into the ,
position app e ars
-
the picture p lane when th e straigh t edge t o coin cide w ith th e li n e of th e ob j ect it its
of
,
directio n in th e dra w i n g i s correc t I h ave d w elt thus care fully upon each .
t est
in
the
hop e that the stude n t may realize their i mportance
,
he
own
w ill
e fforts
,
learn to draw correctly o n ly through his n n ai i g g
w ith
each discovery
never becom e a draughtsman as lo ng a teach er
for
corrections
.
Le t h im
th at a thoro ugh application
far w ill
'
as
of
.
He
c an
h e depends u p o n
c a rry
his dra w i ng so
the tests explained
sho w no error then as it is simply a question ,
exactness to be determined by the eye of
error
of
for
if
,
of
the trained eye
the teach er discovers mistake s so slight t h at the stu
d ent cannot rightly be expecte d to determine th em thes e ,
may be pointed out w hat
.
As
the chie f benefit results fro m
th e student h imsel f sees
b etter
off w
w ork for
and
ithout a teacher than
him
.
does he
w ith
,
one
w ill
be much
wh o
does his
TE S T S
77
.
As
stated on page
2
th e art student should
3
,
u se
fe w
texts and should not require the mechanical aids to test ing
w hich
have been explained
Th ey may sometimes
.
be required by teachers in the public schools stu dents they
w ill
the eye all
ave no capacity
for
not be necessary
if
h
w ork ,
,
the stude n t s hould aim to use
thro w these asid e as soo n as possible There are ma n y
w h o s ay
,
but eve n the n
the glass is used to trai n
see proportio n s or as a m ea n s
to
w ork ,
th e
w he n
for
testi ng
In
fe w
aids and to
.
.
that measurements and tests
are mechanical and that to learn to dra w the stude n t ,
should dra w by eye simply
.
It
is
true that
m easureme n ts
and tests as u n fortunately too many students are taught ,
to use th em can n ot fail to produce hard ,
an d
mecha n ical
l
drawi ngs and retard progress the stude n t tests
,
w hen
far
no farther to be sho w n by ,
,
w hich
can be carried but little
There fore the stu d ent is
tests explained a fter h e has carried ,
an d
w ill
sight
.
a
.
It
,
is b
if
any
dvised to apply the
h is
draw in gs as
not to put any draw ings aw ay
tests sho w to be untruth ful ing
!
as he can by eye and then put the m aw ay
and begin others
he can se e
for
,
ings onl y as
.
se e
se ems better
his eyes have failed rather than to carry draw
w here
farther
he can
St ill it
.
eli e ve d
fa r
w hich
as th e
that this train
most quickl y pro d uce abi lity to draw truth fully at ,
HAPT E R
C
P ERSPE C T I VE (Se e
of
PRI N C IP L ES ,
p a ge
vu
.
.
)
,
moment
the present
an y ob e c t
re fa c e
.
past and especially the ideas and emo
O U R w hole
t ions
P
VI
,
determine
h ow w e
perceive
”
'
j This being tru e .
the student mus t
,
w or
k
long and
e arne stly be fore h e can separate facts fro m appearan ces as
the kno w ledge
from
accepting
ve ye d
of
of
.
it s
'
a
of
to the min d
ppearance
,
w ith w hat
is by
.
prevents the
m ind
The impression
l c on
of
fa r th e
a combination greatest factor
kno w s concerni ng the actual conditions .
of w ,
hat the eye
w hat of
the mind
the obj ect
The student must struggle continually not only this influe n ce w hich of
of
1118
”
one n ot trained to accept the i mage
the eye is the result
s ees
form
the actual
,
a
.
g ainst
m ind but also against the e ffect ,
one line exerts to change the apparent directions
othe rs
T his
.
the pra ctised eye
e ffect is sometimes so strong that even of
the artist is deceive d
,
sa fely say that the most per fect eye
p erspective 8 7
principles governing
we
ma y
the l on gest '
A k nowledge of the th e a p pearance of form
training is liable to be de ceived ,
,
w ith
a nd
.
— FREE HAND
80
DRA WING
.
Figure 1 5 repre sents a circle A placed vertical and in front of the eye Th e cone formed by th e visual rays is ,
.
— é a and a vertical plane
represented by line s
cutting
,
,
of
through th e cone
,
of
,
w ill
w ill
the student
per fectly
at once
se e
Figur e 1 6
If
.
of
to the axis that in Fig
1
.
of
n ow
the base th e plane
A
5,
and
,
— a
circle
This
.
.
of
the p icture is inclined
,
of
A
that a vertical plane be tw een
the con e its intersection
still a picture
the
With th e cone th e
.
th e eye and the base intersects th e cone in circle is the picture
w ill
illustrate
the cone representing th e circle
th e apex repre senting the eye stud ent
If
.
,
hold any cone horizontal it figure the bas e
P
rays by line
w ith
the cone is
th e circle but in shape it di ffers from
which
,
is a circle
The
.
oblique
int e rs e c
tion is an ellipse but it is im p ortant to notice that it doe s ,
not appear such to the eye a t the apex
of
the cone of
appears a circle exactly covering the base ,
It makes no di fference
p laced
,
or
h ow
the plane
th e pro p or t ions
w hat
of
of
the cone
the resulting ellipse ,
of
the base
.
the picture is
it must al ways app ear to th e eye a circle in f act circle
It
}
,
,
the
When th e eye is removed fro m the
.
apex of th e cone the ellipse appears an ellipse and i s not a ,
true picture ellipse
of
of
Fig
in the eye
,
.
,
the circle 16
w hen
.
The circle
are pictures
of
of
Fig
the circle
1
.
A
,
5
and
and crea t e
i t is at th e apex a circular image ,
circle but the former only i s similar to the obj ec t ,
When loo k ing at
p ictures
we
th e
of
A
the
.
na t urally hold them
in
PER SPE C TI VE PRINCIPLE S
81
.
of
front
p osition is
u s at right a ngles to our li n e ,
of
th e pla n e
P of
Fig
1
.
If
5
.
visio n as
of
,
plan e
Fig
P of
thus held the ellipse upon it appears an ellips e ,
cannot create the idea
of
a circl e
,
.
16
an d
We see that the first
.
picture is pre ferable to the second w herever
the
in
,
for
it
is
a circle
,
an d
th e eye is placed creates a circle in the eye
.
of course understood that i t is al w ays looked at It is ( perpe n dicularly ) .
We
w ill
disti n guish the first picture from that given by
any other positio n
the picture plane by calli n g it a
of
,
tru e picture mea n ing that it is S imilar to the image created in the eye by the obj ect There can be b u t one ,
.
position
of
the picture plane
w hich
gives a
“true
,
This must be at right an gles to the direct io n the obj ect is seen ,
A
”
picture
.
in w hich
The pla n e ca nn ot be perpe n dicular
.
to all th e rays but S hould be “true
”
picture
dra w i n g upon a sheet
to the ce n tral
so
on e
.
of
any obj ect may be obtained by
of
glass
a special pe n cil or on a ,
w ith
w ire
an d
a brush
screen
w ith
color or ,
chalk
.
Th e
gl ass or screen should be placed at right a n gles to a li n e from
the centre
screen held in the edges d ent
on e
w hich
the obj ect to the eye the eye
of
,
p ositio n
are see n
make draw i ngs
in
.
,
an d
li n es draw n to cover all
It is desired that every
this w a y a small pan e ,
a sp ecial pencil bei ng the best materials should be mad e also
w hen
w ith
and
.
of
glass
st u and
Th e draw i ngs
the glass at ri ght an gles to the ra ys
it is h eld obliquely
.
,
The dra w in gs may be
FREE
82
-
HAND
DR A
WING
.
compared and the student realize that the glass mus t ,
be perpendicular to the direction in
w hich
th e drawing to give th e real appearance
of t
he look s
he obj ect
for
.
I t appears that a draw ing on any plane or sur face creates the correct impression only ,
th e
All
i I n t o s O p
w hich
it had
w hen
the eye
th e dra w i n g
w hen
1S I n
made
w as
draw ings t h en are best seen fro m some one poi n t ,
,
distance
Th e trained eye
.
w ill
s elect this distance
ho w ever draw ings and pictures
w ill
,
be vie w ed by
,
w hich
,
is
it
s een fro m the proper point
,
w h en
the picture
,
w hen
I s n ot
“true
the picture is a
If
.
picture the distortion p roduced
it is vie w ed fro m
too long or shor t a distance appears not in the shape ,
its parts but only in the re lative S izes ,
Thus the distortion
.
al w ays less than that the vi su al rays
,
an d
of
the
M odel D raw ing
true
”
for ge n e ral /
occ urs
w hen
direction in
p icture p lane
,
picture is
use
.
far
to
the best
It i s called
.
shall mean the position in
its real le ngth
a
of
the obj ects
“true
picture is by
Be fore beginning the problems w hich
of
of
a draw ing on a plane oblique
draw ing that can be made a
be
importa n t that all should be avoided
caus es marked disto rtion
represented
,
un
trained eyes and as th e proper point may not al w ays acce ssible
or
As
.
.
,
w e w ill
w hich
an
choose a term y
line appears
and any plane its real shape
.
This
the line or the plane is p erpendicular to the w hich .
Th e
it is seen that is is parallel to the ,
w ords
“parallel
,
to the picture plane
”
FREE—HAND DRA I VING
84
/
of
angle
inclination
.
Thus all horizontal lines
.
w hose
ends
are not equi distant appear to incline at smaller
or
-
,
greater w hich
of
angles
inclination
th e lines make
w ith
w ith
.
l zor izon t a l l in e s in c r e a s e tl ze
ng s l zi oa n i
-
an gles
the lines
Tl ie
“a n l e s g
poin t
or
Lines
.
inclination
of
of
th e angles
plane and th e ground
according to the angle s
,
the picture plane
l e vel appear inclined at i n crease
”
w ith
f
o
”
no t
w hich
the picture
in cl in a tion
f
o
de c r e a s e w itl z tl ze dis t a n ce
f
o
.
In all the problems explained the picture p lane is ,
s
upposed to touch the obj ect at its n earest poin t and ,
the draw ing is the larges t p ossible to be made on a plane of
in front
the obj ect
.
St n dy
Figure the eye four
of
1
7
Pr in c ipl es
.
,
an d
foreshortened ,
very narro w
.
.
”
face
on e
angles equally dista nt from the eye 18
fe w feet
a large cube a ]
its edges vertical
Figure
.
that its centre is on the l evel
so
,
Place
.
f
o
.
distant from -
of
visible
the eye ,
w ith
its
“ This face is n ot
and appears its real shape
.
Turn the cube so that its le ft side appears It
w ill
be noticed that the upp er end
the farther vertical ed ge B appears belo w the upper of
,
the front edge
A
,
and that th e lo we r end
of
of
e nd
the
farther
edge appears above the lo w er end
edge
The farther edge thus appears sh orter than the
.
of
the fro n t
PER SPE C TI VE PRINCIPLE S
85
.
front
and
edge
It is also seen that the horizontal edges
.
E , w hich
to converge nu e d , ti
they
of
co n nect the ends If
.
w ill
meet
of
representatio n s
of
thes e lines
D
these verticals appear ,
the draw ing are con
The continued lines must be the
.
of
continuations
the edges and ,
N ature
that parallel retreating lines in
we
appear to
verge to a point called th eir vani shing point
se e
con
-
We
fi nd
C is farther from
the
eye an d thus appe ars shorter than the ce n tral edge
A
n ow
that the right edge
.
,
and the horizontal edges F and the horizontal edges
of
appear to converge as
G
,
the le ft face
The edge
.
much nearer the eye than B and appears longer ,
'
really but little farther from the eye than of
vergence
F
an d
opposite the ce n tre
of
that th e upper ends must be the same e n ds
of
B
i ncli n ation same
as
an d ”
C
of
those
as
is very slight
G
of
B and
If
n ow
A and th e con As the eye is ,
”
.
C
.
are belo w that
the appare n t distan ce s
abo v e that
of
the lo w er edges ,
of
It is
,
A D E
edges appear equally i n cli n ed they on the level
.
C is
the cube the apparent distance s
th e upper edges
of
,
the centre
of
and the and
A
the lo w er “a n gles
of
G
must be the
and F
Since these
w ill
.
appear to vanish
the cube tha t is ,
“ th e eye is li fted the angles ,
of
of
of
,
of
the eye
inclinatio n
”
at the top decrease and those at the bottom increase ,
.
.
When the eye comes to the level of the top of the cube i s upper a gles disappear the w hole top seen as a n n d the
,
,
_
,
a
horizontal line
.
“
FREE—HAND DRA WI ZVG
86
From this study r st
That
.
vanish
of
the cube
,
we
se e ,
parallel and equal lines
of t w o
th e nearer app e ars the longer
,
.
w hich
do not
The relative
.
lengths appear to decrease as the distances increase Se e Fig from 2
d
1
.
9
in
,
w hich
of
B being t w ice the distance
A
the eye appears one hal f as long as -
,
.
A
.
That parallel retreating line s appe ar to converg a
.
,
to w ards a point called their vanishing poin t
A l l (
-
,
w hose
ends are unequally distant
fr om
.
lines
the eye are
retreating lines ) n That horizontal retreati g lines appear d 3 .
.
to
,
scend or vanish do w n w ard
w hen
the lines are above the
level of the eye and to ascend or vanish up w ar d ,
they are belo w the level
of
de
th e eye
.
w hen
This is evident from
the fact that the eye must be dropped to look from th e “
nearer to the farther end
of
the l ine above th e eye
be raised to look fro m th e nearer end the eye to its farther end h t 4
th e line belo w
.
That parallel retreating horiz on tal lines appear
.
,
to vanish at the level h t s
of
,
an d
of
th e eye
.
That a horizontal line at th e level
.
of
th e eye
appears horizontal and a horizontal plane at this level ,
is seen edge w ise and appears a horizontal line ,
We
w ill
w hich
lines
A
n ow
dra w upon the
w all of
have the apparent directions ,
B
,
n l r e i c u a d p
C
and
to th e ,
D
,
w all
.
any room lines
of
at floor and ceiling
.
,
the horizontal '
w hich
are per
We find that the lines on
the
FREE HAND DRA ZVI I VG
88
-
.
a model draw ing vertical lines are represented by verti cal lines (se e page Figure 2 1 Place a cube so that its top and front faces .
are see n and
so
,
A A A
edges
,
,
its right side app ears a vertical line
have their le ft ends a little farther fro m
th e eye than their right ends
but the distance is
;
short that the convergence is very S light app ear practically horizo n tal C,
longer than B
Th e
.
B
Li n e
.
C
and yet the edge
,
of
an d
so
the edge s
the dra w ing is
is nearer th e eye than
This proves inexact th e statement freque ntly made
.
of t w o
that
the longer Figure z ont a
,
” .
22
is
,
,
,
parallel and equal lin es
d ista n t from
the eye the nearer ,
When at a less angle than
.
on l y e x a c t
is
,
,
'
for
lines
w hose
larger or smaller tha n The figure also sh o w s th at
of
,
t h e on e
f
o
m us t
a
h t g
ri
an d
AB
and
havi n g one en d a ngl e
w ith th e
,
It S ho w s too that if ,
.
s h es a ngl e va n i
t h g
s h tow a r d th e r i va n i
,
or co n versely the one n earest
s h or t e r ;
parallel appears th e longer
This state
.
equal lines
w h ic h m a h e s th e gr e a t e r
pic t u r e appe a r s th e
as BD
angles are noticeably
t wo
perpendicular to each oth er
common
l in e
,
,
the nearer BD appears the longer
AC ,
,
un equally
C D,
and
°
ment
BD
,
AB AB
It sho w s t h at
.
appears the shorter the lines are at a greater angle than 4 5 w ith the
icture plane p and
a top vie w representi n g the eye a hori
square and a vertical picture plane
l
of t wo
w he n
parallel and eq ual lines th e nearer appears
.
,
t ow a r d th e l ef t, th e
on e
ot h e r
PER SPE C TI VE PRINCIPLE S
89
.
“ I f one side of the right an gle is not foreshortened ,
the other S ide exte n ds directly a w ay from the spectator and vanishes at a poi n t above the shor t ened Figure
” ,
-
2
of
the level
on
w s ho s th at 3
the eye
side
not
,
fore
.
e quidi s ta n t e qu al horizo n
two
,
,
tal li n e s perpe n dicul ar to e ach o th er a n d at e qu al a n gle s ,
th e picture app e ar e qual in l e n gth
w ith
,
above th e level I n Figs
of
2 2 an
.
d
th e eye th ey appe ar equ ally i n cli n e d 2 3,
ture pl ane an d give ,
of
pl a n e
Wh e n b elo w or
.
.
th e vis u al ray s inters ec t t h e pic
th e
th e vertical li n e s
th e
po s itio n s upo n w hich of
lin e s repre s enti n g th e s ide s
picture
co n tai n th e e n ds
th e s qu are
,
w h ich
of
the
are th us
lo n ger th a n th e dis tance s A B C D etc s ee n in th e pl a n The apparent le n gth an d angle of a ny retreati ng line ,
,
depends upon its a n gle ,
,
.
,
the picture the le v el
w ith
line (re ferr e d to the eye ) from the line
.
,
an d
the dista n ce
of
of
the
the eye
.
of
The greater th e angle more it
is foreshortened ,
i n clination
As lines
w ith
the picture the ,
and the greater th e
“angle
of
” .
th e eye is li fted th e
angles
,
AB
any line
an d
C D,
Figs
.
22
an d
of 2
inclination
3,
i n crease
”
of
the
Placi n g
.
the eye n earer the li n es prod u ces th e same e ffect but ,
th e
“an gles
than th e real t u re the
p
lane
e ye
distance
.
of
i n cli n ation
”
i l w hi c h the li n es e s g
ar
Th e
“a n gle
of
approaches the level of
must al w ays be much less
the eye increases
.
m a k e w it h ‘
i n cli n atio n
of
”
th e pic
decreases as
the line and also ,
as
t he
FREE—HAND
90
DRA WI rVG
The statement o ften made that d is t a n t
lines the more
'
a
“of
of
w ithin
of
sary to think for
of
the limits
depend
an d
ordinary dra w ings
this p oint in the case
th ere are other tests upon
good
as
“not foreshortened ” ,
lines
parallel and equal
the shorter
e a r s pp
ably accomplish ed as much harm true
.
w hich
,
”
has prob
,
for
it is only
of
vertical lines
It
is
.
not
meces
of
horizontal lines
is
al w ays better to
it
,
.
Figu re
24
AB
.
the ground and
I
,
,
repre sents a horizontal line lying upon 2,
3,
e tc
equi distant points in the line -
.
,
.
Th e lines from these points to th e eye represent th e visual rays by
w hich
th e points are seen
intersecting th e picture plane S ho w that
th e
,
t a n c es a nd
ppe a r
a
u ne
u l a , q
th e f a r th es t th e
th e
ing a s th e d is t a n c e in c r e a s e s
appearance
of
.
th e
e
a
pp a r e n t
a
This
is
l onge s t,
l e ngth d e c r e a s
al ways tru e
equal lengths on retreating li n es
Th ere are t hre e s ets
q
,
d is
ua l
ppe a r ing th e
ne a r es t
s h or te s t ,
These rays
.
of
the
.
in
th e pri s m
They all app e ar to v an i s h u n l e s s t h e y are
“n ot fore
s horte n ed
” ,
an d are
of
so
repre s e n ted excep t
are vertical or are s itu ate d ,
Th ey v a n i s h and
If
in
of
as
in
th e directio n s
th e s e are p oint s both e n d s
p arallel l i n e s
of
Figs of
.
21
when
and 2
th ey
5
.
th eir f arth er e n d s
th e i n vi s ibl e f ace s
an e dge are p o i n t s
of
of
.
,
th e ob j e ct
.
i n vi s ibl e s ide s
“ n ot o f th e ob j ect , th e e dge m u s t b e co n s idere d a s f ore s h or
ce ntre
.
t e n ed
,
e ven
when
th e eye i s n ot oppo s ite it s
’ — FREE HA A D
92
DRA iVI N G
th e other vanish to w ard the right canno t be avoided in this extend on both sid es
of
W h e n th e questio n
.
and
w a y,
.
parallel straight lines
the spectator
t h e y s h oul d ‘
,
repre se n ted by parallel straight lines and in the case ,
horizontal line s by horizontal li n es ,
Parallel
is sho wn by the shado w s
of
appear cur v ed
clouds at su n set
the
w est
to w ard th e
int opposite the
o p
su n
an d
su n , .
of
the rays
cur v ed lines
of
w ill , if
the electric s earch light
,
b est S ho wn by
N ature
by our leading illus
,
is
very noticeable
the student may have di fficulty in
s e e I ng
.
the
curvature even in long lines h e may very easily
of
,
,
prove that curvature of
long produce
.
long li n es as they appear
of
Although
even
is
This
the
the curvature resulti n g fro m draw ing the di ffer
ent parts e ffect
.
w hich
-
In ma n y draw i ngs fro m t ra t or s ,
con v erging
straight lines
An y
some
in the east to w ard a
mind does not kno w to be straight the impression
,
This
.
w hich
s k y,
times may be seen extending across the in
of
.
N ature
straight li n es in
be
w ill
result
if
S hort lines ,as he se es th em
h e dra w s the parts .
,
This may be do n e
by drawi ng from thre e boxes or prisms placed a short ,
distan ce apart and in a straight line th e central box ,
being directly opposite him so that only ,
seen
faces
t wo
are
.
Figure
26
repre sents th e appearance
of
the le ft hand -
box bot h sets of w hose h orizontal edges appear to van i s h for t w o vertical S ide s of th e b ox are s ee n ,
,
.
!
PER SPE C TI VE Figure O nly
27
one
,
se t
the
than those
e ye
of
if
the long lines
w ill form
Figures tions
of
2 6, 2 7 ,
ap .
the central one
of
of
an d
,
the latter
,
the dra wings are continued they
of
curved lines
.
the box at the le ft
thus appear a little S horter than the edges and
,
w hose
”
the obj ects at the S ides are
of
The vertical edges
,
.
si n ce
for
not foresho rtened
is -
must be similar to that
farther from
the three obj ects
represents the right hand box
28
e a ran c e
of
its horizontal edge s vanishes
of
but one side is seen th e other
p
.
re p resents the central
se t
Figure
PR I rV CI PL E S
,
.
and
28
the appearance
are each correc t represent a a S ingle box
of
but
if
they are
looked at all at once as a si ngle picture the impression ,
f the obj ects being placed in a curve is produced
o
No
one
w ould
s e n t at i on of
think
of
making this draw ing as a rep t e
thre e obj ects placed in a straight line
draw ing belo w Fig ,
.
2
.
ould w 9,
.
The
be made by all but this ,
draw ing does not represent correctl y the appearance
of
the boxes at either S ide and it appears that to give the ,
correct general impression drawings sometimes cannot ,
be exact in detail
.
There are some
wh o
think that the study
tion is unnecessary that ,
w ithout
rally make th e draw ing Fig ,
three boxes that
we
.
se e as
.
29 ,
theory all
thi s ques
w ould
as a representation
This is probably true we
of
;
natu of
the
but the kno w ledge
cannot al w ays represent is very
ne c e s
sary as is proved by the m any illust rations from the p ens ,
FREE—HAND DRA WING
94
'
those
of
ing
w h o fail
w hich
w hich
2
.
9,
reason
and thus produce draw ings
are flagrant violations
spe c ti ve ,
t he
s ub i ect
to apply to a large
gives Fig
.
of
the simplest rul e
and this is frequently the result
draw by eye the appearance
of
of
the parts
of
per
the attempt to of
a large sub
j c e t (s e e page Straight lines a p pear curved but t heir repres entation ,
by curve d lines is generally unsatis factory and th e s t u dent should never be allo w ed to represent straight by ,
curved lines “
As
sho w n on plate
be substituted
for
th e curved lines chang ing the draw ing
very little
w h en
28 ,
straight lines may
,
there are
t wo
vanishing poin t s -
.
The influence
of
diagram p erspe ctive and particularly
the appearances
of
parallel perspective are
,
,
so
po w er ful
that many illustrators do not realize that they d o not parallel persp ectives in t wo
vanishing points
t angul a r
-
N ature
,
obj ect , w hen t w o
of
it s
'
se e
and that there must be
the horizontal lines
for
,
de s si
are seen
rec
of a n y
It
.
is
not
necessary to advise the student not to make as o ne draw ing the Figs of
.
2
6,
2 7,
nd
28 ,
a
or not to represent the end
a room as cur ved ; yet the draughtsman
never think
of
of
making th e latter mistake in the case
single unbroken sur face sur face is broken or di fferent planes
D iagram
w h o w ould
,
w ill frequently
w hen
do it
w h en
there are many short
a
th e
l I ne s
In
.
perspec t ive has created many false ideas and
is responsible
,
for
much bad dra w ing and yet t he ,
p er
— FREE HA N
96
DRA WI /VG
D
.
.
from
It
GH
the eye and appears shorter than the edge ,
a pp e ars
found
f
th e
— length of 1 2
'
of
by means
a plan
.
This distance may be (
.
the cube the picture plane — — and the eye ) C onnecting I G and 2 H t h e vertical edges are represented by inclined lines This is not satis of
,
,
.
,
.
factory
The model draw i ng must represent vertical edge s
.
vertical lines
by
the front face
If
.
w ill
s e em too narro w
verticals are dra w n from
se e m too
if from I
w ide
Th e pro p e r e ffect
.
w ill
G
and
and
H
it
w ill
2,
be given by
verticals bet w een these lines or by verticals from
H
,
and
G
,
— the line I 2 being droppe d a little
,
.
The model draw ing is not th e exact draw ing upon the inclined plane but this dra wing correcte d by substituting ,
vertical
for
Figure
inclined lines Th e cube
33
.
.
w ith
its vertical faces at
the picture plane the top being on the level ,
The top is seen as a horizontal line at equal angles and the edges w hich
l
z on t a
w ith
A
of
°
45
e ye
the
.
The S ides S inc e
.
,
the picture ap pear ,
of
equal
w idth ,
and B vanish up w ard at equal angle s of
depend upon the distance lin es are at angles
plane the distance ,
of
°
of
45
the eye
w ith
.
When hori
a vertical picture
their vanishing p oints -
from
th e
the picture (that is line E ) is the same as distance of the eye from th e picture plane
centre
to
of
,
,
,
the
.
The entire
w idth of — 1 2 of
diago n al foreshortened
the
.
th e app earance is the perspective
the base
of
the cube
,
w hich
is
of
“not
This line is behind the pic t ure plane
,
PE R SPE C TI VE a nd
is
repre s e n ted
n ot
PR I ZV CI PL E S
97
.
it s
r e al
length can be obtained by setting
off
l e n gt h
The exact
.
the act ua l length
of
the diago n al on a horizontal line through the lo w er end
of
t h e fro n t
edge and by draw ing from its ends lines to the ,
,
p oint opposite the eye w ith of
of
the lo w er lines
the S ide verticals
Any k no wn
The intersections
.
of
these lines
the draw ing give the lo wer ends
.
length can thus be measured on the pic
ture plane and carried i n to the picture by means
of
,
parallel lines e ye
vanish at
C,
the point opposite the
.
Figure of
,
w hich
34
The cube
.
the eye and ,
and to th e
it s fi
,
w ith
its lo wer face on th e leve l
vertical faces extending to the le ft at
ht at g
The le ft face is nearest parallel to the picture plane a nd
A A t
distance
of
w ider
than the right face
The ed ges and B vanish do w n w ard at angles w hich depend on
t he
thus appears
ances
of
,
the eye , the
w idth of
of
B
the appearance must be ,
.
The apparent
w idth
c
ube is turned to ward the position in
s
ide is seen
w hen
decreases w hich
they
as
the
only one
.
35
.
The cube
w ith
its vertical faces vanishing
qually its top being four feet b elo w the level ,
H ere
of
For equal dis
.
the faces are se en unequally than
are seen equally
Figure
.
the eye from th e obj ect but the angle
must al ways be less than that
l ess w hen
e
,
the sides appear
of
equal
w idth ,
of
and the
the eye
.
angles
FREE
98
-
inclination
of
H A zVD
DRA
WI N G '
.
and convergence are alike on each side
the central edge
Th ere are four parallel edge s extend
.
ing to the right and four to th e le ft ,
Parallel
.
horizontal
lines appear to converge to w ard a point on the level the eye and there ,
w ill
be
t wo
the edges are at equal angles ,
equi distant o n each side -
of
th e
the square
— cube one diagonal 1 2 ,
,
of
,
is
vanishing points
,
,
va n i ng shi
\ ce ntral \
.
the picture they -
w h ich
of
Since
-
w ith
th e
incline at equal angles and In this position
of
w ill
point sw ill be \
edge
.
is th e base
of
parallel to th e picture
th e not
and ap pears a horizontal line Th e — o the r diagonal 3 4 appears a vertical line and the
foreshortened
.
,
,
,
farther
angle
of
one
Wh e n
t h e th e t op o f
.
the square se ems directly over the nearer c u he
ppe a r of
si hl e s id es a l w ay s a vi
.
is
e qu a l
s ee n
in th is w ay , th e
w id th
.
The diagonals are p erpendicular to each other and it ,
is seen that
if t w o
lines are perpendicular to each other
,
” “ and one is not foreshortened , the right an gles app ear
right angles Figure
.
Th e cube above the eye
6 3
.
edges extending to the le ft at
it s
,
horizontal
and to the right at
O
0 3
Both sets the
l e ft
edge s vanish at po ints in a horizontal l in e
the eye (call e d the horizon ) th e p oint at b e in g nearest to th e draw ing for th e l ine a t th e
at th e level ‘
of of
,
,
pic tu r e appe a
th e
l e r e a t es t a n g g
w it h th e
diagonals
the horizontal sur faces vanish
of
rs
s h or te s t
.
.
Point
The 2
is
FREE
10 0
HAND DRA WI N G '
-
.
Th e R ig h t Squ a r e Py r a m id
The axis at
centre
it s
on al s
of
this pyramid is perpendicular to the base This point
.
is found
39
of
When the base
.
tal the draw ing may be tested ,
of
the centre
the base
th e pyramid When
”
the diag
,
belo w
visible th e ,
C D,
and
4
th e base are
not
if
it is long or
,
Fig ( three or four S ides or the base w it h one
outer one s appeari ng alike ,
When
.
two
time
on e
,
When
.
slant edge is j ust behind th e nearer
— the base 3 4 appears to coincide ,
pyramid and the other
,
1
-
2,
.
w ith
of
sides appear
t wo
,
,
.
si des are seen all the edges
alike th e edges vanish at equal angles
,
.
.
,
the base appear to vanish
,
,
.
.
,
1
of
the pyramid is s een
s ide s m ay b e vi s ibl e at
Figure
a vertical line from
I f Fig the axis is short or ( the eye three of th e triangular faces w ill be
two
O n e , t w o, two
by
This should contain th e vertex
.
AB
of
it is above the eye
w holly
the pyramid is horizon
they app ear perp endicular to the axis
and one side only
or
d ra w ing
.
side s
t wo
foreshortened ,
if
by
.
Figure
of
.
Th e
.
farther
diagonal
O ne
the axis
of
of
the
appears at right angles
to it Figure axis
of
2 4
.
When
t wo
sides are seen
u
nequally the
th e pyramid appears perpendicular to a line
is parallel to the picture plane
.
A
plan
of
,
w hic h
the base and
PER SPE C TI VE PRINCIPLE S
101
.
the picture plane
S ho w the position
w ill
re ference to points
w ith
and
1
in front
nearer point and ,
2
of I ,
the line
of
It passes behind
.
the farth er point
ah
the
2,
When
.
the p yramid is vertical a h appears horizontal When oblique as in Fig 4 3 the line a h has the same relative ,
,
p osition I
,
a nd
w ay
.
,
,
passing in front the
to dra w wi
t h in
a con e
Figure
44
n gle
2
b ut
;
of
the
the base s
imple s t
obliqu e po s i t i on i s
th e
.
a nd
t h e Tr ia ngu l a r
Pr is m
.
h orizontal
line the altitude ,
,
the tri
of
vertical line and intersects the centre
a
to
When the triangle is equilateral or isosceles (
.
its bas e is a
angle is
the farther angle a
pyram id in
Th e Tr ia ngl e ,
base
of
b ehin d th e ne ar e r
in s crib e i t
and
.
the
of
,
.
Figure 4 5 When neither end of the prism is seen its long edges are not foreshortened and must be re p re .
,
,
sented b y parallel lines d ic u l a r s
ce n tres
and
I
2
are in
r e e n p p
to the long edges passing through the p erspective ,
and 3
Figure
4,
of
th e lo w er edges
When an end
6 4
.
appear alike one edge ,
ened
Points
.
” .
Th e central
,
A
,
B
,
of
,
is
of
seen
of
the triangles
w ith t w o
the base is
.
S ides w hich
“not fore sh ort
the receding edges appears at
right angles to this edge and the end does not appear ,
re a l s h a e p
Fig ure
it s
.
47
.
When
an
end and a side are seen the ,
draw i n g may be tested by a vertical line throu gh point 1 — This vertical should int ersect 2 3 n earer 3 than 2 for .
,
,
FRE E—HAND
10 2
th e nearer hal f
The edges
.
of
.
any retreating lin e a p pears long er
of
than the farther h al f the direction
DRA WI N G '
of
their farther poi n ts
,
the end vanish in w hich
— 1 2
are at once —
I f line the edge — — 1 2 1 2 is edge appears to intersect the centre of
seen except in th e case
of
3 7
.
n ot
,
fore shortened 1
nearer
2
-
— 1 2
2
and does not vanish than
1,
point
— I f 3 7 intersects
.
the n earer end
2
— I f 3 7 intersects
.
— 1 2 nearer
I
than
th e ground are at equal angles
w ith
length
of
the pri sm is tw ice that
of
n ation
The nearer hal f
.
of
2
-
Th e R egu l a r H e x agon
the hexagon there are four sets
as
,
,
dra w i n g
,
of
th i s form
p arallel li n e s va n i s h ends — 0
4
,
and
so
th at th e poi t s
Figure
in
8 4
at th e l evel
in
— long as 2 3
,
th e eye
,
.
of
parallel lines as ,
,
C
an d
D
A
.
b e te s te d b y s eei n g th at th e
th e direc t io n s D
»
of
th eir f arth er
inters ect th e diago n a l
it are perspectively e qui di s ta n t -
repre s e n t s th e h ex a go n of
in e li
,
th at t h e diago n al s n
‘
w ill
of
.
— I ts diagonal 0 4 , 1s divided
.
.
Th e
.
.
B C hnd D in Fig 4 8 i n to fo ur equ al p arts b y th e diagon al s B ,
is
its base
angles
appears
6
of
the edge
,
A
I
the face on
the farther hal f a littl e shorter than the nearer
In
point
the picture
— — The edges 2 3 and 2 6 vanish at equal ”
2,
the edge
.
Th e p rism is so placed that the edges of
of
is the nearer end
an d
it i s
w h en
it s ce n tre
“no t f ore s horten ed
” .
.
is
FREE HAND
10 4
DRA
-
WING
.
point 4 appears over 0 D raw AD and BC — — — — that 0 1 is greater than 1 2 and 3 4 less than 2 3
w h en
.
See
.
.
Figure 53 To test the s k e t ch (assu ming the neares t side to be correc tly placed ) .
,
D raw AD and t hat
the diagon al s
and BD and the diagonals — Through 2 dra w 0 4 Se e
AC
BC , giving point
2
,
.
.
the points on this line are equi distant actually equi -
,
” “ distant w hen th e line is not foreshor t ened , and
ve l y sp e c t i
so
w hen
the line vanishes
Th e H ex agon a l Pr is m
p er
.
a nd
I
y
r a mi d
.
Figure 52 may represent the top of a vertical prism ll be seen equally w hen 4 appears t w o of w hose sides w i ‘
just over — o B
,
— The side o A in c lin e s at th e sam e angle as
0
.
of
at both the top and the bottom
the angles upper
of
,
the lo w er lines are greater than those
When
.
th e prism though
is not vertical
,
two
the
the hexagon ,
of
the p rism
the
S ides are se en equally and the prism
— — directions of th e lines o A and o B may
be determined by means of
of
w hich
of
the diago n al s .
AB
and
CD
appear perpendicular to the axis
.
Figure 53 m ay represent th e to p of th e prism w hen three of its vertical faces are se en the t wo outer ones ,
appearing
AB is
ax
and of
of
CD
equ al
t he
of
the pris m
w idth
.
.
When thus seen the edges
ends a p pear
,
p erp endicular
to the
PE R SPE C TI VE PR INCIPLE S
105
.
Figure 54 represents the prism w hen three faces appear The narro w er A is the farthest from of unequal w idths .
the eye than
Points
.
and
h
and
a
and
d,
are thus farther from the eye
c
and
ah
arallel horizontal lines p
vanish to the le ft
cd
The
.
the ends vanish in four points
of
,
must be th e same distance a b ove the draw ing (at — appear 0 the level of the The equal spaces on 4 which
unequal
The vanishing
.
lo w er base
the proper
of
ca se than that may appear
of
of
the top
the parallel lines brings the
w idth ,
it being greater in this of
The invisible end
.
a prism
or narro w er than the visible end (s e e
w ider
page F igure of
55
represents a prism
the diago n al
of
its base
.
w hose
length is t w ice that
The prism rests
on the ground and is belo w the eye ,
on
one f ac e
The edges
.
face
are at equal angles w ith the picture Th e diago n al s a d a n d e h are vertical li n e s
this
of
.
th e diago n al s
a h an
d
ed,
give poi n ts
are perspe ctivel y e qui dis ta n t i s th e more dis ta nt
;
po i n t
a
an d th e edge v a n i s h e s up w ard ”
of
hd
1
Th e
-
tion
-
.
is
i s th e s ame as th at
3,
w h ich
,
n
arro w er f ace
th e f arth er of
etc
.
,
end
a n gl e of i n cl in a
df
Th e s ide
.
fu lly
l on g
S hor t diago n al s
of
th e b as e s
.
,
Th e q u e s tion m ay ari s e
an d
the
C o n ti n ue
line s to s e e th at th ey va n is h to w ard
on e
S h al l th e
v
-
— 0
,
A
— of o a
i s perspectively t w ice a s lo n g as th e diago n al te s t dra w th e i n vis ible edge s
w it h
2,
Th e
.
an d
n
4
.
— 0 5
To an d
all p arallel
poi n t
.
e arer h al f
of
the
FREE—HAND DRA WING
6 10 a d,
di agon al
th e f arth er
b e repre s en ted b y a gre ater dis t ance th an
h a lf of
co n vergen ce tance s
,
an d
ac
6 5
Figure s
th e
s ame a s
” P
it
;
w ill
b e s een th at o mitti n g th e
th e vertical l in e s m ake s th e equ al dis
ed ,
equ al
in
th e dra w i n g
Th e te s ts
for
.
an d
57
f or
th e pris m an d t h e s qu are pyramid
f ace s
Wh en three
.
.
th e pyramid are
are s ee n th e o u ter on e s e qu ally th e ,
,
axi s appe ar s p erpen dicul ar to a lon g diago n al b as e
Wh en
.
t w o f ace s
p erp en dicul ar to a three are s ee n c u l ar
in
u
s
of
th e
appe ar e qu al th e axi s appe ars ,
hort diagon al
n equ ally
,
th e
Wh en
.
or
two
rp e n d i e p
axi s appe ars
,
.
2 4
.
circle app ears its real Sh a p e
Th e
fore sh ortened
,
” and
w h en
it is
this means any position in
not
w hich
the
circle is seen in a direction p erpendicular to the circle its centre
I t appears a straight line
.
th e plane
of
the circle
.
w hen
In other positions ,
at
the eye is in ,
in w hich it s
entire circum ference is seen it appears an ellipse
.
If
suppos e th e picture plane to be a plane sur face the ,
cone
'
to a lin e b et w een t h e lon g a n d S h or t di agon al a s
Fig
we
.
of
visual rays
ellipse but ,
if w e
w ill
be intersected by it in a per fect
suppose th e picture plane to be a sphere
or other curved sur face the s ection w ill not be an ellipse ,
p ractically
,
th e circle a p pears an ellipse
.
Figure 58 is an eleva t ion re p resenting t h e eye , a
FRE E
10 8
Figure ing
HAND
-
w ith
63 is
Fig
.
a p lan
61
of
WING
.
th e same both vie w s correspond ,
V I su al
The
.
D RA
rays
to points
r, r,
and
1
determine at the picture plane th e short axis ellipse
P,
The line
.
of
,
appears th e longest line
,
of
of
points M and
N
A ll
lines
to vanish w hich
.
is
,
MN
the chord
the circle
The eye is above the ground r
th e
the ellipse and continued to
the ground , gives the position
r,
,
bisecting the angle bet we en the
rays gives the centre
visual rays
of
2
an d
,
w hich
.
thus in the plan the ,
do not come tangent to the circle
at
.
w hose
ends are unequally distant must app ear
In any circle there can be but one diame ter not fore shortened
” .
perpendicular to the direction in
This is the one w hich
w hich
is
th e circle is seen
.
Suc h a horizontal line appears horizontal and thu s a ,
horizontal circl e al w ays appears a horizontal
though th e diameter does not appear the long axis ellipse it is parallel to the chord ,
,
ax 15
of
bisects the long axis
.
i l ar n c u e d p
The short diameter of
to the circle at its centre
of
the long axis
to a line
.
,
w hich
the circle at its centre
.
of
of
the ellipse
a horizontal circle
and i n any circle appears to coincide C onversely ,
th e
an ellipse i s p erpendicular to and
ap p ears a vertical line in th e case ar i c u l e n d p
of
appears th e long
not foreshortened
axis and this chord is thus Th e short
w hich
f
for
e ll i se p
w ith
,
a line per
.
any elli p se app ears per
~
is at righ t angles to the plane
PE R SPE C TI VE PRINCIPLE S
10 9
.
Figure
64
of
on the level whose
of
— is 3 4
,
vertical
the long axis
of
s
u nd e r
A
ca l ,
f
e
ey
'
at
the
,
the ellipses th e
a x is
or e s h or te n e d
m u s t he
of
of
the ellipse
the same S ize as
.
A
and in the same plane
,
,
.
,
an
f
o
vertical plane
,
w ill
of
the eye
.
re p resent B and
p
r c l e , on ci
The circles being
These lin es — the long axes 7 8 and
el l i s e
in cl in e d l in e
,
of
w hich an
of
level
determine the directions seen that
,
a horizontal line on
lines perpendicular to these circles at their
,
of
for
vertical circles
an d
centres vanish I
is
,
directly over
— 1 12
centre
the eye appears horizontal and this line
C are
H orizontal
w hen it s
,
determines the direction B and
,
the eye appears a circle or an ellipse
lo n g axis
the level
A
The vertical circle
.
w hic h
a ny
l e ve l
C,
an d
it is
p r es e n ts a ve r ti h e x c ep t th a t o t e f re
.
the same size and in the sam e
be tangent to
two
vertical lines
are represe nted by vertical lines R and S
.
which
In order
that the upper and lo w er ellipses shall be ta n gent to — — R and S their short axes 5 6 an d 9 1 0 must be shorter ,
than
— 1 2
,
,
,
that
of
the central ellipse
.
The
w idth of
the
ellipse de creases as a vertical circle is raised or lo w ered — — Th e long axes 7 8 and 1 1 1 2 appear a little shorter .
than
—4
3
.
Whether this di fference shall be represented
or not is a question similar to that considered on page
5
1
.
FREE
110
HAND DRA l VI N
-
Th e Cy l in de r
not foreshortened
,
,
an end and th e curved
If
.
.
.
When an end only is seen it is and ap p ears its real shap e
G
surface are seen th e end is foreshortened and a p pears ,
an ellipse
Less
.
,
than hal f th e curved s ur face
cylinder can be seen at one time Figure
65
.
When one end
straight line th e
ot h e r a
,
the
of
.
the cylinder a p pears a
of
t an ellipse B
a e s pp
,
.
When n either end surface is visible as a straight line or
a sur face both en d s appear narro w ellipses
as
,
cylinder
A
is
not foreshortened
then
When one end
of
w hen
a vertical cylinder appear to converge
of
in
it s
centre
.
any draw ing
of
the eye but ,
.
w hich
is at right angles to th e
.
of
the cylinder the long axes
G enerally ,
ellipse is not th e centre
th e fact that th e centre
of
of
the axis
of
of
the solid
.
of
the elli p ses be
,
the of
the
the circle may be disregarded
and the line connecting the centres si de re d
r ci
In the cylinder this line is its axis
ellipses must al ways be at right angles to the axis the cylinder
ar e
th e ellipse representing any circle is
perpendicular to a line cle at
ellipse than the
.
represented by vertical lines
and
w ider
the cylinder is not on the level
Th e long axis
.
D)
and
of
”
,
,
C
Th e
.
a vertical cylinder is visible the
other is invisible and ap p ears a visible end (see The elements
,
c on
,
— FR EE HAN D DRA
112
it also a pp ears S horter and ,
,
tion a l ly w ide r th a n th e vis ihl e
can be given
.
the distance increases
of
a
the eye and decreases of
the eye is
.
represents a horizontal cylinder on the level
67
°
The cylinder extends to the le ft at
.
as
,
When the distance
.
,
the eye
pp ea rs p r opor
a l w ay s
This is the only ru le that
.
short the di fference is marked of
.
Th e di fference betw een the ap parent sizes
de p ends upon th e distance
Figure
WING
45
w ith
the picture and its bas e extends to the right at th e same ,
angle
I t s length is twice its diameter
.
— Th e S hort axis 1 2
tive hal f of
the visible end A is a p e rsp e c — the ele ment 1 3 Th e contour elements con of
.
verge to ward the le ft Figure
.
68
.
repres ents the same cy l inder st ill at ,
°
to
45
the picture but inclining up ward to the right ins t ead ,
being horizontal
.
Th e app earance is the same as that in Fig obj ect at an angle
w ith
the picture is
appearance as long a s this angle
w ill
unchanged
,
of
the appearance
Figure s C,
69
and
0 7
w ith
re ference
67
.
.
An
present the same
volve through a circle and the only change tion
of
to
.
It
15 I n
m ay
re
the posi
a horizontal line
.
represent horizontal cylinders B and
respectively over and under and the same S ize as the ,
horizontal cylinder
A
s ented by dotted lines those
in
,
Fig
.
be tangent to
64 ,
in Fig .
67 , w hich
.
is here
r e p re
The ends are circl es situated as
and the ellipses repr esenting them mus t
t wo
vertical lines
.
PER SPE C TI VE
PR I I VC I PL E S
113
.
Figure 7 1 re presen t s a horizontal cylinder belo w the e
and
ye ,
that
xtendi ng directly aw ay from the spectator so
e
axis appears a vertical line
it s
The end appears an ellipse of
right angles to the axis line
.
w hose
long axis being at
the cylinder is a horizontal
The t endency is to represent th e end by a circle
but it can
'
a p p e ar s o
sur face is seen Figure
2 7
only
1 7
.
no
represents a cylinder Fig
of
p art
of
of
the cylinders
of
.
the elements converge on the level of
To this point the axis and elements
.
cylinder appear to extend best represented by points of
centres
the curved
the same size and
the ends
1 7 ,
.
being in the same planes In Fig
w hen
.
parallel to that
eye
,
.
of
the ends
The centres
.
of
the
of
the parallel the end s are
horizontal lines through the
in
the first obj ect
The long axes
.
of
the ellipses pass through th ese points perpendicular to the axis
of
than those
the cylinder of
Fig
horizontal lines Fig
.
1 7
,
.
1 7 ,
The short axes
.
for
w hich
are tangent to the elli p ses
o m t p .
of
.
The cone appears a circle line
be shorter
the ellipses must be tangent to
Th e C one
a
w ill
a triangle
,
.
w hen
w hen it s
its axis
w ould
base is seen as a straight
The e n tire curved sur face is visible
cone points to ward the eye
appear
;
none
of
w hen
the curved
the su r
FREE—HAND
114
face
is s een
the eye
w hen
DRA WING
.
the cone points di rectly a way from
Betw e en these p ositions any part
.
the
of
curved sur face may be visible th e circle a p pearing an ,
ellipse
.
The base
of
the cone being at right angles to th e axis
as in the cylinder it appears an ellipse
w hose
,
perpendicular to th e axis
of
the con e
The contour ele
.
ments must appear tangent to the ellipse Figure
A
73
B and '
,
,
C one
represents three cones
C,
A
long axis is
of
the base
th e sam e siz e
of
on a horizontal sur face belo w th e eye
is vertical
.
of
The long axis
th e base ap p ears horizontal
.
,
.
th e ellipse
of
The contour elements are
.
tangent to the ellipse above its long axis
Sh ow m g
,
that
mo fe than hal f of th e ellipse represents the visible e d ge of
the base C one
.
B rests on an ele ment on the ground
base is visible and app ears ,
w ider
axis thus appears shorter than that the tangen t points
of
th e elements
hal f th e curved sur face is seen C one
appears
C
,
we
A
of
.
more than hal f th e curved sur face is seen ,
Th e
that less than
se e
and its axis shorter than that
To draw the cone
.
and noting
,
inclines to w ard the spectator
w ider
A
of
than that
The
.
cylinder or any ,
the m ethods explained on page
.
of
Its base B
.
M uch
.
m ilai si
should 33
-
obj ect
b e follo w ed
,
.
The mass should be draw n fi rst and visible lines be fore ,
i maginary one s
.
The axis (w hich ,
is
an
imaginary line ) ,
FREE— HAND DRA WING
116
th e equal divisions upon it appe ar equal CD
is not the long axis
of
.
Th e diameter
.
eithe r ellipse but is parallel ,
to b oth and generally there is so little space bet w een ,
the m that practically
we
may say that th e equal divis
ions
on
of
the circle ap p ear in th e long
axis
of
ellipses
the diameter
t he
,
entire lo ng axis
AB of
fourths
,
AI
the distance
m easured ho rizontally
,
sp e c t i ve
if
ellipse and
,
th e distances
the entire
is
betw een th e
one fourth
of
-
EG
HF
and
sh ort a x i s
th e
are per
EF
.
Th e apparent distances a t front and back bet w een ,
elli p ses representing concentric circles are al w ays the ,
same perspective parts
of
the entire short axis that the ,
distances bet w een th e ellipses on the long axis are
of
the entire long axis T h e distance
betw een the long axe s
of
the ellipses is
equal to one hal f the di fference in length -
of
HF
and
EG .
Figure
75
re presents concentric circles more nearly
they generally appear the distance F G ,
shorter than
AB
,
and th e long axes
being y ery n ear together
.
of
The distance
b e I ng
of
but little
the ellipses thus 6 5 -
— of the axis 0 6, and sho w s that the spaces
m u st be p erspective sixths
is on e si xth -
AB
the short axis
and F G
AG
.
draw ing sho w s th at the retreating parallel circles do appear to con v erge except beyond the centre cle
.
as
of
The n ot
the cir
Th us curved parallel retreating lines may app ear ,
to converge or diverge
.
PE R SPE C TI VE PR INCIPLE S Figure w hich
represents 6 7
is a square
'
a ci rc u l a r
117
.
ring a cross se ction -
,
.
The circles are co n centri c on each S ide — The distance 4 8 is actually one seventh -
of
.
The square
very nearly
it s
w hich
of
is the section
the ring
of
the lo n g axis
— and the dista n ce 2 9 is a persp ective seventh
axis
of
of
the
.
,
short
the ring appears
real shape at th e ends the horizontal ,
— — side 4 8 a p pearing a little longer than the vertical 3 4 — The distance 1 2 at the front , is longer than and at .
3
th e b ack 5—6 i s s h orter th a n
— 3 4
houl d al w ay s b e s ketch ed
so
s
,
are s een m ay h ave th e righ t
Th e invi s ibl e li n e s
.
th at th e l i n e s
d ir e c t ion fi
wh
ch i
mu s t b e
C are
t aken n o t to exaggerate th e di s tance b et w een t h e long axe s n
of
th e ellip s e s
I n ma n y
.
ece s s ary to draw more th a n
b oth ellip s e s
ca
it w ill
ses
on e
no t
be
as a te s t
for
'
-
aX I S
.
Th e Fr us t u m
f
o
th e
Py r a m id
a nd
th e C one
.
When any pyramid is cut by a plane parallel to it s base of
the section is similar to the base and the lines fi gures are parallel Figure 7 7 represents the frustum
,
both
.
of
a square pyramid
.
This is a form frequently found in furniture chai rs tables etc The draw ings from these obj ects may be tested by ,
,
,
.
seeing that the sla nt lines point over the centre
of
,
w hen
continued meet at a ,
the base and that the lines ,
‘
the
u
r e pp
b as e
are parallel to those
of
the lo w er
.
of
FREE—HAND
118
Figure eye
,
represents the frustum
8 7
with
A visible
the larger base
of
Th e contour ele ments of
the ellip ses
DRA WI
of
the cone
of
.
b
a cone
elo w th e
.
the cone app ear tangent to
both bases and
poin t in the axis
VG
r
,
w hen
continued meet at a ,
Th e smaller base
.
is
invisi
ble and thus being more distant appears proportionally ,
,
w ider
,
than the visible
Figure
.
represents the same obj ect but seen from a
79
,
nearer position the ellipses appearing ,
w ider
.
The contour ele ments are tangen t to th e ellipses farther from
the ends
of
,
vex sur fac e is visible two
of
their long axes an d thus less
A
.
circle A
hal f w ay -
,
th e con
bet w een the
bases is represented by an ellip se tangent to th e con ,
tour elements and p erspectively hal f wa y bet we en the -
,
ellipses
the
of
bases
The
.
nearest
element
cone appears a vertical line and extends fro m end h aw ay from the eye a
than
h
I ts
.
position in
w hi c h
it is
is
,
80
of
it s
upper
the cone is nearer the
c
and
d
.
” ,
the lo wer
represents the cone
and
oint p
w idth of
of
th e upper
.
w ith
its smaller base
visible and a conical band about its sur face
.
Th e ele
me n ts are tange n t to the ellipses behind the ends .
their lo n g axes and more than hal f '
,
face
is seen
.
AS
of
the convex
already sho w n the vi sible curved ,
2
The
p roportionally greater than that
ellipse but less tha n th at Figure
of
not foreshortened
is practically mid w ay betw een the ellipse
.
centr e I thus appears nearer
The farther element
.
th e
of
of
su r
su r
FREE
120
stood this elevation ,
ples clear Fig ure
83
WING
DRA
.
o ften help to make the princi
w ill
represents a double cone , composed
in diameter and
A
and B
w hose
,
length is eight inches
w hose
axes are
,
w hich
inches
x si
.
The
w hole
.
of
of
th e
t wo
obj ects
The smaller
.
circl e is co mmon to both cones and the ellipse ‘
,
repr es ent s it must be tangen t to th e ele ments h al f m t
Less
.
of
ents
hose
B is visible ,
the nearer one
of
le ft
of
of
A
w hich
of
both
and more than
I t follo w s that the ele
.
the farther cone B must a p pear to intersect
foreshorten ed t he
than hal f the sur face
the sur face
the
are equidistant from the bases and
the inte rse ction
cone s
of
bases are four inches
el ements converge to points in th e axis
double cone fro m
H AN D
.
intersecting cones
T he
-
t his
,
A
.
point is
,
When the cones are much
p romine n t
,
as in the Sk etch at
.
Th e Tor u s The
a nd
R ing
f
o
C ir cu l a r Se c tion
torus is a c onvex moulding frequently found
architecture and in m a n y com mon obj ects ,
Figure
84
.
An
its bases
.
In
.
easy w ay to draw this form is to s k etch
the ellipse s representing the circles d e re d si
.
of
The section
,
w hich m ay
be
c on
th e sur face connecting
th ese bases appears nearly its real shape at the ends of
the long axes
of
the ellipses
.
The semicircle in this (
PER SPE C TI VE PRINCIPLE S
121
.
position belo w the eye appears hal f
a horizo n tal
of
ellip se ) The curved contour of the moulding w ill be represented by a line tan gent to th e s e m ic 1rc l e a n d .
,
n
early
are
so
to the upper and lo wer ellipses or ,
w ider, farther
Figure
85
e n ed
but
,
ellipses
represe n ts the ri n g
C rcles i
,
This obj ect
.
w he n
w hen foreshortened ,
is on th e contour
is
outline
of
a circl e
n ot
its outlines
w ill
be
n ot
,
.
When much w ill
be
w hich
for e s h ort
pass behi n d
,
the section
the circle around th e circle ,
th e ring
in all its positions by a circle w hen
,
w ith
The sphere
.
Th e sphere
.
w hich , if
Suppose a sphere
.
the ring to move
of
slightly smaller th an
.
th e ri n g is a circle
of
appear an ellipse
of
the ring and
the nearer part as in t he draw i ng
The centre line
the sur face
of
the farther part
of
,
of
be rep
Thus th e line on the ring
.
ened the i n ner outline
eter
w ill
This is due to th e fact that the outer visual rays
.
hind above the c entre
w ould
.
“not fore sh or t
it is
are ta n gent in fro n t belo w the ce n tre
t he
th e ellipse s
above and belo w th e ellipse s
rese n ted by concentric ”
,
if
.
w ill
of
seen
,
the diam
its centre
w ould
in
describ e
be represe n te d
When behind by a circl e ,
in front
.
The outline
of
the
ring must be represe n ted by a line tan ge n t to the circle s repre senti n g the sphere
pa r a l l e l
t o th e
p
el l i s e
is
not an ellipse
.
I ts
ou tl in e s a r e th u s ve ry n e a r ly
p r es e n ting
re
It should be noted that it
.
if
f a line is parallel to an ellipse th e
ce n tre
o
th e
Parallel ellipses are impossible
.
ng ri
.
,
FREE—HAND
122
DRA WING
Fr a m e s of
In the frames polygons
of
diago n als ings
of
86
of
represents a cubical frame of
AB C D
as
e nd
and
EL
of
other lines
t wo
three lines C ontinue
.
.
Thus
.
contain the
,
of
w hich
A ny
angle
,
,
from E
being extend
any inner line to an outer
,
is found
gives point
I, w
Thus
.
hich is in
the
of
the obj ect and a point in the continuation
second inn er line
I K,
,
and
top gives a point in an inner e dge ,
le ft
.
the inner square any line
obj ect is an of
face ,
an y
,
edge
the inner figure being in the
.
dra w n gives p oints in E F, E G ,
of
concentric
,
Th e diagonals angl es
found
th e outer this point enable s us to test dra w
these obj ects
Figur e
.
regular shapes are
The angles
.
.
of
AB
EG
continued to
EF
continued to the ext ends to the
w hich
.
Figur e 8 7 represents an equilateral triangular frame The an gles
of
to th e centre s se ct each other of
a
the inner triangle are in perpendiculars
of
the opposite S ides
at
,
other sides B and
C
.
Figure
88
the triangle
A ny
.
side
w hich
,
3 .
,
From
a parallel to t 3
is in the edge
represents a square
tange nt to th e inner square
.
2
1
,
,
4,
Th ese lines inter
.
A gives points and in the Any side as A may be co ntinued
to the outer triangle giving short edges gives
of
the centre
the inner triangle as ,
.
D
,
A circle A
p arallel to
fr ame w ith
a
he .
FREE
124
HA ND DRA WH VG
-
.
.
ing of a cylindrical obj ect having a moulding and gro oves about its sur face .
Figure
0 9
p icture
represents the
plane and the visual ,
rays converging to w ard the eye These rays inte rsect th e p icture pl a n e a n d give u po n it th e pers pective s of .
,
th e vario u s poi n t s to Th e upper form on
p age
,
w h ic h
A
th ey p as s
i s th at
,
of
.
th e tor u s expl ai n ed ,
1 20
.
Th e central B i s th e revers e of this form ,
,
appe ar l i n e s to p oin t s
,
—6 5
an d
6 8 5, , 7 , , — axe s 6
t h e s h ort 5 lines N and M ,
,
the ellips e
p age
,
in t h e el evation
Th e rays
.
i n ters ec t th e picture pl an e an d give ,
an d
if
—8 , 7
of
th e ellip s e s
.
Th e curve d
visible end above the long axis ,
of
.
is tha t
C
Form
7
—8
Th e circle s
.
of
the double cone
,
explained
on
1 20
.
Va s e For m s
Figure
9
2
is an elevation representing t he vase sho wn
by the model draw ing Fig ,
tak e is sho w n
at
.
9 3,
th e right side
line representing th e body long a xi s
.
of
the ellipse
of
in
of
of
w hich
a common mis
th e draw ing
,
w here
th e
th e vase extends to th e
the neck
.
The outline
of
the body must at l east pass tangent to the ellipse as ,
at the le ft and it ,
neck body
of .
m ay
pass above the ellipse
the vase t hus extends inside the outline
The
.
of
th e
PER SPE C TI VE When the top ‘
i
of
th e vase
PR LV CI PL E S
is
at right an gles in
circles are conce n tric and appear as
ts
,
Figure
94
,
,
appear s fuller and more nearly th e handle is foreshortened
the ellipse
,
,
.
any conical form
6 9
a vase
of
w hich
the eye must have more than hal f of Fi gure
intersection
of
,
w hose
the section
th e stem appear to end above the ce n tre
for
is
of
elevatio n
an
and the visual rays
of
real shape the more
indicated by the light li n es
is
of
it s
represents the botto m
95
li n es
.
Whe n the
.
of
handle exte n ds to w ard the eye the li n e
Th e
75
.
Whe n a handle proj ects from the side
.
actual form
the axis
to
Fig
the vase its thickne ss breaks the outlines
Figure
125
.
it s
.
of
exte n ds to w ard sur face visible
.
a vase the picture plane ,
,
.
The rays intersecting the picture plane give th e posi ,
,
tions and the le ngths
of
the short axes
represe n ti ng the thre e plinths being draw n the other line s
of
,
9 7,
are readily placed
The cu rved lines
,
A B ,
and
,
C
These
.
,
.
.
of
th e neck appear above to i n tersect
plinth
A
of
the long axis
the upper ellipse plinth
of
the ellipse s
the model draw ing Fig
the lo wer ellipse of
of
,
and belo w they end above ,
B
.
Th e body
th e vase is represented by a line tangent to or above
the lo w er ellipse Figure w ith
8 9
of
plinth
B
is an elevation
.
of
the lo w er part
of
a vase
a spherical shaped body and a cylindrical base
having a curved moulding
.
FR EE
126
The curve d edge body
the vase
of
ellipse
w ill
in Fig
as
When
of
the position
,
w ider ,
DRA WING
.
be dra w n as the t orus
The
.
represented by a line tangent to th e
is
narro w the line ,
ma y
the upper base
of
ing u pon
ellipse
ND
99
.
of
the plinth at poi n ts depend ,
the eye
.
When the ellipses
a re
of
the
be tangent near the ends .
the tangent p oints may be near th e short
axis (Fig I f still w ider the curve of th e body appears a co n tinuous line covering part of the base (Fig .
,
.
Figu re
1 02
is an elevation
of
a vase
w hos e
appearance
convergence
of
the
Th e elevation gives the positions and lengths
of
the
to the eye situated at th e point ( visual rays ) is given by Fig 1 03 ,
.
,
short axes
of
of
.
the ellipses representing th e di fferent circles
The long axes are shorter tha n the actual diameters ,
v ase
The upper edge
of
th e
straight lines
a,
tangent to the
and
C , w ill
visib l e
,
a,
is
‘
c on i c al
The short
.
t wo
be seen until the larger ellipse
ellipses
,
.
of
the circles because they are behind th e picture plane
.
,
B
C is w holly
.
The student Proj ection of
,
m ay test
the form and
e c ti on
w h o h as
it s
h is
a kno w ledge
O rth ographic
of
ability to draw from a description
position by taking any sheets ,
of
pro
sho w ing obj ects one a fter another supp osing the
j obj ects to be se en
model dra w ings
,
fro m
w hich
a certain point and making ,
shall represent them
.
Thus Fig ,
.
FREE— HA ND
128
D R A l VI zV G
.
allo w so that they may be given the pro p er convergence ,
.
The student should not attempt to have the vanishing points come on th e paper
of
give th e tangent points l ice
a nd
f
s ax i
,
p
The distanc e bet w e en t he centre centre
of
able
The long axis
of
.
th e square is of
the centre
w here
so
of
is l zor i
lzor izoh fa l l in e
a
.
the ellipse and th e
5
w ide , if
is,
ho w ever in front ,
and in a larger
d raw m g,
the axis should be draw n
,
.
of
the ellipse
through the centre the di fference able
is
r cl e ci
slight as to b e hardly notice
th e square
the ellipse is
Tl ie
.
el l i se
l l ze
o
the base
th e circle and square and
th rough them the ellipse must pass zon t a l ,
of
The diameters
.
w ould
be very notice of
The axis passes through th e centre
and must b e represented by a vertical line
.
th e square
,
Its length
is readily determine d by re ference to the vertical ed ges of
the cube
w hich
,
are hal f
as
long as th e axis
The cylinder is next to be considere d circle is in the plane w ill
of
the front face
be best draw n by means
scribes it
The
.
of
side s
of
of
of
.
The nearer
.
th e cube and i t ,
the square
w hich
circum
the square are parallel and equal
th e right front face
of
the cube O f course — — — the distanc e 5 6 must be less than 3 4 as 3 4 is less than
to those
.
,
— — 0 2, and 4 5 is less than
diagonal s
of
point the axis
3
se e
is
a
Th e
.
,
of
the cylinder is draw n
.
horizontal diameters give four points in long axis
F ig
( the square give its centre and through this 2
-
little in front
of
The vertical and t he
the centre
ellipse
of
,
w hose
the square
,
PER SPE C TI VE PRINCIPL ES
129
.
and at right angles to the axis sam e
the cylinder
of
the farther end may be draw n
w a y,
In the
.
The length
.
of
the cylinder being t wice the side of the cube the dis — — t ance 7 8 is perspectively equal to 5 7 ,
.
The h exagonal prism is the last obj ect w ith
it s
one face in the plane
base is parallel to
AB
,
from 9
to
1 0,
AB
line
of
AB
It is vertical
.
A d iagon al
.
_
,
of
Its length m ay be placed on perspectively equal to 5—6 the dis .
,
— tance 6 9 being perspectively equal to
— 4
'
Points
5
.
1 1,
—1 0
and 1 3 (dividing 9 into four perspectively equal p art s ) b ei n g pl aced diago n al s of th e h exago n exte n d from 1 1 and 1 3 t o w ard the le ft ha n d vanishi n g point — The side 1 4 1 5 having been draw n th e diagonals 1 1 1 5 1 2,
,
,
,
-
-
.
-
,
and
1
— 14 give 3
the
centre
of t he
h exagon
Through
.
— this point the diagonal parallel to 1 1 1 3 p a sses , and the l ines from 9 of n
the base
arro w e st
t he
,
and 16
10
and
T his
.
diameter
place in it th e 1
7
Th e le ft vertical fac e
.
sho w s that for
c
be
alled
by m ean s
w ell
for
is nearer than
6
of
d
16
.
Such angles may be de
.
the cube and ,
for
to dra w this obj ect fi rst even ,
th is reas on it w hen
it is not
.
The edges
of
the cube Fig ,
.
the
If
smaller angles are desired they
t wo
planes the diagonals
1 06,
to -
1 3, a n
lines at definite angles w ith th e
round and the vertical plane g w ill
1
A appears
—1 3 inclines u p w ard slightly from
These draw ings call t e r m in e d
remaining angles
t wo
,
,
of
being p erp endicular it s faces c an
are at
be obtained by
— FR EE HA ND DRA WING
130
subdividing the angles oc c u
pl a n e
Figure
(
e n e cl
1 07
fore s horte n ed an d
’
sho w s that equal
an
l e s g
M e f
si d es o
an
y
a ngl es a r e
,
m u s t b e repre s en te d b y th e gre ater a n gl e ”
th ey
,
angle l e s s th a n
w ill
s ide s are m uch
angl e gre ater th a n
app e ar
an
f ore s horten ed
°
0 9
an
y
in
m ay
inc
a ny
s m a l l es z ‘
18
0
°
w ay
as to appe ar
so
I n th e
.
an y ob tu s e a n gl e m ay b e pl ace d s o a s to
appe ar s m aller or s een th at
f act ,
n
s iz e up to
y
w ay
see
th e s a me
s m aller or gre ater th a n it s actu al dime n s io n s s ame
I
.
a n gle up to
acute a n gl e m ay b e p l ace d
Any
.
m ay appe ar gre ater th a n
0 9
th e s malle s t a n gle m ay app e ar An
,
w h ich
appe ar s m aller
w ill
,
w h e n it s
,
mo s t
is
By h oldi n g a tri a n gul ar card th e s tude n t an
i c p
or es nor l
f a n g l e th e p art w h ich
n o t f ore s horte n ed
th ey are th at
ual
appear unequal
e qu al a n gl e s appro ach th e po s itio n in
as
q
to tlze
r e a ra
g
e
,
.
s o th at to divide
,
n e ve r a
w it/z
‘
l a rger , !l ie m or e Zne
an d
ppea r
e qu a l a ngl e s
py ing l ifi e r e n l p os izions
w hen l u re
In making this division
of
it must be noticed that
.
‘
re ater th an g
a ngl e
m ay
p er cep t ibl e
Su c h p ra c t ic e w ill
it s
pp ea r of
a
a ngl e u
p
re al s iz e
d im en s ion s
a ny
t o one o j
'
more quickly th a n
'
,
and
1
80
an
it i s
f
r om
°
y
.
o ther
w ork
s h o w th e s tu dent w h eth er h e re ally u n ders t a n d s th e prin ci l e s , p
or h a s b ee n merely memorizi n g th em
w h ich
u n fortun ately
f o un d
e n tirely u s ele s s
is ,
th e o n ly and
w ay
.
Th e l atter
m an y s t u dy
tho s e w h o h ave b ee n
,
w ill
be
w orki n g
th u s mu s t s tart agai n w ith th e determi n atio n to s e e ,
,
w ith
— FR EE HA ND
132
DRA WI N G
’ .
retreating lines appear to converg e or vanis h to w ard a point called their v a nishing point Parallel ,
,
-
.
O f t wo
parallel and e qual lines
the nearer appears the longer
w hich
do not vanis h
,
.
retreating line app ear unequ l a y the nearest appearing th e longest E qual
spaces on
an
,
.
All
lines
en ds are unequally distant fro m th e eye
w hose
ap pe ar to va n i s h
H orizontal
,
.
retreating lines above the eye appear to ,
descend or vani sh do w n w ard ,
H orizontal
,
,
.
retreating lines belo w the eye ,
ascend or vanish up w ard ,
,
a
ppe ar to
.
P aralle l re t reating horizon t al lines app ear to van is h ,
at th e level
A
of
th e eye
.
h orizontal line at th e level
z on t al ,
z on t al
of
and a horizontal plane at this level a p pears a hori
~
line
.
The vanishing point -
of
se t of
any
parallel lines is
parallel to them passing through the eye the vanishing point -
direction
of
any lines
,
we
.
H ence
,
in .
"
a
t o se e
must look in thei r
.
O f t wo
th e
h o ri
the eye appears
parallel and equal lines
nearer
O f t wo
m ay
w hich
appear th e shor t er
equal lines
w hich
are fo reshorte ned
,
.
are perpendicular to each
other and have one end common the one at the greater ,
a ngle v
w ith
the picture plane ap pears the sh or t er and
anish es at the greater angle
,
.
PER SPE C TI VE PRINCIPL E S If
of
one side
a square vanishes tow ard the le ft the ,
other side vanishes to w ard th e right
When a n gl e s ge n ce
'
Th e
-
w ith
l e n gth s
th e picture pl an e
are equ al
7
“a n gl e s
th e
an d
,
u
of
.
a s qu are m ake equ al
t h ey
,
appe ar
i n cli n atio n
an
equ al
of
d
co n ver
.
“a n gl e of
depe n ds
of
equi dis ta n t s ide s
two
133
.
i n cli n atio n
po n th e l evel
of
of
an
an d
th e eye
retre ati n g li n e
y
its di s ta n ce f rom
th e l i n e b ut it i s al w ay s much l e s s th a n th e real a n gle ,
th at th e li n e m ake s Th e converge n ce
w ith
b oth e n d s
If
f ace s ,
ened
'
” ,
Th e
.
e nd
w h ich
alw ay s th e f arth er en d
is
i n vi s ible f ace
p arallel l i n e s i s
of
th eir f arth er en ds
of
th e p icture pl an e
of
an
in
.
th e dire ctio n
i s a poi n t of a n
th e edge m u s t b e co n s idere d
as
l in e
an
.
f in vi s ibl e
edge are poi n t s
y
y
of
o
“n ot for e s h or t
eve n if it s e n ds are u n equ ally dis ta n t from th e eye
.
S traigh t li n e s m u s t gen erally b e repre s ente d b y straigh t l i n e s I f two
of
an d
,
vertical l i n e s b y vertical s
th e vertical s ide s
s ee n b oth s et s ,
of
th e
,
th e
a cub e or pri s m are
of
h orizo n tal l i n e s appe ar to co n verge
Wh e n on e diago n al a vertical li n e
of
oth er appe ars a h orizo n tal l i n e
Wh e n th e pyramid
is
vertical
tical li n e thro ugh th e centre of
of
,
an d
it s x
,
and
.
vertex
th e b as e
is in
a
ve r
.
an i s o s cele s or e quil ateral tria n gl e
in a p erpe n dic u l ar to th e b as e at Th e lo n g
.
a h orizo n tal s qu are appears
s ide s van i s h equ ally in e ach dir ectio n
Th e vertex
.
s hort diago n al s
it s
of
ce n tre
is
.
th e regular h exago n
FR EE
134
-
divide the diagonal p arts
HA ND DRA WING
w hich
.
they intersect into four equal
.
The circle generally a pp ears a circle a straight line or ,
an ellipse
.
A horizontal circle
,
ab ove or belo w th e level
appears a horizontal ellipse of
The centre
the circl e
of
of
a line
w hich
O nly
at
On e
If
of
any
w h ose
the ellipse appears perp endicular to
of
the curved sur face
of
w ith
an
.
the visible en d app ears an ellipse the invisible end ,
app ears an ellipse proporti onally
w ide r
than the visible
.
of
The long axes axis
.
the cylinder
,
end
.
a cylinder can appear a straight line
end is se en the end does not appear a circle If
long axis
.
Th e othe r end appears an ellipse
.
of
above or belo w
is at right angles to th e circle at its centre
one end
tim e
w hen
,
The long axis
of
the ellipse is not a
th e eye appears an ellipse
is not a vertical line
,
.
The foreshortened vertic al circle the level
the eye
the circle does not appear the centre
,
of
of
.
the ellipse and the long axis diam eter
,
of
the cylinder
A ny p art
of
th e ellipse s are perpendicular to th e .
the convex sur face
se en at on e time
.
of
the
c
one may be
When the cone is vertical and belo w
th e eye more than hal f is visible 5 w hen above the eye ,
less than hal f
.
,
HA PT E R
C
U ES T I O N S Q a n sw e r ed
To be w r it ing
Draw
Un l es s
.
in
ll owi g q
lo
ng
1
all
l
in
th
d r a w ings
w e r e gi
of
an d
f ace
3
z on t a l
l
centre
t w o f ace s
and
s ite ce n t re
1 s tu
of
t ra c e
e a r n a c e s p
of
r i n c i p
are
pl e s
l
it s
1 t e a c h t h is
l m
r p ob e
e s s on
.
th e
an d
a
4
and
,
’
t wo
lo n g
fo ur
'
,
s,
to
—A
.
upper edge
su b
j
u p on
the
ect
l g
d is c o
v
to
ass
f or
t yp e
e re d
m
-
to gro un d
fo ur
edge s verti
.
.
vertical f ace s vi s ibl e
s,
an d
K
C R O SS
,
.
e dge s vertical w ith
,
top
,
eye o pp o
4,
an d a se co n d cub e
h ool
h
s tu d e nt s
by
h a v ing
l v
of
e ac
h
C r os s p e n c i a ri ou s a p a nd s tu d h n gs u n t i t h e e t ra c i t y
w it
ans w e re d a t .
45
°
.
a rt s c
be .
“not fore s h or t
,
a s in Proble m
C ub e
d e nt
h ou r
appe ari n g equal
,
5
as s of
e dge s ver t ical lo w er f ace ho ri
an d on eye l evel e d ge s
,
o n eye l e vel on ly o n e f ace vi s ible
.
an
l
.
eye l evel
on
vi s ible
at
f ace
cub e on eye l evel
C ub e ,
.
f ace
by
,
M od e l
t o be
a re
e s s on s ,
th e righ t o n e appe arin g very n arro w 4
y
t o t h e e n t e rin g c
vi s ibl e an d
th is
of
C ub e w ith f our
.
en
S99, in fi ft e e n
I
on e
C ub e w ith
.
v
u e s ti on s
Th e edge s
.
C entre
c al ,
s t a te d ,
i f
n e ce s s a r
1
C ube w i
en e d
l e m n e ted , pp
su
.
.
.
2
n
A r t Sc h oo
a
h alf
se ot /ie r w i
XAM I NAT I O N S
g
ml
or
by d r a w ings ,
.
s.
T h e fo N
E
FO R
VI I
f or
th e
m l
h om e
h e n giv e w rit t e n e x p l ai n t he m at th e n ex t
u at e d
,
an d
l
.
I
t
Q UE s
w ith four
am e s iz e
vertical s th e m
S TIO NS FO R wi
,
1 37
.
j us t
edge s v e rtical an d
lo w er cube
of
EXA M INA TIO NS
th
of
a sp ace
4
over th e bet ween
’
.
A
6
.
s qu are pr is m
4
’
x
8
its ax i s h orizo n t al on eye
’ ,
,
le vel and appe aring a po in t it s face s vertical or ,
,
z on t a l
7
S am e ob j ec t hori z o n t al b elo w eye ,
appe ari n g a ver t ical l in e If
.
G ive
.
o n eye level 1
of
C ub e
.
C ube
0
.
f ac e 4 1 1
’
edge
s
C ub e
.
at
°
vi s ible an d appe ari n g e qu al 9
c l ne d
i
14
f ace s
,
vertical 1
5
cube
an d
ed ge s vertical
belo w eye abov e eye
of
b e l ow
,
to p
of
1
6
.
vi s ibl e
,
n
,
arro w er
lo we r
t w o f ace s
w ide
vertical
l e ft vertical
f ace
,
an d
th e
as
,
two
.
edge s ver t ical
f our
‘
e ye
v
an d at the le ft i s ible
s ame s ize directly in
ri gh t
w ith
an d
th e .
e dge s
t w o in
C ub e
edge s
.
f ro n t
w ith
of
a s eco n d
sp ec t ato r
,
w ith
.
above
fo ur
,
f our
an d i n s ame plan e s a s co rre spo n di n g
first cub e
an d
th
o n eye level
a s in l as t probl e m b u t
t w o f ace s v i s ibl e
face s
t he
th re e face s
C ub e
.
wi
vi s ible
C ub e
.
excep t
4
.
.
to ground ;
45
f ac e
,
le ft vertical f ace a pp e aring t w ice a s 13
a
,
,
C ub e
.
ati m ake s f a c t ory
vi s ibl e th e le ft appearin g t h e .
le ft b as e
edge s vertical l o w er
s am e a s in Probl em
C ub e , f o ur
f a ce s
th
.
fo u r
,
t w o f ace s
above eye
.
12
,
4
’
w i ,
ac t u al appe arance
abo v e dra w i n g i s no t
s a t i s factory repre sen t ation 9
l
.
.
8
hO I
‘
e
e y
an d at righ t
edge s vertical
.
,
w ith
thre e f ace s
FR EE —H A N
13 8
1
7
C ub e
.
of t h e s
,
,
wi
of
cub e a t ri gh t
t h t hre e
an o t h e r cub e
f ace s as
vi s ib le an d
co rre s pon d
.
Th ree s qu are pri s m s
.
.
w ith
an d lo w er face s in s ame pl an e s
ing f ace s 18
WING
in l a s t probl e m b ut
as
am e s i z e a t t h e le ft
it s fro n t
DRA
D
4
,
’
x
the
above
eye
,
t h t heir axe s in th e s ame horizon t al l in e Th e f ac e s of t he pri s m s a r e ver t ical or horizon t al an d t h e cen t ral “ o n e h s it s lon g e dge s no t fore s h or t en ed ; s pace b e t we e n pri s m s 8 T h e interior a h ollo r c t angul ar pri m a s f w o e s 9 s e e n fro m a po in t in on e end s ur fac e the e y e 4 t o t h e ri gh t of it s le ft e dge an d 4 above its lo w er e d ge s z a w e P ri s m 8 x i h o ri on t l ith th e e d x s 4 g l o n g h o ri z o n t al T h e i n t e rio r of a h o r izo ntal h ollo w s qu ar e 20 k f qu are a e en ro m a poin t s s s 1 2 t h ick an d h l n t i 4 p v e r t ic a l e d ge ab ove t h e ro un d in a g 5 l on g ver t ical w i t h t h e A pri s m 3 s qu ar e “ hori z o n t al ed ge s of on e v e r t ica l f ac e n o t fore s h o t wi
.
,
a
’
,
1
.
’
,
’
.
,
’
12
’
z
’
12
,
,
’
.
,
.
'
'
2
,
’
.
’
21
12
,
.
’
,
,
r
e ne d ; 22
e ye
8
’
ab ove
ro un d g
S ame pri s m
.
for e s h ortene d ;
wi
6
’
e ye
a
th
.
two
bo ve
ver t ic a l
ro un d g
f ace s
equ ally
.
i f s t h ick the t op ace ; 3 “ f o re s h o rten e d b elo eye i t h n o t A t w o e d ge s w w 4 ed e i s s uppor t ed cen t r ally ab o ve t h e pl in t h f o cub e g 3 b y a v e r t ical w ir e p as s in g t hro u gh t h e c e n t r e of a b o ve b o t h o b j e ct s T h e botto m f ace of cube is f s e o f e an d v ertical ace s are p arall l to t ho h e t e ye 2
A
.
plinth
6
’
s
qu are
,
2
'
”
’
.
,
’
.
,
plin th
.
2
’
FR EE
14 0
of
b as e s
’
s
3
ide
,
is
—H A N D
v e r t ical b elo w eye ,
t en ed
35
6 3
f ac e
.
l a t eral
f ace
an d
belo w eye
w ith
,
” “ an d no t fore s horten ed ,
it s
centre
one
fac e
on e l ateral
the eye b ein g oppo
.
S am e ob j e c t h o ri z on t al above
.
,
w ith
.
S ame obj ect vertical
vi s ible
,
vis ibl e an d the ri gh t l a t eral f ace appe arin g
a ver t ical lin e .
w ith t w o
.
S ame obj ect vertical
.
8 3
th is
“n ot
”
l a t e ral face s vi s ibl e equally
ite
one l a t eral
S am e o b j ect vertical an d abov e eye
.
37
.
w ith
of
,
fo re s h or
,
e ye ,
th e t o p
w ith
horiz o n t al an d th e l o w e s t h orizon t al l ateral edge
f ac e a
,
vi s ibl e an d t h e h orizon tal edge s
face
s
WING
DRA
,
ppe aring a ver t ical l in e 39
.
S ame ob j e c t ho rizon t al ab o ve eye
.
,
l a t eral f ac e s h o r t en ed .
” .
t h l a t eral ri gh t at th e t h e l e ft
wi
,
lo w e s t
“ h o rizon t al and th e l a t eral edge s no t fore
S am e ob j e ct h orizon t al o n
0 4
w ith
e
d ges
of
f ace
s am e angl e
on
,
,
ro un d ex t ending t o the g
th e
as
ro und b elo eye w g
s
hor t edge s extend to
.
4
1
.
R egular h e x ago n al card
“no t fore s h or t ened ;
i t s cen t re oppo s i t e eye an d a lon g diago n al ver t ical ,
2 4
it s
.
S am e ob j ec t
w hen
revolve d direc t ly b ack ab ou t
lo w e s t co rner t ill a t ab o u t 43
.
S ame o b j e c t
lo n g di ago n al 44
.
w hen
S am e ob j ec t
s ho rt di agon al s
w h en
°
45
wi
th
groun d
.
h orizon t al b elo w eye ,
5n ot f o re s hor
‘
.
,
w ith
a
t en e d
horizon t al ab ove eye
“n ot fo re s h ortene d
,
” .
,
wi
th
Q UE S
A
45
.
fac e
edge s 6 4
,
w ith t h e
t fores h ortened
h orizontal edge s
La t eral edge s
.
o t h er
,
t h t h re e n arro w e s t
lateral f ace s vi s ibl e th e righ t appe arin g ,
.
of
Pro bl em 4 5, w i t h
of
Th e plinth
.
s ame s ize j u s t ove r th e firs t and ,
plinth s at pl an e
12
’
th e
to
righ t
righ t
are
12
’
of t h e
abo ve gro un d
ame ver t ical pla n e
plinth are h o rizo n tal righ t 8 4
of
of
axe s
,
two
;
on
groun d
E ye 6
“n o t f ore s hor t ene d
S am e ob j ect
.
gro und ex t endin g to ,
ex t en d t e le ft 0 5
.
5
8
’
lo ng b ase s ,
e ye ,
5
face s
2
’
s id e
,
” .
t h l ateral ed ge s of f ac e on righ t at s ame angl e a s s hort edge s
S am e ob j ec t vertical
t hre e l at eral n arro w e s t ,
inverted b elo w eye ,
face s
vi s ibl e
,
.
edge s
,
w ith
two
of
l ateral fa c e s
.
S ame a s
P ro b lem 5 1 ,
excep t
vi s ible th e le ft appe ari n g th e ,
5
to
its l a t eral
,
.
'
.
vi sible equ ally 2
e ach
.
; R egul ar h exago n al pyramid axi s
b as e
the
wi
th e ri gh t app e arin g t h e 1
of
f ace s
.
upper
ab ove gro un d an d
’
l eft so lid s
l a t eral
two
,
49
of
ax e s
th e fro n t h ex agon s are in
an d
.
h t e ;
re s t s o n a l a t eral f ace o n gro un d b elo w edge s
o t her e qual
o bj ect s a t t he l e f t
of t h e
axe s
R egul ar h exagon al pri s m
.
a s econ d plin t h
th eir axe s b ein g in a ver t ical
,
Th e lo w er pl inth s re s t
7
of
.
wi
47
s
14 1
.
S am e o bj ect re sting on a b as e on gro und b elo w
.
the
“n o
long
3
INA TIO NS
regul ar hexagon al plin t h re s t s o n a l at e ral ,
’
E XAM
FO R
on gro un d b elo w eye
hexagon s
e ye ,
TIO NS
n
w ith t hre e
arro w e s t
.
l ateral
FR EE
14 2
53
b elo w
e ye ,
axi s appe arin g v ert ical
th e
T wo
.
s
“n o
and
t
,
er t ice s
t o ge t h er
,
one h o riz o n t al l ine belo w
t e ned horizon t al
f ore s h or
is
round g
on
.
v
,
f o rmin g
e ach h e x ago n b ase
p yr amid s t heir
uch
an d t h eir a xe s eye
.
S am e ob j ec t re s t in g o n a l a t eral f ac e
.
54
HA ND D R A WING
-
A
” .
E ye
.
th e
lo n g diago n al to ri gh t
’
4
of
l e ft
of
.
A
55
.
“n o t f o r e s h o r t ene d ,
circul ar t abl e t
cen t r e o n
level
e ye
.
S a m e ob j ec t v e r t ical
6 5
.
w ith
and
b elo w eye
“n o t fo re s h o r t ened
ho riz on tal diam e t er
,
w ith it s
” .
b u t ob j e c t mo ved in S am a s P rob le m e 57 55 o w n pl ane to t h e ri gh t ,
.
it s
.
8 5
A
.
leve l
circul ar t abl e t
h o rizo n t al
w h en
on
e ye
.
59
Th e s am e b u t ab ove eye
.
,
A cir c ul ar tab l e t v e r t ical
60
.
in g a
lin e
righ t
of
62
t h e t ab le t T wo
.
w h en
to th e
60
.
and
b elo w eye
w heel s
u po n
.
S am e obj ect axl e h o rizon tal o n eye level an d
.
64
,
circul ar di s k s rep r e s en t in g
,
n ot
b e lo w eye an d ap p e ar
in a p arall e l pl an e
in P ro b le m
an axle th e axle v er t ical 63
,
.
.
S ame o b j e c t
,
,
te n e d ob j ect
f o re s h or
.
S am e
.
,
axl e b e lo w and at
,
65
.
S ame
w he el s of of
s
Probl e m
as
am e
s
ize
,
wh o s e
64 ,
the
righ t
of
eye
,
.
w ith
axle i s in
firs t b u t s ligh t ly at th e l e ft ,
,
”
horizo n t al an d S l i gh t ly fore s ho rtened
th at
an d
an o t h er p air t he
o f e ye
.
s
of
ame l i n e a s
FR EE —H A N
144
8 7
A
.
WING
DRA
D
h ollo w cylinder diame t er ,
diameter g v er t ical an d ab o ve eye S am e ob j ec t horizontal o n 79 ,
,
ax i s ex t en din g to right at an angle 80
.
,
ing b ack 8
1
82
,
in ner di ameter
6,
p ail
of
.
b elo w 84
e ye ,
A
.
wi
th
,
ho r t e n ed .
w ith
.
,
wi
.
The
.
ide s
A
.
w ire
9
.
of
9
.
.
.
b o tt om vi sible
e iven el v ation g
th
s ide s
of
s
circul ar con ical
A
;
cen t re w hen
s
,
qu are in
se c
qu are s u n e qu ally f o r e
t im e s l arger 5 ver t ical b elo w e ye 1
w he n
.
,
p an of
,
wi
th
it s
pan o n
inv e r t ed
,
‘
.
rc l e s ci
l evel
e ye
,
abov e
ver t ical
.
wi
e ye ,
th
.
doubl e co n e
of
giv e n
s
ec t ion
w h en
vertical
.
S am e o b j e ct o n
A
,
.
s qu are s equ ally fore s h ortened
rin g circul ar
s ho rten ed ; cen t re 2
.
h o op s dividing its s ur
e qu al h eigh t
w round b elo eye g ,
h orizont al an d f ore s h orte n ed 1
;
rin g o n eye l evel
of
S am e ob j e c t
b elo w eye 0 9
of
ob j e c t ill u s t ra t e d
circle s h orizon t al 89
o uter diam
.
and fo re s h or t ened 88
s e c t I on
,
‘
s
e ye ,
.
Th e s am e b u t lo w er plin t h
85
.
of
part
pe de s t al
tion b elo w eye
86
,
,
th
of
in s id e
S am e obj e c t re stin g o n an e lemen t o n gro und
83
87
,
in t o th re e b an d s
f ace
s
wi
1,
ro un d b elo w g
w iven s ec t io n b elo eye g
S am e ob j e ct
.
length
circle s vertical an d exten d
4 ;
to right ; ce n tr e
A
.
in
circul ar rin g s qu are
A
,
.
.
.
eter
1
.
A cyli n der
on
,
in
th
,
axi s
.
s ec t io n ver t ica l an d
ey e level
w ith
,
wi
,
f or e
.
mo ul ding at b as e
,
See
s ketch
.
X M UE S TIO N S F O R E A I NA TIO N S Q
145
.
A
93
.
s
qu ar e fra m e s q uare in s ection ve r t ical ,
,
th with wi
,
cen tre o n eye level i t s s quar e s fore s hor t en e d an d ,
,
a n in s crib ed c ircul ar plin t h 94 e
S ame ob j e c t b e l o w
.
x t ending b ack t o righ t 95
An
.
w hen
,
hor t ened
s
97 wi
s
;
qu a r e s
e ye
s
er t i c al and ,
;
qu ar e s hori z on t al
t rian gul ar frame s quar e in s e c ab ove eye w i t h t riangl e s ver t ical an d fo re a n d t h eir lo w e s t s ide s horizo ntal ,
,
.
o n gro un d b elo w eye e xt endin g t o righ t a t the
f rame w hen
lo n g hor izon t al e dge s
,
,
,
ame angle a s the s ho r t ho riz on t al s e x t end t o le ft
s
8 9
S ame objec t vertical and b elo w eye
.
,
urf ace s e qu ally fore s hor t en ed
s
99
A
.
,
.
equil a t eral
Th e given
.
th
,
v
.
s ide s u ne qu ally for e s horte n e d
6 9
t ion
e ye
S ame ob j ec t belo w
.
t h eir
.
circul ar di s k
,
w ith
it s
,
v
.
er t ical
.
a h an dle t o fo rm a
circ l e and h a n dle vertical b elo w eye ,
circle
;
fa n
°
fore s h ort
ened ! 1
S ame ob j ec t hori z o n t al belo w eye ; h an dle
00
.
,
fore s horte n e d 1
u
01
,
,
02
w ide,
4
S ame ob j e c t re stin g ob liquely o n gro un d and
.
pon a cube b elo w t h e eye 1
e
.
e y ’
R epre s ent
.
to
5
s quare
w al l s ,
e ach s ide
righ t
of
l e ft
an d
’
an d
t h e l ef
en d
of
an d part ’
th e
3
w all ,
th
of
a
w all ,
an d
t w o face s
roo m
an d floo r '
5
vi s ibl e
1
’
.
h igh
0
,
1
’
5
l in g ; and c e i '
above floo r
.
A
b ox
h igh i s in t he righ t corn er a gain st th e
another b ox
t w al l
,
wi
,
'
2
s
quare an d
8
’
long i s again s t
.
B e gin b y repre s ent in g
th e
box a t
the
righ t a s it
FR
I 46
appe ar s
and
,
of t h e
line s
— EE H A N D
WING
van i s h in g p oin t s
it s
use
DRA
o t h er ob j ec t s
.
th e
for
parallel
.
M a ke ano t her dra win g b e gin n in g b y re p re s en t in g fi r s t t h e b ox a t t h e l e ft and u s in i van i s h in g t s g poin t s for t h e parall el line s of t h e o t h er o bj e c t s 04 I f P rob lem s 0 03 are unsa t i s fac t o ry m ak e a b e tt er dr a w in g T h e s ame roo m s e en fro m a po in t 3 ab ov e 05 fl o or a n d 7 5 t o ri gh t of l e ft w all R epre s en t circul a r h o l e s of t h e s am e s iz e in fl o o r an d ceilin g t h e ir c e n t re s in t h e s am e ver t ical l in e ; t wo circul ar h ol e s in t he ir c e n t re s 4 b elo w t h e t h e end w all diam e t er s ceilin g ; a n d t w o m or e hole s of t h e s a m e s ize an d o n s ame level O ppo s i t e e ach o t h er on e in e a ch s ide w all S ho w t hic k n e s s of h ol e s in all w all s 03
1
.
,
,
.
1
2, 1
1
.
,
,
.
’
1
.
.
,
’
,
,
,
,
.
.
Th e
06
1
.
t wo
s
ide
1
wi
E ye
.
07
th
4
An
.
’
ce
on
it s
,
08
.
The
angl e s to flo o r an d ,
floo r
.
w in do w ,
a
arch ed t o p
in
b ove eye in ri gh t ,
.
ilin g;
w all
t h e w all , w i
o ne ver t ical and s
t h e w all
18
th the
,
per p e ndi c ular t o 1
,
l o n g b ox in
,
h igh a gain s t ,
th e
i n t e rior r e pre s en t in g o n e re t re a t in g w al l
floor an d
t op
,
,
t
ab ove floor
10
’
,
ho w in g fl oo r ceil in g an d
w i h s emicircul ar
an d a circul ar
w all ,
w all
,
door w ay
a
s
equ ally fore s hor t en e d
w all s ,
th e co rn er le ft
am e ro o m
s
’
h i gh
,
wi
S tair s
6
in c h e s
h igh
.
,
,
ab o ve flo o r
th
t h e w a ll l e adin g t o a t hen c e b a c k t o an o t her ,
b o o k ca s e
o th e r h o rizon t a l an d
E ye 6
am e in t erio r
A
cyl i n drical va s e s
t wo
’
.
.
,
s
t air c as e
righ t
at
l andin g l an din g
.
4 1
’
’
0
a
b o ve
ab ov e
WING
FREE —H A N D
14 8
th e
b e low e q u ally
an d
e ye ,
face s
t wo
of
.
th e
cu
v s
.
A
1 22.
r
e gul a r
pli nt h r e s t s
h e xagon al
o n gro un d b elo w e ye w i t h t h re e l a t e ral t h e ri gh t f ac e a pp e a rin g t h e n arro w e s t ,
.
are s qu ar e s 12
i ib l e
be
3
a
fac e s La
b ase
vi s ibl e
t e ral
,
fa c e s
.
S am e o b j e c t r e s t in g
.
on
w ro un d b el o g
th e
e ye ,
s
id e s
on
a
of
s
l a t eral
qu a r e
fa c e
on
on
ro un d g
e qu ally fore s hor t en e d 1 24
Thre e
.
e
b y fro n t an d t o p th e
a
rro w
qu al v
s
p l aced
qu ar e pri s m s
dire c t io n
f ro m t h e
ie w s an d s e e n ,
a s s h ow n
of
.
18 h i h and w id e 5 5 g w h e n t h e end w i t h fl oo r ce ilin g an d b o t h s id e w a ll s is
12
A
.
room
end is
wh o se
’
'
1
,
,
,
,
i
s
een f ro m a po in t
righ t
w al l
6
ab o ve
’
S h o w a door
.
,
t h e floo r
t able
w indo w ,
to
l e ft
of
and c
h a ir
of
an d
’
6
p ro p o r t ion s F I RS T E X A M I N A TI O N FE B 2 8 99 “ A s qu ar e card v er t ical an d n o t fore s h ort 26 it s ed ge s a t 4 5 t o t h e gro und e ne d s A qu ar e card h oriz on t al a n b lo i t h d e w w e e 7 y n o t fore s h orten e d t w o e d ge s 8 A s quar e card h orizo n t al an d o n e ye l e vel w i t h it s e dge s equ ally fo re s hor t en ed A circul ar c ard i s ver t ical i t h en t r w i t s c e 9 () t s s urf ace extendin g t o le ft a t a n angle on eye l e vel an d i b u f A s c o n d c irc l ar card o s am i in z e e s n e a d () s ame pl ane w i t h i t s c e n t r e dire c tly o v e r t he c e n t r e of th e fi rs t usu
al
.
1
.
1
.
,
,
1
.
,
°
.
,
12
.
,
,
”
.
12
,
.
,
.
12
a
.
,
.
,
.
Q UE S
A
1 30
.
TIO NS
cub e
wi
,
E X AM I
FO R
th
edge s ver t ical
of
“no t fo r e shor t ened
edge s
A
pyramid b as e ,
u p on t h e t op the
of
th e
s ide s p arallel
1 '
of
3
1
py
w id 1
3
A
.
ey e level
.
8
’
long h as it s b a s e ,
cen t re s co inciding and
.
two
s
th
e ye
of
obj ec t s appe aring
wi
,
ide s
b elo w top
'
3 ,
the
33
4
’
level a t cen t re
2
di ame t er and
'
of
axi s
of
equal
6
h igh
4
,
,
’
,
.
di ame t er axi s
cylinder
A
.
face
”
t he
vertical cylin der
co n e b as e
b as e on 1
,
,
,
,
.
2
A
an d
,
two
c ube
9
lon i s ab ov e and e e 4 g y f ac e s vi s ible an d o n e s e t
qu are ax i s
s
S ame o bj ec t s
.
ram i d
th
8
’
,
14
.
'
edge s
h a s fo ur
NA TIO NS
th e
lon g re s t s
’
,
u
axe s fo rmin g on e l ine
s quare pri s m
4
’
x
4
’
x
8
o n th e groun d b elo w t h e eye
’
,
po n
it s
.
re s t s o n a l a t e ral
t he
lon g ed ge s ex
t endin g t o t h e righ t at the s am e angl e t h a t t h e s hor t on e s ex t en d to th e le ft A circle i s in s cribe d in t h e .
vis ibl e b a se
co n e s b a s e s
T wo
,
to p la t eral
f ace w ith
4
’
diame t e r axe s
1 34
T hre e
.
cube s
th e b a s e s t an gen t t o t h e edge s of 4
’
.
edge
,
on e
is
4
G ive 1
35
.
’
Th e upper cub e i s
.
,
Th e
cub e i s on eye level and o ne f ace i s vi s ibl e
belo w th e cen t ral o n e
4
t h eir ver t ical edge s cen t re of t h e central not fo re s h o r t en ed above an d t he l o w er
”
,
,
.
ac t u al appearan ce in every p ar t icul ar If
th e above i s
n o s sible repre s e tatio n p
of
.
s ame ver t ical line s
the
re s t o n th e
,
top an d t o e ach o t h er
th e
in
.
n ot
of
.
s ati s fac t ory m ak e
th e o b j ects
,
.
th e
best
r
FREE
0 5
HAN D
-
DRA
WING
.
Wri t e b rie fly th e f ac t s re gardin g t h e di ffe r e n c e s
tw e en
dra w ing s E
1
34
.
1
35
.
XA M I NAT I O N
A vertical
1 36
an d
be
FE B 3, .
cylin der b el o w
diam e t er
t h e e ye ,
length 7
13
S am e ob j e ct ab ove eye
.
1 38
S am e o b j e c t
.
9
.
S am e as Prob le m
h ori z o n t al o n
is
axi s
no t fo re s h o rten ed
l e vel and 13
when
.
e ye
” .
1 38
,
b ut
e
lem e n t s and vi s i
bl e b as e fore s h orten e d e qu ally an d a s e con d cyl in der ,
of s 1
am e S ize j u s t un der t h e fir s t 0 4
.
A
cub e b elo w eye
wi
.
t h t h re e
f ace s
vi s ible an d
un equ ally fore s h or t e ned an d a h orizo n t al circul ar h ol e ,
pen e t ra t in g t h e cube 1
4
f ace
1
.
2 4
.
regul ar h e x agon al pl in t h re s t in g o n a l a t eral
on groun d b elo w eye
Face o n grou n d
.
edge s are u nequ ally fore s h or t ened
whose 1
A
S e e vie w s
.
.
A
s
is
a s qu are
.
qu ar e pl in t h re s t s o n gro u n d b elo w
e ye ,
t h t w o v er t ical f ace s vi s ibl e equ ally A con e i s ce n t rally pl ace d o n the pl in t h S e e fro n t vie w R epre s n t th e o b j ec t ho w n b y f ron t and top s e s 43 vi e w s w hen th ey are b elo w t he e ye and s e en fro m t h e direc t ion of th e arro w wi
.
.
.
1
.
.
X A M I NAT I O N A PR I L 30 8 9 6 n s A h oriz o t al circul ar ring qu a re in ection s 44 b elo w th e eye the o u t s ide diame t er 5 t h e in s ide 3 E
1
,
Q
u e sti on s
for t h e
.
,
.
s e c on d
1 36 t o exa
mi
1 60,
nat i on
in c .
l siv u
e,
,
.
,
,
1
1
v
w e r e gi
en
in p r e p a ra t ion
FREE
I 52
E 1
c
A
6 5
.
H A ND
-
DRA WI
X A M I N AT I O N JU N E
circul ar ring
ircle s are ver t ical ab o ve ,
VG
4,
s
.
6 9
18
s qu are in
,
I
.
ec t io n
w h e n it s
an d fore s hor t ene d
t h e e ye
.
D iame t er of rin g on e s ixth it s o u t s id e diame t er A circul ar ring circul ar in ec t io n w hen ho ri s 57 z on t a l belo w t h e e e y f The lo er p ar t vase ho n in ron t vie 8 w o w f w s 5 w h e n ver t ical b elo w eye T h w f ob j ec t s h o n in ro n t ie h en vertical s v w w e 59 -
.
1
.
,
.
1
.
,
,
.
1
.
b el o w eye 1
The
60
.
w h en
.
b elo w
arro w
obj e c t s S h o w n b y fro n t an d
th e
eye an d s een fro m t h e
61
.
E
X A M I N A T I O N A P RI L
f ace s
2,
18
of
the
99
.
R epre s e n t a regul ar h e x agon al plinth
r e s t s o n a l ateral are
s
f ace
qu are s an d ,
o n t h e gro un d th e
righ t b ein g t h e b as e
th e
th e
on e
,
w h ich
Th e l a t eral
.
of
ed ge s
ro un d are equ ally f ore shor t en e d g
th e
vi e w s
.
S EC OND 1
to p dir e c t io n
o n e on
the
vani s h i n g
to
t h e vi sibl e h e x a go n T h e ce n tral por t io n of t h e plin t h i s c u t a w ay t o form a he x a gon al p ipe w h o s e inn er diame t er i s h al f t h e o u ter R epre s en t a circul ar ring circular in s e c t ion 6 w h en i t i s horiz o n t al an d ab ove t he eye R epre sent a do ubl e cro s s w h en it re s t s o n t h e 63 groun d b elo w t h e ey e w ith on e a m ver t ical and t w o arm s h orizon t al and equally fo re s horten ed R epre s e n t a cub e w h ich re s t s on on e edg e on 64 th e gro u n d b elo w th e eye w i t h t h re e fa c e s vi sible it s of
.
,
1
2
.
.
,
,
.
1
.
r
,
.
1
.
,
s
,
Q UE
S TIO NS
i nclined edge s a t
I
E XAM N
FO R
i s ibl e N
45
,
.
w h en
M ake
R
8
’
s
een
ab ov e th e ground
EC T I ONS
FO R
Ex AM I N
produce a plea s in g ge n eral e ff ect dime n s io n s u pon th e
The
tion s de s ired m e n s ion s
An y
.
are
s
1
A T I oN s
the
x
I
s
vie w
1
.
i n ch e s
5
,
u sI n
g
s pace s t o
an d
.
k etch e s
give the prop o r
cale m ay b e u s ed
Wh ere di
.
giv e n t hey are un important b ut t h e
n ot
,
gen eral app eara n ce s ho uld b e given b e t w ee n
in t h e t op
.
arra n gin g th e dra w i n gs
an d
,
by fro n t an d top
indicated
as
th e dra w i n g s upo n p aper
ide s
Wh o s e
.
they are
DI s
is
a cub ical
its p arts b e in g a s qu are
fo urth
and from a level
both
of
t h a t of t h e cub e R epre sen t t h e ob j ects s ho w n
on e
-
f or m
,
th e s ec t io n
65
vie w s
Th e le ft v e r t i c al f ace
.
a w ay t h e in n er por t io n to
ow c u t
ide i s 1
53
.
frame , s
1
.
to t h e gro un d an d th e ho rizon t al
°
edge s v an i shin g to t h e righ t v
A TI O NS
D e fi n ite
.
ob j e ct s are u n n ece s s ary
in
s pace s
que stio n s
1 18
Th e dra w ings are to be m ade fr e e h a n d b ut th e
,
c or
-
rect van i sh i n g of all l i n e s i s t o b e S ho w n equ al s pace s ,
are t o b e mark e d
,
al l
importa n t
w orki n g
e iv n an d invi s ible e d ge repre en t ed s s g ,
Fini s h
w ill
co u n t
for
corre c t ly in an arti stic ro ve and ac en c t p N
a n d on e
-
.
.
w ay ,
t h e w ork
— T h e t im e h a l f h ou rs
OTE
l i t tl e ;
a
ll ow
ed
a
and
,
are
to be
.
n swe r if
l in e s the
qu e stion s
tim e
remain s
mi
wa s
,
im
.
f or t h e s e
exa
n at i on s
on e
D E FI N I T I O N S
.
A lt i t u d e
t he
Th e p erpen dicul ar
.
b as e s o r be t w een the
v
,
lid o r pl an e fi gure
so
A n gl e w hich
th e
,
of
a
.
mee t o r ten d to m ee t an d t h e po in t
si de s ,
angle
ertex an d t h e b a s e
The di fferen ce i n
.
di s tance b et w e e n
of
d irec
t ion
of
t wo
lin e s
Th e l in e s are c a lle d
.
mee t in g
,
t he
ve r t ex of
of
an
the
.
An
an gl e i s me a s u re d by m e an s
c ircl e de scrib e d cl ude d b e tw e en ver t ex
th e
of
I f the
fro m it s
it s
s
an gl e
radiu s
of
i de s
v
er t ex
a cen t re an d
as
of t h e a r c
Th e centre
.
a
of
a rc
in
i s th e
.
t h e C ircl e
of
move s th ro ugh
th e
C ircum feren ce i t pr oduce s an a ngle w h ich i s ta k e n a s t h e un i t for me a s u rin g an gl e s a n d i s c a lled a d g T h e de gree 5 divid e d in t o s ix t y e qu a l p ar t s call e d m in t an d t h e m in u t e s into s ix t y equ a l p a r t s c all e d ,
e
,
r ee
.
1
u es ,
.
D e gr e e s bols w rit
,
min u t e s an d ,
T hu s 5
.
te n
se c
de gr e e s
13
,
o nd s
d eno t e d b y
are
min u t e s
,
12
se c
sym
ond s
,
is
’
°
5
13
A R I G HT ‘
AN
G LE
is
on e w
radi u s movin g t hr ou gh 71 I t is a n an gl e of 9 0 »
h ic h i s
of
th e
form e d c
by t he
ir c u m fe r e n c e
.
°
AC UT E an
l e g
.
AN
GLE
.
An
a
n gl e l e s s
t h an
a
r
igh t
DE FINITIO N S O BT a
ngle
U S E A N GL E
An
.
l
.
angl e greater t h an
57
right
a
.
D I H EDRA L A N G L E in t er s ecti n g plan e s O BL I Q U E A N GL E
open ing be t w een
The
.
two
.
O n e w h ich
.
angle
ANGL E
mee t at a point ex
of
it s
An
.
of
cen t re an d ab o ut
through
th e
Fig u r e
a
centre
equal par t s
Bas e
of
A
.
s
O
parall e l s
s
id e s
of
a
ho rte st or long e s t
a ny s
a figure
a nd
,
C ir c cu
le
A
h ich
w ith i n
ca
,
c
a re
ll e d
The
ENC E
I
i nto
t
a pyramid
con e s
The
.
s
of
ide
e
.
into
a
cir c u m fe r e n ce
,
cen t r e
Th e
.
,
an d
lo w e s t
th e
.
.
a
poi nt s
al l
q u a lly di s tan t fro m
the
oppo s i t e
eq ual par t s
t wo
.
T he
.
an i s o s c e l e s t riangle
l a n e fi ur bo unded by e g p
alled
pri sm s
of
p arallelo gram or trapezoid
d ivide
To
.
r ve d lin e
of w
a nd
ylinder s
of
,
.
di ffer
p as s in g
divid ing
id e in any oth e r tria ngle b ut u s u all y
Bis e c t
.
.
ppo s i t e p arallel p olygon s
of C
urf ace s
th e
w h ich
s traight lin e
Th e po ly gon oppo s ite th e ver t ex
p l ane
an o b j ec t
of
.
Th e
.
w hich
im agin ary s t raight lin e
parts are symme t rically arranged
A x is
two
b y plane s
.
S o l id
a
pa ss in g thro ugh e nt
formed
O ne
.
The s ummi t or highe s t p oin t
.
A x is
a right
n ot
.
SOLID Ap
is
a
poin t
.
b ou n d a ry lin e
is
call e d
th e
U
C I R C M FER
.
D I A M E T ER
.
A
s
traigh t lin e dra w n thro ugh
the
— REE H A N D
r 58
F
WING
DRA
.
cen t re an d con n ecting oppo s ite poin t s in t he ,
c u m f e re n c e ,
R A DI
US
as
b
.
The di s t anc e fro m
.
c ircum ference w ith
a
as c e
,
S E M I C I RC L E in g it
a
it s
centre to th e
.
H al f
.
r Ci
a circle
d ia m e t e r ,
~
,
d b
as a
f orme d a
by b isect
.
A ny p ar t of th e circum fe rence as b A s traight l in e w h o s e end s are in t h e C H O RD
AR C
.
,
e
.
.
C
ircu m ference a s f g S E G M E N T The p a rt .
,
of
.
c h or d
and a
a rc
S EC TO R
f Th e p ar t
.
radii an d an
h
as
a rc , a s
b
a circle bo unded by an
l z gf of e c
.
a C ircl e b o und e d b y b
t wo
.
U A DR ANT A sector boun ded by w rad o t Q an d on e fo ur t h of th e circum fe rence a s a c d T AN G E NT A s t raight l in e w h ich mee t s a c i b u t b ein g produc e d doe s n o t c u t it c u m fe r e n c e Th e po in t of meetin g i s call ed the p oin t as b d u
.
a
,
.
r
.
,
,
.
f o C s
con t a ct o r
p oin t of
i r c u m s c r ib e
.
crib ed a b out a C ircle
a tangen t t o b ed c u m s c ri
the
A
ta nge n cy
.
polygo n i s s aid t o b e circum
w hen e ach
circle ; an d a
ab o u t a poly go n
s
polygon
w hen
on c a v e
C
one
.
C urvin g in w ardly
.
A
s
olid b o unded
b a s e , w h ich
is a
C
by
polygon i s
i s s aid t o b e C ir
th e th e
circum ferenc e ver t ice s
of t h e
.
a pl an e s urface calle d
ircl e ellips e o r o ther curved ,
figure an d by a l ateral s urface ,
t he
.
C
th e
of
fc l e ci
th e circl e p a s s e s thro ugh all
of
id e
,
w hich
i s every w here
FREE HA ND D R A WING
1 60
C or n e s
‘
-
,
u
b
The
.
of t w o s
ol id o r C
r
e
A
.
C y l in d e
and by
r
s
poin t
id e s
of
mee t in g of
a pl an e fi g u re
o lid b o un de d b y
A
.
s
x s si
t h e e d ge s of a
.
qu a re f ace s
olid b o und e d by a curved
o ppo s i t e
two
of
f ace s
c alled b as e s
.
su
r fac e
h t e ;
b as e s m ay b e ell i ps e s circle s or o t h er curve d fi gure s an d n am e t h e cylind e r Th u s a c ir ,
,
,
c u l ar
w ho s e
.
cyli n der (t h e ordin ary b ase s a re c ircl e s
fo rm )
is
o ne
.
A R I G H T C I R C U LA R C Y L I N DE R i s gen era t ed by t h e r e vol u t ion of a rec t angle ab o u t on e s ide a s an a xi s Th e s ide ab o u t w h ich the rec t angl e r e v olve s s call e d t h e b n t of t h e cyl in der al s o i ts i T he side oppo s i t e t h e axi s de s crib e s t h e .
i
ax s
c
e
.
urved s ur f ac e
o i t ion s s p D e ve lop
th e
s ur face
is
of
th e cyl in der an d in an y ,
called an
e l e m e n t of
of
an obj ec t
.
l ong w he n
t hey s nor t
an d
p arall e l s ide s D ia m e t e
,
r.
ven n umb e r
t wo
O
The
b
,
.
Se e
C ircl e
of s
ppo s it e s ide s .
call e d
t h ro ugh t h e c e n t r e a s w h e n t h ey e x t end b e t w e e n
as a
,
are
p ass
an e
E d ge
w h ich
.
,
d,
.
in any poly go n
I n re gul ar poly gon s di a gon a l s c
it s
.
A s t raigh t l i n e ver t ice s no t a dj acen t
o nn ect s
th e s ur face
of
To unro ll o r l ay o u t upo n o n e pl an e
.
D i a go n a l c
,
is
I n a re gul ar p oly gon
.
wi
ide s a l in e j o in i n g t h e cen t re s ,
o ft en
ca
in t e r s e c t ion
ll e d
a
d i ame te r
of a n y t w o s
th of
.
u rf a c e s
.
The
DE FINITIO NS bo un dary li n e
E
.
1 61
.
dg e s are straigh t or curve d
r e pre sen t e d b y lin e s
a n d a re
,
.
A dra w ing m ad e on a vertical pl an e by m ea n s of pro j ec t ing l in e s perpe n dicular t o t h e pl an e fro m th e po in t s of t he ob j ect Th e t erm s ele vatio n ver t ical pro j ec t ion and front vie w all h av e th e E l e v a t io n
.
.
,
,
s
ame me an ing Ellip
s e
.
A
.
,
pl ane fi gure bo unded by a lin e
t h a t the s um of th e di s tan ce s of any po in t in i t a s c fro m t w o given po i n t s and f called e
,
,
is
f po in t mid w ay bet w een oci,
equ al to a given l in e
as
t h e foci
The T RA N S V ERS E
\
a
b
Th e
.
i s called the
AX I S
of
ce n t r e
is
It
al s o called t h e
m aj
UGAT E AX I S
w h ich
c an
m inor
or
b e dra w n a s ,
s l zor t
axi s
or
or
C O NJ
Th e
b e dra w n
c an
c
or
d
th e
in
axi s
-
it , a s
a
b
.
.
i s t h e s horte s t diameter d
I t i s al so called
.
p oints in th e lo n g diameter c
l ong
T h e fo ci ,
.
.
an ellip s e i s _
lo n ge s t diamete r th at
uch
,
'
,
s
i s equ a l to o ne h al f
a
-
b
e
and f are
w ho s e
the
t wo
,
di s t a n ce fro m
.
t h e pl an e s ur face s of a s olid It may b e b oun ded by s t raigh t or curved e dge s A ppare n t d ecre as e in leng t h Fo r e s h o r t e n i n g due t o a po sitio n o blique to th e vi s u al ray s Fa c
e
.
of
O ne
.
.
,
.
.
i
H o riz o n
level
of
.
th e eye
H o r iz o n t a l wa
A ccording t o geometry l ly I n pictorial art a horizo ntal l in e at
om e t r c a
Ge
te r
.
.
.
,
the
.
.
Parall el
to the s ur f ace
of
s mooth
FREE [ IA N D DRA WING
1 62
-
.
I n dr aw in gs a l in e p arall el to t h e t o p ,
of
the
s
lns c
circl e the
h e e t i s called horizon t al r ib e
.
t ouche d
polygon i s s aid t o b e in scrib ed in a
an d a
ra
l
S u rfa c
e
The
.
cludi n g t he b a s e or b a s e s ve
a is
circle
l
of t h e
Ey
e
s u r f ace
of
a
s
o lid ex
.
.
A
l in e
r e pre sen tatio n h a s S T RA I G H T
h as
len g t h only
w idth
.
fa
Th e level o r po s itio n
.
ho riz o n t al plan e p a s s in g t hro ugh t h e specta t o r L in e
in
in s crib e d th e
of
.
La t e
Le
.
C ircle i s s aid to b e w h en th e C ircum ference of b y e ach s ide o f t h e po lygon
po lygon
b o ttom
all it s ver t ice s are in t he circum f erence
w h en
C ircle ;
A
an d
.
s
eye
.
I n a dra w in g it s
b ut i s called a l in e
O n e w h ich
’
o
.
h as t h e s am e direc t io n
t h ro ugho ut i t s en t ire leng t h C U R V ED O n e n o p ar t of w h ich i s s t raigh t N ei t h er h o rizo n t al nor ver t ical O b liq u e H aving th e s am e direc t io n an d e v e ry Pa r a l l e l w h ere e qu ally di st an t At an angle of Pe r p e n d i c u l a r Pe r s p e c t i v e Th e art of m aking upo n a p l an e call e d the p ict p l n s u ch a rep re s e n t atio n of ob f e c t s th a t th e line s th e dra n app ar to co in cide o w i e j g w i t h t h o s e of t h e obj e ct w he n t h e eye i s at one fixe d po in t calle d t h e t t ion p oin t D I A G R A M A n e x ac t perspec t ive dra w in g ob It t a ine d s cien t i fi cally by p ers pec t ive me t hod s i s o ft en very f al s e pictorially w h e n no t s een fro m t h e s t a t io n p oint .
.
.
.
.
.
.
.
,
.
ure
a
e,
,
s a
.
.
.
.
FRE E—HA ND
1 64
A
.
cyl i n de r o r pri sm
lea s t dimen s ion s
e tc
u r e a , q
an gle s
s
,
WING
.
figure s are tho s e th at h ave th e s ame s h a p e
Sim il a r
Pl in t h
DRA
.
ci rc
,
acco rding a s i t h a s
,
qu are s
Po l y g o n
ul a r
It is
.
.
,
e tc
A
.
for
,
base s
who s e
,
.
it s
axi s i s
t r ia ngu l a r , C
ircl e s
t ri
,
.
pl an e figure b o unde d b y
s
trai gh t
I
lin e s
An
EQ
U I LAT E R A L
are all equ al
An
EQ
A
is one
wh o s e
side s
.
U I AN GUL A R
are all equal —
PO L Y G O N
PO L Y G O N is
o ne
w ho s e
angle s
.
R E GUL A R
PO
LYGO N
eral an d eq ui angul ar
i s on e
w h ich is e q u ila t
.
PA RA LL E L PO L Y G O N S are th o s e re s pec t ive l y p a rall el T R I AN GL E
A
.
w ho se
s
ide s are
.
po lygo n h aving th re e s ide s
.
s n f s U A DRI L A T E R A L A p o lygo h aving o ur ide Q PE NT A G O N A p o lygo n h avin g fi ve s ide s H E X A G O N A po l ygon h aving Si s ide s H EP TA G O N A p o lygo n h avi n g s ev n s ide s A polygon h aving eigh t s ide s O C TAG O N N O N A G O N A pol ygo n h avi ng n in e s i d e s D E C A G O N A polygo n h avin g ten s ide s A pol ygon h avin g eleve n s id e s U N D EC AGO N D O DE C A G O N A polygon h aving t we lve s id e s .
.
.
x
.
.
e
.
.
.
.
.
.
.
.
‘
.
.
.
.
Th e centre in t ers e ctio n
.
of of
m iddl e poin t s
'
of
a regular p olygon perpen dicul ar s it s
s ide s
.
is
th e com m o n
e rec t ed
at
the
DE FINITIO NS
i s a s oli d b o u n ded b y p l an e s
A PO l y h e d r o n '
15
regul ar Th ere I
h a s f our 2
s
be b ut
fi ve
tria n gu l ar f ace s
PY R A M I D , w h ich
or
,
.
H E X A H EDR O N
Th e
.
,
or
C
U BE
,
w h ich
x si
has
qu are face s .
O C T A H EDR O N , w hich
The
3
.
a n gul ar f ace s 4
5
angul ar f ace s
l ar po lyh edron
!
th e
,
applied o nly t o a regu
o th er term s m ay be applied
i n fini t e n umb er
an
t w elve p en
h as t w e n t y t ri
w h ich
is
to irregul ar p olyhedro n s al s o
h as
.
Th e term h exahedron
An
,
w hich
.
Th e I C O SA H EDR O N
.
t ri
h as eigh t
.
D O DE C A H EDR O N
Th e
.
t agon a l face s
.
of
infi n ite n umbe r
irregul ar polyh edro n s oth
of
1
,
Pr i s m
polygo n s
A
.
s olid b o un de d b y
h avi n g th eir e qu al
,
thre e or more p arallel o gram s Th e polygo n s
a re
p arallelogram s th e l a t eral f ace s the ,
Pri sm s on a l , e t c
-
.
,
f
a ce s ,
e dge s
l a te r a l
\
t wo
e qu al
ide s parallel
p arallel ,
b a s es
of
th e
th e inter s ectio n s
,
A R I G HT
,
by
,
of
the
th e
.
t r ia ngu l a r ,
e tc
an d
pri sm
s
q
ua re,
p
en t ag
accordi n g a s th e b as e s are t ri angle s
qu are s pen tagon s
.
.
called th e
l a te r a l
are c alle d
s
,
s olid s bo u n ded
b y pl a n e or curved s urf ace s m a y, b e con ceived ‘
s
.
regular pol y h edro n s
Th e T E T RAH EDR O N
.
It
.
its f ace s are regul a r eq ual po lygo n s
w he n
c an
1 65
.
,
.
PR I S M
is
on e
in w h ich
th e edge s
— FREE HA ND
1 66
DRA
WING
.
co nn ec t in g t h e b a s e s are perp en di c u l ar b ases
to
the
.
An
U
O BL I Q E PRI S M
i s o ne in
w h ich t h e
edg e s
onn e c t ing t h e b as e s are n o t p erp endicul a r t o t h e
c
bases
.
A R E GU LA R P R I S M are regul ar polygo n s
A
i s a righ t pri s m
whose
b as e s
.
T R U N C AT ED P R I S M
is
th e
in cl uded b e t w een th e b a s e an d
p ar t
a s
a pri s m
of
ec t io n m ade by
p l an e in cline d t o t he b as e an d cu tt in g all t h e l at e ral ed ge s T h e A L TI T U D E of a pri s m is t h e perp e ndicul ar di s t ance b e tw een t h e b a s e s T h e AX I S of a re gul ar pri s m i s a s t rai gh t line c on ne c t in g t h e c en t re s of it s b a s e s A R I G H T S E C T I O N of a pri s m is a s ect ion m ade b y a p l an e p erpen dicul ar t o it s l a t eral e d ge s A PA R ALL E L O P I PED is a p ris m w h o s e b a s e s are a
,
.
.
.
.
p a rallelo gr am s Pr o f il e
The
.
Pr o j e c t io n sc u
j
t a t ion
n e c ti g
Py
f
ra
m id
O rtho graphic
.
.
of
an ob j ec t
T he
.
A
s
of w
ol id
,
the
h ic h
on e
ar e
vie w or
re p r e
pyramid
c a lled
.
.
f ac e ,
o th er f ace s
are t riangle s h a vin g a commo n
th e
.
an ob j ec t ob t ain ed upo n a pl an e b y p ro
a p olygon an d
ver t ex of
fa c e s
co n t o ur o u t lin e
line s p erpendicul ar to t h e pl ane
ba s e , is a ces ,
of
.
ve
,
c
edges .
all e d
alled the
the
l a te r a l
r t e x call e d
T he in t er s e c t io n s of
t h e l a te r a l
c
th e
l ate r a l
FR E E
1 68
s
-
I I A I VD
A R E C TAN GL E are righ t angle s
is
DRA
WING
.
a quadril ater al
w ho s e
a n gle s
.
A S Q U ARE i s a re cta n gl e w h o se s id e s are equ al A R H OM BO I D i s a p arall elogra m w ho s e a gle s .
n
ob l ique a n gle s
a re
A R H OM BU S
.
i s a rho mbo id
w ho s e
s ide s are
e qu aL
The O
s
id e upo n
w h ich
a p arallelo gram s tand s
and
ppo s i t e S ide are called re s pectively its lo w er
upper b a se s Q
u a
an d
.
i
d
the
r s e c
t
.
To divide in t o fo ur equ al p arts
.
t r e a t in g G oin g a w ay from A pro j ectio n upo n a pl an e p arallel to a Se c t ion cu t ting pl an e w h i ch inters e cts an y ob j ect Th e s e c t io n gen erally repre s e n t s th e part b eh i n d th e c tti g p lan e and repre se n ts t he c t s ur face s b y cro s s h a t ch i n g Sh ade an d s h ado w h av e abo u t th e S h a d ow s ame me an i n g a s gen erally u se d ; b ut i t w il l b e w ell t o de sign a t e b y s h ado w t h o s e p art s of an ob j e ct w h ich w h il e a re t urne d a w ay fro m t h e d ire ct ray s of l ight t h o s e s r face s w h ich rece ive in direct ray s an d are in te rmedi a t e in val u e b et w e e n t h e light n d th e s h ado w Re
.
.
.
.
u
n
u
,
.
.
,
,
u
a
are
calle d s h ade s ur face s C AS T
.
.
The s h ado w pro j e cted
s urf ace b y s ome o th er body Sol id
;
A
sol id
has
b re adth an d th ic k n e s s ,
s ur face s
,
.
t hre e I t m ay
b y curved s ur face
,
on a n y
b ody o r
.
dime n sion s
,
le n gth
,
b e b o u n de d b y pl a n e
o r b y b oth pl an e an d
DE FINITIO NS c u r ve d
'
s u rfa c e s
As
.
9
commo n l y unders to od s p ace filled
of
i s a l imited portio n
16
.
w i th
a solid
,
m atter b u t ,
s ider eometry do e s no t con th e m at t er g .
s imply Sp h
t h e s h ap e s A solid
w ith e re
.
every point w ithi n
A c
of w
an d
S ph ere may b e ge n erat e d by th e revo l utio n
e
an
axi s
Th e b o un dary
.
dimen s ion s le n gth ,
an d
A PL A N E S U R FA C E lin e
b e dra w n
c an
in
w h il e
of
a so lid
b re ad t h
of
th e
s ur f ace
is
a s traigh t
.
of
w h ich is
curved in every of
io n s o nly an d
any n
,
no
nt
th ickne s s .
of
A
curve d li n e s
th e s olid
umb er
d ir e c
the cyl i n der an d
.
a so lid i s no p ar t
of
s
two
w hich
i s on e n o part
curved s ur face s
imply t h e b o undary
T a n ge
I t h a s b ut
.
an y directio n
th e sphere
s
give
.
.
con e are s t raigh t in on e dire c t ion The
a
.
Th e s u rface ,
of
.
i s on e up o n
A C U R V ED S U R FA C E pl an e
,
.
S urf ace s are plan e or curved
w ill
.
hich i s equ ally di sta n t fro m a poi n t
calle d th e centre
S u rfa c
t ion
s o lids
de al s
bo un ded b y a curved s ur face
ircl e abo ut a diameter a s
two
of
s ize s
an d
.
of
It
th e s olid b ut i s ,
h a s t w o d im e n
s ur face s pu t t ogeth e r
of
.
s tr aight li n e an d a curved li n e o r ,
,
are t a n ge n t
w he n
they h ave
on e
poin t co mmo n a n d ca n n o t i n ter sect ; l i n e s o r s u rface s are ta n ge n t to curved s ur face s w h e n th ey h ave on e poin t o r
on e
T r ia n g l e
l i n e commo n .
A
pl a n e
and
ca n n ot inters ect
figure
.
bo u n ded by thre e
FREE —HA ND DRA WIN G
1 70
.
.
t raigh t l in e s Th e s e l i ne s are call ed t h e id Th e angle s t h at t hey form are called t h e ngl of t h e tri a ngl e an d t h e ver t ice s of t h e s e a n gle s the v t i of t h e t ri angl e
s
s
.
.
es
a
,
es
ces
er
,
.
Tri angle s are n amed by th eir s ide s and a n gl e s
A
S C A L E N E T R IA N GL E i s o n e in
s ide s are e qu al
An
A ri E Q
t wo
w h ich t w o
.
U I L AT ERA L
T RIA N G L E i s o ne in
th e th re e s ide s are e qu al
A RIGHT
no
.
I S O S C E L ES T R IA N GL E i s o n e in
s ide s are equ al
U
w h ich
o ne
of
th e
.
T R I A N GL E i s o n e
O BT S E
w h ich
.
T R I AN G L E i s one in
angle s i s a righ t an gle
An
w h ich
.
in w h ich
one
of
t h e an gle s i s o btu s e A n A C U T E T R I AN G L E i s o n e in w h ich all t h e angl e s are acu t e Th e H Y P O T E N U S E i s t h e s ide of a righ t t i a n gl e oppo s i t e t h e righ t angle T h e o t h er s ide s are called t h e l g A n E Q U I AN GUL A R T R IA N GL E i s o n e in w h ich t h e thre e a n gle s are equ al Th e v al ue of e ach .
.
r
.
e
s
.
.
angl e i s Th e B AS E s
is
th e
uppo s ed to s tand
.
s
ide o n
;
Th e
,
l egs ,
in o t her tri a n gle s an y
b e call ed th e b as e
AL T I T U DE
th e tri angl e i s
I n an i so s cele s t riangle th e
e qu al s ide s are called th e b a se
w h ich
th e o th er s ide th e
on e of
th e s ide s m ay
.
i s th e p erpen d icul ar di s ta n c e
FREE
172
of t h e
vie w
-
HAN D
DRA
WING
o b j ect s ho w n a s e dge vie w end vie w o r f ace ,
,
,
.
W ork i n g
D r a w in g
.
O n e w h ich
in fo rm a t io n n ece s s ary to e n ab l e t h e s
.
truc t
th e
ob j ec t
.
give s
w orkman
ESTI ONS FOR FI RST LESSONS I N THE PUBLI C SCHOOLS
.
a n d S im i l a r one s s h o
re
C
u ld b
e st
ed i i n di f f e re n t p os i t i d o n s u
C ul C
a rd .
irc
ar
a rd
u n ti l t
h
e y car
Su q
.
t ic a l
a rd
u C
R e c t a ng l a r
.
a rd
Horizont a l
Sq
u
a re s
.
a nd
V
e rt i ca
l
Sq u
a re
c ad r
ul C
T ria ng
.
He xagon a l
l
a nd e a s i y
C
a rd
ar
a rd
.
.
u C
T ria ng l a r
.
Horizont a l
a re s .
V
e rt i ca
l
T ria ngl e s
.
drawn
.
u
.
C
ll
Rec t a ng l a r C a rd
Sq ua re C a rd
ar
b e we
a rd
.
.
]
