APPENDIX

If you add a line of 5 inches to one of 8 inches you produce one 13 inches long, and if you proceed by always adding the last two you arrive at a series of lengths, 5, 8, 13, 21, 34, 55 inches. Mr. William Schooling tells me that any two of these lines adjoining one another are practically in the same proportion to each other; that is to say, one 8 inches is 1.600 times the size of one 5 inches, and the 13-inch line is 1.625 the size of the 8-inch, and the 21-inch line being 1.615 times the 13-inch line, and so on. With the mathematician's love of accuracy, Mr. Schooling has worked out the exact proportion that should exist between a series of quantities for them to be in the same proportion to their neighbours, and in which any two added together would produce the next. There is only one proportion that will do this, and although very formidable, stated exactly, for practical purposes, it is that between 5 and a fraction over 8. Stated accurately to eleven places of decimals it is (1 + sqrt(5))/2 = 1.61803398875 (nearly).

We have evidently here a very unique proportion. Mr. Schooling has called this the Phi proportion, and it will be convenient to refer to it by this name.

 

THE PHI PROPORTION

EC is 1.618033, &c., times size of AB,
CD " " " " BC,
DE " " " " CD, &c.,
AC=CD
BD=DE, &c.

Testing this proportion on the reproductions of pictures in this book in the order of their appearing, we find the following remarkable results:
"Los Meninas," Velazquez, page 60. The right-hand side of light opening of door at the end of the room is exactly Phi proportion with the two sides of picture; and further, the bottom of this opening is exactly Phi proportion with the top and bottom of canvas.

It will be noticed that this is a very important point in the "placing" of the composition.

"Fête Champêtre," Giorgione, page 151.
Lower end of flute held by seated female figure exactly Phi proportion with sides of picture, and lower side of hand holding it (a point slightly above the end of flute) exactly Phi proportion with top and bottom of canvas. This is also an important center in the construction of the composition.

"Bacchus and Ariadne," Titian, page 154.
The proportion in this picture both with top and bottom and sides of canvas comes in the shadow under chin of Bacchus; the most important point in the composition being the placing of this head.

"Love and Death," by Watts, page 158.
Point from which drapery radiates on figure of Death exactly Phi proportion with top and bottom of picture.

Point where right-hand side of right leg of Love cuts dark edge of steps exactly Phi proportion with sides of picture.

"Surrender of Breda," by Velazquez, page 161.
First spear in upright row on the right top of picture, exactly Phi proportion with sides of canvas. Height of gun carried horizontally by man in middle distance above central group, exactly Phi proportion with top and bottom of picture. This line gives height of group of figures on left, and is the most important horizontal line in the picture.

"Birth of Venus," Botticelli, page 166.
Height of horizon line Phi proportion with top and bottom of picture. Height of shell on which Venus stands Phi proportion with top and bottom of picture, the smaller quantity being below this time. Laterally the extreme edge of dark drapery held by figure on right that blows towards Venus is Phi proportion with sides of picture.

"The Rape of Europa," by Paolo Veronese, page 168.
Top of head of Europa exactly Phi proportion with top and bottom of picture. Right-hand side of same head slightly to left of Phi proportion with sides of picture (unless in the reproduction a part of the picture on the left has been trimmed away, as is likely, in which case it would be exactly Phi proportion). I have taken the first seven pictures reproduced in this book that were not selected with any idea of illustrating this point, and I think you will admit that in each some very important quantity has been placed in this proportion. One could go on through all the illustrations were it not for the fear of becoming wearisome; and also, one could go on through some of the minor relationships, and point out how often this proportion turns up in compositions. But enough has been said to show that the eye evidently takes some especial pleasure in it, whatever may eventually be found to be the physiological reason underlying it.

INDEX

A

Absorbent canvas
Academic drawing
Academic and conventional
Academic students
Accuracy, scientific and artistic
Anatomy, study of, its importance
"Ansidei Madonna," Raphael's Apelles and his colors
Architecture, proportion in
Art, some definitions of
Artist, the
Atmosphere indicated by shading
Atmospheric colors
Audley, Lady, Holbein's portrait of

B

"Bacchus and Ariadne," Titian's
Backgrounds
Balance
Balance between straight lines and curves
Balance between flat and gradated tones
Balance between light and dark tones
Balance between warm and cold colors
Balance between interest and mass
Balance between variety and unity
"Bank-note" papers
Bastien Lepage
Bath for etching
Beauty, definition of
Beauty and prettiness
Beauty and truth
"Birth of Venus, the," Botticelli's
Black chalk
Black Conté
Black glass, the use of a
Blake, example of parallelism
Blake's designs
Blake's use of the vertical
Blocking in the drawing
Blocking out with square lines
"Blue Boy," Gainsborough's
Botany, the study of Botticelli's work
Boucher's heads compared with Watteau's
Boundaries of forms
Boundaries of masses in Nature
Bread, use of, in charcoal drawing
Browning, R., portraits of
Brush, manipulation of the
Brush strokes
Brushes, various kinds of
Burke on "The Sublime and the Beautiful"
Burne-Jones

C

Camera, use of the
Carbon pencils
Carlyle
Circle, perfect curve of, to be avoided
Chalks, drawing in
Charcoal drawing; fixing solution
Chavannes, Peuvis de
Chiaroscuro
Chinese art
China and Japan, the art of
Color, contrasts of
Colors for figure work
Colors, a useful chart of
Classic architecture
Claude Monet
Clothes, the treatment of
Composition of a picture, the
Constable
Conté crayon
"Contrasts in Harmony"
Conventional art
Conventional life, deadness of the
Corners of the panel or canvas, the
Corot, his masses of foliage
Correggio Crow-quill pen, the
Curves, how to observe the shape of
Curves and straight lines

D

Darwin, anecdote of
Deadness, to avoid
Decorative work
Degas
"Dither"
Diagonal lines
Discord and harmony
Discordant lines
Draperies of Watteau, the
Drapery studies in chalks
Drapery in portrait-drawing
Draftsmanship and impressionism
Drawing, academic
Drawing, definition of

E

East, arts of the
Edges, variety of
Edges, the importance of the subject o
Egg and dart molding
Egyptian sculpture
Egyptian wall paintings
El Greco Elgin Marbles, the
Ellipse, the
"Embarquement pour l'Île de Cythère," Watteau's
Emerson on the beautiful
Emotional power of the arts
Emotional significance of objects
Erechtheum, molding from the
Etching Exercises in mass drawing
Exhibitions
Expression in portrait-drawing
Eye, anatomy of the
Eye, the, in portrait-drawing
Eyebrow, the
Eyelashes, the
Eyelids, the

F

"Fête Champêtre," Giorgioni's
Figure work, colors for
"Finding of the Body of St. Mark"
Fixing positions of salient points
Flaubert
Foliage, treatment of
Foreshortenings
Form and color
Form, the influence of
Form, the study of
Frans Hals
French Revolution, Carlyle's
French schools
Fripp, Sir Alfred Fromentin's definition of art
Fullness of form indicated by shading

G

Gainsborough, the charm of
Genius and talent
Geology, the study of
Giorgioni
"Giorgioni, The School of," Walter Pater's
Giotto Glass pens
Goethe
Gold point
Gold and silver paint for shading
Gothic architecture
Gradation, variety of
Greek architecture
Greek art in the Middle Ages
Greek art, variety in
Greek vivacity of molding
Greek and
Gothic sculpture
Greek type of profile
Greuze

H

Hair, the treatment of
Hair, effect of style upon the face
Half tones
"Hannibal crossing the Alps," Turner's
Hardness indicated by shading Harsh contrasts, effect of
Hatching
Health, questions of
Henner, the work of
High lights
Hogarth's definition
Holbein's drawings
Holl, Frank
Horizontal, calm and repose of the
Horizontal and vertical, the
Human Anatomy for Art Students
Human figure, the outline of the

I

Impressionism
Impressionist vision
Ingres, studies of
Ink used in lithography
Intellect and feeling
Intuitions Italian
Renaissance, the
Italian work in the fifteenth century

J

Japanese art
Japanese method, a
Japanese and Chinese use of contrasts of color

K

Keats' definition of beauty

L

Landscapes of Watteau, the
Lang, Andrew, his definition of art
Lawrence, Lord, portrait of
Lead pencil
Lecoq de Boisbaudran, M.
Lehmann, R., portraits by
Leonardo da Vinci
Light Light and shade, principles of
Lighting and light effects
Likeness, catching the
Line and the circle, the
Line drawing and mass drawing
Lines expressing repose or energy
Line, the power of the
Lines, value of, in portrait-painting
Lines of shading, different
Lithographic chalk
Lithography
"Love and Death," Watts'

M

Manet
Mass drawing
Masters, past and modern
Materials
Mathematical proportions
Measuring comparative distances
Measurements, vertical and horizontal
Medium, the use of
Michael Angelo, the figures of
Michael Angelo and Degas
Millais
Mist, effect of a, on the tone of a picture
Model, the
Monet, Claude
Morris's definition of art

N

Nature, variety of forms in
Nature's tendency to pictorial unity of arrangement
Newspaper as a background
Norman architecture

O

Oil, surplus in paint
Originality
"Our Lady of the Rocks," L. da Vinci's
Outline drawing
Outline studies and models

P

Paint, the vitality of
Paint, the consistency of
Paint, effect of oil in thick
"Painted Poetry" Painter's training, the object of the
Painting and drawing
Panel or canvas, the
Paolo Uccello
Paolo Veronese
Paper for drawing
Parallel shading Parallelism of lines
Parthenon, the
Pater, Walter
Pen-and-ink drawing
Pens for pen-and-ink drawing
Perspective, the study of
Philip IV, Velazquez' portrait of
Photograph, failure of the
Picture galleries, the influence of
Pictures, small and large, treatment of
Planes of tone, painting in the
Pre-Raphaelite paintings
Pre-Raphaelite movement, the
Preparatory drawings, disadvantage of
Primitive art
Primitive emotions
Procedure, in commencing a drawing
Profiles, beauty of
Proportions
Poppy oil and turpentine, the use of
Portrait-drawing
"Portrait of the Artist's Daughter," Sir E. Burne-Jones's
Pose, the
Peuvis de Chavannes

Q

Quality and texture, variety in

R

Radiating lines
"Rape of Europa, The," Paul Veronese's
Raphael
Red rays
Reed pens
Rembrandt and his colors
Reproduction, advantages of up-to-date
Retina, effect of light on the
Reynolds' contrasts of color
Rhythm, definition of
Right angle, power of the
Roman sculpture, lack of vitality in
Rossetti Royal Academy Schools
Rubens
Ruskin

S

Schools of Art
Scientific and artistic accuracy
Scientific study, necessity for
Scumbling
Shading
Shape, variety of
Silhouette, the
Silver-point
Silver-point work, shading in
Sitter, the
Softness indicated by shading
Solar spectrum, the
Solids as flat copy
Spanish school, the
Straight lines indicative of strength
Straight lines and flat tones, analogy between
Strong light in contrast with dark shadow
Study of drawing, the
Stump, the
Style
"Sublime and the Beautiful, The," Burke's
"Surrender of Breda, The," Velazquez'
Sympathetic lines

T

Talent and genius
Teachers in Art Schools
Technical side of an art, the
Thickness and accent, variety of
Tintoretto
Titian
Tolstoy's definition of art
Tone, meaning of the word
Tone values, variety of
Toned paper, drawing on
Tones, large flat, the effect of
Touch, the sense of
Trafalgar Square lions, the
Trees, the masses of
Turner
Types, lifelessness of

U

"Ulysses deriding Polyphemus," Turner's
Unity and variety
Unity of line

V

"Vale of Best," Millais'
Value, meaning of the word as applied to a picture
Values of tone drawing, the
Van Dyck, his use of the straight line
Variety in symmetry
"Variety in Unity"
"Varying well"
Velazquez
Venetian painters, and the music of edges
Venetians, the, their use of straight lines
Venetians, system and principles of design of the
"Venus, Mercury, and Cupid," Correggio's
Vertical, the, associated with the sublime
Vertical lines, feeling associated with
Vision
Visual blindness
Visual memory, the

W

Ward, the animal painter
Warm colors
Watteau, the charm of
Watts, G.F., portraits by
Watts' use of the right angle
Windsor, Holbein's portraits at
Whistler, a master of tone
White casts, drawing from
White chalk
White paint
White pastel

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