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