ect teaching can help you, but rests between your own consciousness and those higher powers that move it.
289
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, &c. 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.
THE PHI PROPORTION
EC is 1.618033, &c., times size of AB,
CD BC,
DE CD, &c.,
AC=CD
BD=DE, &c.
290Testing 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 [Transcribers Note: Plate IX].—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 [Transcribers Note: Plate XXXIII].—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 centre in the construction of the composition.
"Bacchus and Ariadne," Titian, page 154 [Transcribers Note: Plate XXXIV].—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 [Transcribers Note: Plate XXXV].—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 [Transcribers Note: Plate XXXVI].—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 291with 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 [Transcribers Note: Plate XXXVII].—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 [Transcribers Note: Plate XXXVIII].—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.
292
INDEX
A B C D E F G H I J K L M N O P Q R S T U V W
A
Absorbent canvas, 192
Academic drawing, 34
Academic and conventional, 68
Academic students, 68
Accuracy, scientific and artistic, 36
Anatomy, study of, its importance, 36, 122
"Ansidei Madonna," Raphael's, 231
Apelles and his colours, 31
Architecture, proportion in, 230
Art, some definitions of, 18
Artist, the, 27
Atmosphere indicated by shading, 102
Atmospheric colours, 39
Audley, Lady, Holbein's portrait of, 248
B
"Bacchus and Ariadne," Titian's, 154, 193
Backgrounds, 93, 141
Balance, 219
Balance between straight lines and curves, 220
Balance between flat and gradated tones, 221
Balance between light and dark tones, 222
Balance between warm and cold colours, 223
Balance between interest and mass, 224
Balance between variety and unity, 225
"Bank-note" papers, 285
Bastien Lepage, 204
Bath for etching, 283
Beauty, definition of, 23
Beauty and prettiness, 135
Beauty and truth, 22
"Birth of Venus, the," Botticelli's, 163
Black chalk, 179
Black Conté, 280
Black glass, the use of a, 120, 202
Blake, example of parallelism, 145
Blake's designs, 51, 169
Blake's use of the vertical, 155
Blocking in the drawing, 90
Blocking out with square lines, 85, 120
"Blue Boy," Gainsborough's, 223
Botany, the study of, 36
Botticelli's work, 34, 51, 145, 163
Boucher's heads compared with Watteau's, 211
Boundaries of forms, 93
Boundaries of masses in Nature, 195
Bread, use of, in charcoal drawing, 276
Browning, R., portraits of, 250
Brush, manipulation of the, 114
Brush strokes, 115
Brushes, various kinds of, 115
Burke on "The Sublime and the Beautiful," 135
Burne-Jones, 55, 71, 125, 177
C
Camera, use of the, 286
Carbon pencils, 180
Carlyle, 64
Circle, perfect curve of, to be avoided, 138
Chalks, drawing in, 125
Charcoal drawing, 54, 111, 113, 192, 275;
fixing solution, 277
Chavannes, Peuvis de, 55, 103
Chiaroscuro, 53
Chinese art, 21
293
China and Japan, the art of, 59
Colour, contrasts of, 208
Colours for figure work, 273
Colours, a useful chart of, 191
Classic architecture, 148
Claude Monet, 62, 190
Clothes, the treatment of, 253
Composition of a picture, the, 216
Constable, 149
Conté crayon, 192, 277
"Contrasts in Harmony," 136
Conventional art, 74
Conventional life, deadness of the, 270
Corners of the panel or canvas, the, 160
Corot, his masses of foliage, 197, 214
Correggio, 206
Crow-quill pen, the, 283
Curves, how to observe the shape of, 90, 162, 209
Curves and straight lines, 220
D
Darwin, anecdote of, 243
Deadness, to avoid, 132, 193
Decorative work, 183
Degas, 66
"Dither," 71
Diagonal lines, 160
Discord and harmony, 173
Discordant lines, 172
Draperies of Watteau, the, 211
Drapery studies in chalks, 125
Drapery in portrait-drawing, 253
Draughtsmanship and impressionism, 66
Drawing, academic, 35
Drawing, definition of, 31
E
East, arts of the, 57
Edges, variety of, 192
Edges, the importance of the subject of, 198
Egg and dart moulding, 138
Egyptian sculpture, 135
Egyptian wall paintings, 51
El Greco, 169
Elgin Marbles, the, 135
Ellipse, the, 138
"Embarquement pour l'Île de Cythère," Watteau's, 211
Emerson on the beautiful, 214
Emotional power of the arts, 20
Emotional significance of objects, 31
Erechtheum, moulding from the, 138
Etching, 283
Exercises in mass drawing, 110
Exhibitions, 57
Expression in portrait-drawing, 242
Eye, anatomy of the, 105
Eye, the, in portrait-drawing, 242
Eyebrow, the, 105
Eyelashes, the, 108
Eyelids, the, 106
F
"Fête Champêtre," Giorgioni's, 151
Figure work, colours for, 273
"Finding of the Body of St. Mark," 123, 236
Fixing positions of salient points, 86
Flaubert, 68
Foliage, treatment of, 196
Foreshortenings, 93
Form and colour, 18
Form, the influence of, 32
Form, the study of, 81
Frans Hals, 246
French Revolution, Carlyle's, 64
French schools, 68
Fripp, Sir Alfred, 91
Fromentin's definition of art, 23
Fulness of form indicated by shading, 102, 124
G
Gainsborough, the charm of, 209, 223
Genius and talent, 17
Geology, the study of, 36
Giorgioni, 151, 196
"Giorgioni, The School of," Walter Pater's, 29
Giotto, 222
Glass pens, 283
Goethe, 64
Gold point, 275
Gold and silver paint for shading, 125
Gothic architecture, 148, 150
Gradation, variety of, 199
Greek architecture, 221
Greek art in the Middle Ages, 130
Greek art, variety in, 133
Greek vivacity of moulding, 134
Greek and Gothic sculpture, 147
294
Greek type of profile, 140
Greuze, 221
H
Hair, the treatment of, 77, 102
Hair, effect of style upon the face, 180
Half tones, 98
"Hannibal crossing the Alps," Turner's, 163
Hardness indicated by shading, 102
Harsh contrasts, effect of, 171
Hatching, 118