START OF THE PROJECT GUTENBERG EBOOK THE THEORY AND PRACTICE OF PERSPECTIVE*** E-text prepared by Louise Hope, Suzanne Lybarger, Jonathan Ingram, and the Project Gutenberg Online Distributed Proofreading Team (http://www.pgdp.net/c/) Transcriber's Note: The html version (see above) is strongly recommended to the reader because of its explanatory illustrations. In chapters LXII and later, the numerals in V1, V2, M1, M2 were printed as superscripts. Other letter-number pairs represent lines. Points and lines were printed either as lower-case italicized letters, or as small uppercase letters. Most will be shown here with _lines_ representing italics. Words and phrases in bold face have been enclosed between + signs (+this is bold face+) Henry Frowde, M.A. Publisher to the University of Oxford London, Edinburgh, New York Toronto and Melbourne THE THEORY AND PRACTICE OF PERSPECTIVE by G. A. STOREY, A.R.A. Teacher of Perspective at the Royal Academy [Illustration: 'QUÎ FIT?'] Oxford At the Clarendon Press 1910 Oxford Printed at the Clarendon Press by Horace Hart, M.A. Printer to the University DEDICATED to SIR EDWARD J. POYNTER Baronet President of the Royal Academy in Token of Friendship and Regard PREFACE It is much easier to understand and remember a thing when a reason is given for it, than when we are merely shown how to do it without being told why it is so done; for in the latter case, instead of being assisted by reason, our real help in all study, we have to rely upon memory or our power of imitation, and to do simply as we are told without thinking about it. The consequence is that at the very first difficulty we are left to flounder about in the dark, or to remain inactive till the master comes to our assistance. Now in this book it is proposed to enlist the reasoning faculty from the very first: to let one problem grow out of another and to be dependent on the foregoing, as in geometry, and so to explain each thing we do that there shall be no doubt in the mind as to the correctness of the proceeding. The student will thus gain the power of finding out any new problem for himself, and will therefore acquire a true knowledge of perspective. CONTENTS BOOK I Page THE NECESSITY OF THE STUDY OF PERSPECTIVE TO PAINTERS, SCULPTORS, AND ARCHITECTS 1 WHAT IS PERSPECTIVE? 6 THE THEORY OF PERSPECTIVE: I. Definitions 13 II. The Point of Sight, the Horizon, and the Point of Distance. 15 III. Point of Distance 16 IV. Perspective of a Point, Visual Rays, &c. 20 V. Trace and Projection 21 VI. Scientific Definition of Perspective 22 RULES: VII. The Rules and Conditions of Perspective 24 VIII. A Table or Index of the Rules of Perspective 40 BOOK II THE PRACTICE OF PERSPECTIVE: IX. The Square in Parallel Perspective 42 X. The Diagonal 43 XI. The Square 43 XII. Geometrical and Perspective Figures Contrasted 46 XIII. Of Certain Terms made use of in Perspective 48 XIV. How to Measure Vanishing or Receding Lines 49 XV. How to Place Squares in Given Positions 50 XVI. How to Draw Pavements, &c. 51 XVII. Of Squares placed Vertically and at Different Heights, or the Cube in Parallel Perspective 53 XVIII. The Transposed Distance 53 XIX. The Front View of the Square and of the Proportions of Figures at Different Heights 54 XX. Of Pictures that are Painted according to the Position they are to Occupy 59 XXI. Interiors 62 XXII. The Square at an Angle of 45° 64 XXIII. The Cube at an Angle of 45° 65 XXIV. Pavements Drawn by Means of Squares at 45° 66 XXV. The Perspective Vanishing Scale 68 XXVI. The Vanishing Scale can be Drawn to any Point on the Horizon 69 XXVII. Application of Vanishing Scales to Drawing Figures 71 XXVIII. How to Determine the Heights of Figures on a Level Plane 71 XXIX. The Horizon above the Figures 72 XXX. Landscape Perspective 74 XXXI. Figures of Different Heights. The Chessboard 74 XXXII. Application of the Vanishing Scale to Drawing Figures at an Angle when their Vanishing Points are Inaccessible or Outside the Picture 77 XXXIII. The Reduced Distance. How to Proceed when the Point of Distance is Inaccessible 77 XXXIV. How to Draw a Long Passage or Cloister by Means of the Reduced Distance 78 XXXV. How to Form a Vanishing Scale that shall give the Height, Depth, and Distance of any Object in the Picture 79 XXXVI. Measuring Scale on Ground 81 XXXVII. Application of the Reduced Distance and the Vanishing Scale to Drawing a Lighthouse, &c. 84 XXXVIII. How to Measure Long Distances such as a Mile or Upwards 85 XXXIX. Further Illustration of Long Distances and Extended Views. 87 XL. How to Ascertain the Relative Heights of Figures on an Inclined Plane 88 XLI. How to Find the Distance of a Given Figure or Point from the Base Line 89 XLII. How to Measure the Height of Figures on Uneven Ground 90 XLIII. Further Illustration of the Size of Figures at Different Distances and on Uneven Ground 91 XLIV. Figures on a Descending Plane 92 XLV. Further Illustration of the Descending Plane 95 XLVI. Further Illustration of Uneven Ground 95 XLVII. The Picture Standing on the Ground 96 XLVIII. The Picture on a Height 97 BOOK III XLIX. Angular Perspective 98 L. How to put a Given Point into Perspective 99 LI. A Perspective Point being given, Find its Position on the Geometrical Plane 100 LII. How to put a Given Line into Perspective 101 LIII. To Find the Length of a Given Perspective Line 102 LIV. To Find these Points when the Distance-Point is Inaccessible 103 LV. How to put a Given Triangle or other Rectilineal Figure into Perspective 104 LVI. How to put a Given Square into Angular Perspective 105 LVII. Of Measuring Points 106 LVIII. How to Divide any Given Straight Line into Equal or Proportionate Parts 107 LIX. How to Divide a Diagonal Vanishing Line into any Number of Equal or Proportional Parts 107 LX. Further Use of the Measuring Point O 110 LXI. Further Use of the Measuring Point O 110 LXII. Another Method of Angular Perspective, being that Adopted in our Art Schools 112 LXIII. Two Methods of Angular Perspective in one Figure 115 LXIV. To Draw a Cube, the Points being Given 115 LXV. Amplification of the Cube Applied to Drawing a Cottage 116 LXVI. How to Draw an Interior at an Angle 117 LXVII. How to Correct Distorted Perspective by Doubling the Line of Distance 118 LXVIII. How to Draw a Cube on a Given Square, using only One Vanishing Point 119 LXIX. A Courtyard or Cloister Drawn with One Vanishing Point 120 LXX. How to Draw Lines which shall Meet at a Distant Point, by Means of Diagonals 121 LXXI. How to Divide a Square Placed at an Angle into a Given Number of Small Squares 122 LXXII. Further Example of how to Divide a Given Oblique Square into a Given Number of Equal Squares, say Twenty-five 122 LXXIII. Of Parallels and Diagonals 124 LXXIV. The Square, the Oblong, and their Diagonals 125 LXXV. Showing the Use of the Square and Diagonals in Drawing Doorways, Windows, and other Architectural Features 126 LXXVI. How to Measure Depths by Diagonals 127 LXXVII. How to Measure Distances by the Square and Diagonal 128 LXXVIII. How by Means of the Square and Diagonal we can Determine the Position of Points in Space 129 LXXIX. Perspective of a Point Placed in any Position within the Square 131 LXXX. Perspective of a Square Placed at an Angle. New Method 133 LXXXI. On a Given Line Placed at an Angle to the Base Draw a Square in Angular Perspective, the Point of Sight, and Distance, being given 134 LXXXII. How to Draw Solid Figures at any Angle by the New Method 135 LXXXIII. Points in Space 137 LXXXIV. The Square and Diagonal Applied to Cubes and Solids Drawn Therein 138 LXXXV. To Draw an Oblique Square in Another Oblique Square without Using Vanishing-points 139 LXXXVI. Showing how a Pedestal can be Drawn by the New Method 141 LXXXVII. Scale on Each Side of the Picture 143 LXXXVIII. The Circle 145 LXXXIX. The Circle in Perspective a True Ellipse 145 XC. Further Illustration of the Ellipse 146 XCI. How to Draw a Circle in Perspective Without a Geometrical Plan 148 XCII. How to Draw a Circle in Angular Perspective 151 XCIII. How to Draw a Circle in Perspective more Correctly, by Using Sixteen Guiding Points 152 XCIV. How to Divide a Perspective Circle into any Number of Equal Parts 153 XCV. How to Draw Concentric Circles 154 XCVI. The Angle of the Diameter of the Circle in Angular and Parallel Perspective 156 XCVII. How to Correct Disproportion in the Width of Columns 157 XCVIII. How to Draw a Circle over a Circle or a Cylinder 158 XCIX. To Draw a Circle Below a Given Circle 159 C. Application of Previous Problem 160 CI. Doric Columns 161 CII. To Draw Semicircles Standing upon a Circle at any Angle 162 CIII. A Dome Standing on a Cylinder 163 CIV. Section of a Dome or Niche 164 CV. A Dome 167 CVI. How to Draw Columns Standing in a Circle 169 CVII. Columns and Capitals 170 CVIII. Method of Perspective Employed by Architects 170 CIX. The Octagon 172 CX. How to Draw the Octagon in Angular Perspective 173 CXI. How to Draw an Octagonal Figure in Angular Perspective 174 CXII. How to Draw Concentric Octagons, with Illustration of a Well 174 CXIII. A Pavement Composed of Octagons and Small Squares 176 CXIV. The Hexagon 177 CXV. A Pavement Composed of Hexagonal Tiles 178 CXVI. A Pavement of Hexagonal Tiles in Angular Perspective 181 CXVII. Further Illustration of the Hexagon 182 CXVIII. Another View of the Hexagon in Angular Perspective 183 CXIX. Application of the Hexagon to Drawing a Kiosk 185 CXX. The Pentagon 186 CXXI. The Pyramid 189 CXXII. The Great Pyramid 191 CXXIII. The Pyramid in Angular Perspective 193 CXXIV. To Divide the Sides of the Pyramid Horizontally 193 CXXV. Of Roofs 195 CXXVI. Of Arches, Arcades, Bridges, &c. 198 CXXVII. Outline of an Arcade with Semicircular Arches 200 CXXVIII. Semicircular Arches on a Retreating Plane 201 CXXIX. An Arcade in Angular Perspective 202 CXXX. A Vaulted Ceiling 203 CXXXI. A Cloister, from a Photograph 206 CXXXII. The Low or Elliptical Arch 207 CXXXIII. Opening or Arched Window in a Vault 208 CXXXIV. Stairs, Steps, &c. 209 CXXXV. Steps, Front View 210 CXXXVI. Square Steps 211 CXXXVII. To Divide an Inclined Plane into Equal Parts--such as a Ladder Placed against a Wall 212 CXXXVIII. Steps and the Inclined Plane 213 CXXXIX. Steps in Angular Perspective 214 CXL. A Step Ladder at an Angle 216 CXLI. Square Steps Placed over each other 217 CXLII. Steps and a Double Cross Drawn by Means of Diagonals and one Vanishing Point 218 CXLIII. A Staircase Leading to a Gallery 221 CXLIV. Winding Stairs in a Square Shaft 222 CXLV. Winding Stairs in a Cylindrical Shaft 225 CXLVI. Of the Cylindrical Picture or Diorama 227 BOOK IV CXLVII. The Perspective of Cast Shadows 229 CXLVIII. The Two Kinds of Shadows 230 CXLIX. Shadows Cast by the Sun 232 CL. The Sun in the Same Plane as the Picture 233 CLI. The Sun Behind the Picture 234 CLII. Sun Behind the Picture, Shadows Thrown on a Wall 238 CLIII. Sun Behind the Picture Throwing Shadow on an Inclined Plane 240 CLIV. The Sun in Front of the Picture 241 CLV. The Shadow of an Inclined Plane 244 CLVI. Shadow on a Roof or Inclined Plane 245 CLVII. To Find the Shadow of a Projection or Balcony on a Wall 246 CLVIII. Shadow on a Retreating Wall, Sun in Front 247 CLIX. Shadow of an Arch, Sun in Front 249 CLX. Shadow in a Niche or Recess 250 CLXI. Shadow in an Arched Doorway 251 CLXII. Shadows Produced by Artificial Light 252 CLXIII. Some Observations on Real Light and Shade 253 CLXIV. Reflection 257 CLXV. Angles of Reflection 259 CLXVI. Reflections of Objects at Different Distances 260 CLXVII. Reflection in a Looking-glass 262 CLXVIII. The Mirror at an Angle 264 CLXIX. The Upright Mirror at an Angle of 45° to the Wall 266 CLXX. Mental Perspective 269 BOOK FIRST THE NECESSITY OF THE STUDY OF PERSPECTIVE TO PAINTERS, SCULPTORS, AND ARCHITECTS Leonardo da Vinci tells us in his celebrated _Treatise on Painting_ that the young artist should first of all learn perspective, that is to say, he should first of all learn that he has to depict on a flat surface objects which are in relief or distant one from the other; for this is the simple art of painting. Objects appear smaller at a distance than near to us, so by drawing them thus we give depth to our canvas. The outline of a ball is a mere flat circle, but with proper shading we make it appear round, and this is the perspective of light and shade. 'The next thing to be considered is the effect of the atmosphere and light. If two figures are in the same coloured dress, and are standing one behind the other, then they should be of slightly different tone, so as to separate them. And in like manner, according to the distance of the mountains in a landscape and the greater or less density of the air, so do we depict space between them, not only making them smaller in outline, but less distinct.'[1] [Footnote 1: Leonardo da Vinci's _Treatise on Painting_.] Sir Edwin Landseer used to say that in looking at a figure in a picture he liked to feel that he could walk round it, and this exactly expresses the impression that the true art of painting should make upon the spectator. There is another observation of Leonardo's that it is well I should here transcribe; he says: 'Many are desirous of learning to draw, and are very fond of it, who are notwithstanding void of a proper disposition for it. This may be known by their want of perseverance; like boys who draw everything in a hurry, never finishing or shadowing.' This shows they do not care for their work, and all instruction is thrown away upon them. At the present time there is too much of this 'everything in a hurry', and beginning in this way leads only to failure and disappointment. These observations apply equally to perspective as to drawing and painting. Unfortunately, this study is too often neglected by our painters, some of them even complacently confessing their ignorance of it; while the ordinary student either turns from it with distaste, or only endures going through it with a view to passing an examination, little thinking of what value it will be to him in working out his pictures. Whether the manner of teaching perspective is the cause of this dislike for it, I cannot say; but certainly most of our English books on the subject are anything but attractive. All the great masters of painting have also been masters of perspective, for they knew that without it, it would be impossible to carry out their grand compositions. In many cases they were even inspired by it in choosing their subjects. When one looks at those sunny interiors, those corridors and courtyards by De Hooghe, with their figures far off and near, one feels that their charm consists greatly in their perspective, as well as in their light and tone and colour. Or if we study those Venetian masterpieces by Paul Veronese, Titian, Tintoretto, and others, we become convinced that it was through their knowledge of perspective that they gave such space and grandeur to their canvases. I need not name all the great artists who have shown their interest and delight in this study, both by writing about it and practising it, such as Albert Dürer and others, but I cannot leave out our own Turner, who was one of the greatest masters in this respect that ever lived; though in his case we can only judge of the results of his knowledge as shown in his pictures, for although he was Professor of Perspective at the Royal Academy in 1807--over a hundred years ago--and took great pains with the diagrams he prepared to illustrate his lectures, they seemed to the students to be full of confusion and obscurity; nor am I aware that any record of them remains, although they must have contained some valuable teaching, had their author possessed the art of conveying it. However, we are here chiefly concerned with the necessity of this study, and of the necessity of starting our work with it. Before undertaking a large composition of figures, such as the 'Wedding-feast at Cana', by Paul Veronese, or 'The School of Athens', by Raphael, the artist should set out his floors, his walls, his colonnades, his balconies, his steps, &c., so that he may know where to place his personages, and to measure their different sizes according to their distances; indeed, he must make his stage and his scenery before he introduces his actors. He can then proceed with his composition, arrange his groups and the accessories with ease, and above all with correctness. But I have noticed that some of our cleverest painters will arrange their figures to please the eye, and when fairly advanced with their work will call in an expert, to (as they call it) put in their perspective for them, but as it does not form part of their original composition, it involves all sorts of difficulties and vexatious alterings and rubbings out, and even then is not always satisfactory. For the expert may not be an artist, nor in sympathy with the picture, hence there will be a want of unity in it; whereas the whole thing, to be in harmony, should be the conception of one mind, and the perspective as much a part of the composition as the figures. If a ceiling has to be painted with figures floating or flying in the air, or sitting high above us, then our perspective must take a different form, and the point of sight will be above our heads instead of on the horizon; nor can these difficulties be overcome without an adequate knowledge of the science, which will enable us to work out for ourselves any new problems of this kind that we may have to solve. Then again, with a view to giving different effects or impressions in this decorative work, we must know where to place the horizon and the points of sight, for several of the latter are sometimes required when dealing with large surfaces such as the painting of walls, or stage scenery, or panoramas depicted on a cylindrical canvas and viewed from the centre thereof, where a fresh point of sight is required at every twelve or sixteen feet. Without a true knowledge of perspective, none of these things can be done. The artist should study them in the great compositions of the masters, by analysing their pictures and seeing how and for what reasons they applied their knowledge. Rubens put low horizons to most of his large figure-subjects, as in 'The Descent from the Cross', which not only gave grandeur to his designs, but, seeing they were to be placed above the eye, gave a more natural appearance to his figures. The Venetians often put the horizon almost on a level with the base of the picture or edge of the frame, and sometimes even below it; as in 'The Family of Darius at the Feet of Alexander', by Paul Veronese, and 'The Origin of the "Via Lactea"', by Tintoretto, both in our National Gallery. But in order to do all these things, the artist in designing his work must have the knowledge of perspective at his fingers' ends, and only the details, which are often tedious, should he leave to an assistant to work out for him. We must remember that the line of the horizon should be as nearly as possible on a level with the eye, as it is in nature; and yet one of the commonest mistakes in our exhibitions is the bad placing of this line. We see dozens of examples of it, where in full-length portraits and other large pictures intended to be seen from below, the horizon is placed high up in the canvas instead of low down; the consequence is that compositions so treated not only lose in grandeur and truth, but appear to be toppling over, or give the impression of smallness rather than bigness. Indeed, they look like small pictures enlarged, which is a very different thing from a large design. So that, in order to see them properly, we should mount a ladder to get upon a level with their horizon line (see Fig. 66, double-page illustration). We have here spoken in a general way of the importance of this study to painters, but we shall see that it is of almost equal importance to the sculptor and the architect. A sculptor student at the Academy, who was making his drawings rather carelessly, asked me of what use perspective was to a sculptor. 'In the first place,' I said, 'to reason out apparently difficult problems, and to find how easy they become, will improve your mind; and in the second, if you have to do monumental work, it will teach you the exact size to make your figures according to the height they are to be placed, and also the boldness with which they should be treated to give them their full effect.' He at once acknowledged that I was right, proved himself an efficient pupil, and took much interest in his work. I cannot help thinking that the reason our public monuments so often fail to impress us with any sense of grandeur is in a great measure owing to the neglect of the scientific study of perspective. As an illustration of what I mean, let the student look at a good engraving or photograph of the Arch of Constantine at Rome, or the Tombs of the Medici, by Michelangelo, in the sacristy of San Lorenzo at Florence. And then, for an example of a mistake in the placing of a colossal figure, let him turn to the Tomb of Julius II in San Pietro in Vinculis, Rome, and he will see that the figure of Moses, so grand in itself, not only loses much of its dignity by being placed on the ground instead of in the niche above it, but throws all the other figures out of proportion or harmony, and was quite contrary to Michelangelo's intention. Indeed, this tomb, which was to have been the finest thing of its kind ever done, was really the tragedy of the great sculptor's life. The same remarks apply in a great measure to the architect as to the sculptor. The old builders knew the value of a knowledge of perspective, and, as in the case of Serlio, Vignola, and others, prefaced their treatises on architecture with chapters on geometry and perspective. For it showed them how to give proper proportions to their buildings and the details thereof; how to give height and importance both to the interior and exterior; also to give the right sizes of windows, doorways, columns, vaults, and other parts, and the various heights they should make their towers, walls, arches, roofs, and so forth. One of the most beautiful examples of the application of this knowledge to architecture is the Campanile of the Cathedral, at Florence, built by Giotto and Taddeo Gaddi, who were painters as well as architects. Here it will be seen that the height of the windows is increased as they are placed higher up in the building, and the top windows or openings into the belfry are about six times the size of those in the lower story. WHAT IS PERSPECTIVE? [Illustration: Fig. 1.] Perspective is a subtle form of geometry; it represents figures and objects not as they are but as we see them in space, whereas geometry represents figures not as we see them but as they are. When we have a front view of a figure such as a square, its perspective and geometrical appearance is the same, and we see it as it really is, that is, with all its sides equal and all its angles right angles, the perspective only varying in size according to the distance we are from it; but if we place that square flat on the table and look at it sideways or at an angle, then we become conscious of certain changes in its form--the side farthest from us appears shorter than that near to us, and all the angles are different. Thus A (Fig. 2) is a geometrical square and B is the same square seen in perspective. [Illustration: Fig. 2.] [Illustration: Fig. 3.] The science of perspective gives the dimensions of objects seen in space as they appear to the eye of the spectator, just as a perfect tracing of those objects on a sheet of glass placed vertically between him and them would do; indeed its very name is derived from _perspicere_, to see through. But as no tracing done by hand could possibly be mathematically correct, the mathematician teaches us how by certain points and measurements we may yet give a perfect image of them. These images are called projections, but the artist calls them pictures. In this sketch _K_ is the vertical transparent plane or picture, _O_ is a cube placed on one side of it. The young student is the spectator on the other side of it, the dotted lines drawn from the corners of the cube to the eye of the spectator are the visual rays, and the points on the transparent picture plane where these visual rays pass through it indicate the perspective position of those points on the picture. To find these points is the main object or duty of linear perspective. Perspective up to a certain point is a pure science, not depending upon the accidents of vision, but upon the exact laws of reasoning. Nor is it to be considered as only pertaining to the craft of the painter and draughtsman. It has an intimate connexion with our mental perceptions and with the ideas that are impressed upon the brain by the appearance of all that surrounds us. If we saw everything as depicted by plane geometry, that is, as a map, we should have no difference of view, no variety of ideas, and we should live in a world of unbearable monotony; but as we see everything in perspective, which is infinite in its variety of aspect, our minds are subjected to countless phases of thought, making the world around us constantly interesting, so it is devised that we shall see the infinite wherever we turn, and marvel at it, and delight in it, although perhaps in many cases unconsciously. [Illustration: Fig. 4.] [Illustration: Fig. 5.] In perspective, as in geometry, we deal with parallels, squares, triangles, cubes, circles, &c.; but in perspective the same figure takes an endless variety of forms, whereas in geometry it has but one. Here are three equal geometrical squares: they are all alike. Here are three equal perspective squares, but all varied in form; and the same figure changes in aspect as often as we view it from a different position. A walk round the dining-room table will exemplify this. It is in proving that, notwithstanding this difference of appearance, the figures do represent the same form, that much of our work consists; and for those who care to exercise their reasoning powers it becomes not only a sure means of knowledge, but a study of the greatest interest. Perspective is said to have been formed into a science about the fifteenth century. Among the names mentioned by the unknown but pleasant author of _The Practice of Perspective_, written by a Jesuit of Paris in the eighteenth century, we find Albert Dürer, who has left us some rules and principles in the fourth book of his _Geometry_; Jean Cousin, who has an express treatise on the art wherein are many valuable things; also Vignola, who altered the plans of St. Peter's left by Michelangelo; Serlio, whose treatise is one of the best I have seen of these early writers; Du Cerceau, Serigati, Solomon de Cause, Marolois, Vredemont; Guidus Ubaldus, who first introduced foreshortening; the Sieur de Vaulizard, the Sieur Dufarges, Joshua Kirby, for whose _Method of Perspective made Easy_ (?) Hogarth drew the well-known frontispiece; and lastly, the above-named _Practice of Perspective_ by a Jesuit of Paris, which is very clear and excellent as far as it goes, and was the book used by Sir Joshua Reynolds.[2] But nearly all these authors treat chiefly of parallel perspective, which they do with clearness and simplicity, and also mathematically, as shown in the short treatise in Latin by Christian Wolff, but they scarcely touch upon the more difficult problems of angular and oblique perspective. Of modern books, those to which I am most indebted are the _Traité Pratique de Perspective_ of M. A. Cassagne (Paris, 1873), which is thoroughly artistic, and full of pictorial examples admirably done; and to M. Henriet's _Cours Rational de Dessin_. There are many other foreign books of excellence, notably M. Thibault's _Perspective_, and some German and Swiss books, and yet, notwithstanding this imposing array of authors, I venture to say that many new features and original problems are presented in this book, whilst the old ones are not neglected. As, for instance, How to draw figures at an angle without vanishing points (see p. 141, Fig. 162, &c.), a new method of angular perspective which dispenses with the cumbersome setting out usually adopted, and enables us to draw figures at any angle without vanishing lines, &c., and is almost, if not quite, as simple as parallel perspective (see p. 133, Fig. 150, &c.). How to measure distances by the square and diagonal, and to draw interiors thereby (p. 128, Fig. 144). How to explain the theory of perspective by ocular demonstration, using a vertical sheet of glass with strings, placed on a drawing-board, which I have found of the greatest use (see p. 29, Fig. 29). Then again, I show how all our perspective can be done inside the picture; that we can measure any distance into the picture from a foot to a mile or twenty miles (see p. 86, Fig. 94); how we can draw the Great Pyramid, which stands on thirteen acres of ground, by putting it 1,600 feet off (Fig. 224), &c., &c. And while preserving the mathematical science, so that all our operations can be proved to be correct, my chief aim has been to make it easy of application to our work and consequently useful to the artist. [Footnote 2: There is another book called _The Jesuit's Perspective_ which I have not yet seen, but which I hear is a fine work.] The Egyptians do not appear to have made any use of linear perspective. Perhaps it was considered out of character with their particular kind of decoration, which is to be looked upon as picture writing rather than pictorial art; a table, for instance, would be represented like a ground-plan and the objects upon it in elevation or standing up. A row of chariots with their horses and drivers side by side were placed one over the other, and although the Egyptians had no doubt a reason for this kind of representation, for they were grand artists, it seems to us very primitive; and indeed quite young beginners who have never drawn from real objects have a tendency to do very much the same thing as this ancient people did, or even to emulate the mathematician and represent things not as they appear but as they are, and will make the top of a table an almost upright square and the objects upon it as if they would fall off. No doubt the Greeks had correct notions of perspective, for the paintings on vases, and at Pompeii and Herculaneum, which were either by Greek artists or copied from Greek pictures, show some knowledge, though not complete knowledge, of this science. Indeed, it is difficult to conceive of any great artist making his perspective very wrong, for if he can draw the human figure as the Greeks did, surely he can draw an angle. The Japanese, who are great observers of nature, seem to have got at their perspective by copying what they saw, and, although they are not quite correct in a few things, they convey the idea of distance and make their horizontal planes look level, which are two important things in perspective. Some of their landscapes are beautiful; their trees, flowers, and foliage exquisitely drawn and arranged with the greatest taste; whilst there is a character and go about their figures and birds, &c., that can hardly be surpassed. All their pictures are lively and intelligent and appear to be executed with ease, which shows their authors to be complete masters of their craft. The same may be said of the Chinese, although their perspective is more decorative than true, and whilst their taste is exquisite their whole art is much more conventional and traditional, and does not remind us of nature like that of the Japanese. We may see defects in the perspective of the ancients, in the mediaeval painters, in the Japanese and Chinese, but are we always right ourselves? Even in celebrated pictures by old and modern masters there are occasionally errors that might easily have been avoided, if a ready means of settling the difficulty were at hand. We should endeavour then to make this study as simple, as easy, and as complete as possible, to show clear evidence of its correctness (according to its conditions), and at the same time to serve as a guide on any and all occasions that we may require it. To illustrate what is perspective, and as an experiment that any one can make, whether artist or not, let us stand at a window that looks out on to a courtyard or a street or a garden, &c., and trace with a paint-brush charged with Indian ink or water-colour the outline of whatever view there happens to be outside, being careful to keep the eye always in the same place by means of a rest; when this is dry, place a piece of drawing-paper over it and trace through with a pencil. Now we will rub out the tracing on the glass, which is sure to be rather clumsy, and, fixing our paper down on a board, proceed to draw the scene before us, using the main lines of our tracing as our guiding lines. If we take pains over our work, we shall find that, without troubling ourselves much about rules, we have produced a perfect perspective of perhaps a very difficult subject. After practising for some little time in this way we shall get accustomed to what are called perspective deformations, and soon be able to dispense with the glass and the tracing altogether and to sketch straight from nature, taking little note of perspective beyond fixing the point of sight and the horizontal-line; in fact, doing what every artist does when he goes out sketching. [Illustration: Fig. 6. This is a much reduced reproduction of a drawing made on my studio window in this way some twenty years ago, when the builder started covering the fields at the back with rows and rows of houses.] THE THEORY OF PERSPECTIVE DEFINITIONS I Fig. 7. In this figure, _AKB_ represents the picture or transparent vertical plane through which the objects to be represented can be seen, or on which they can be traced, such as the cube _C_. [Illustration: Fig. 7.] The line _HD_ is the +Horizontal-line+ or +Horizon+, the chief line in perspective, as upon it are placed the principal points to which our perspective lines are drawn. First, the +Point of Sight+ and next _D_, the +Point of Distance+. The chief vanishing points and measuring points are also placed on this line. Another important line is _AB_, the +Base+ or +Ground line+, as it is on this that we measure the width of any object to be represented, such as _ef_, the base of the square _efgh_, on which the cube _C_ is raised. _E_ is the position of the eye of the spectator, being drawn in perspective, and is called the +Station-point+. Note that the perspective of the board, and the line _SE_, is not the same as that of the cube in the picture _AKB_, and also that so much of the board which is behind the picture plane partially represents the +Perspective-plane+, supposed to be perfectly level and to extend from the base line to the horizon. Of this we shall speak further on. In nature it is not really level, but partakes in extended views of the rotundity of the earth, though in small areas such as ponds the roundness is infinitesimal. [Illustration: Fig. 8.] Fig. 8. This is a side view of the previous figure, the picture plane _K_ being represented edgeways, and the line _SE_ its full length. It also shows the position of the eye in front of the point of sight _S_. The horizontal-line _HD_ and the base or ground-line _AB_ are represented as receding from us, and in that case are called vanishing lines, a not quite satisfactory term. It is to be noted that the cube _C_ is placed close to the transparent picture plane, indeed touches it, and that the square _fj_ faces the spectator _E_, and although here drawn in perspective it appears to him as in the other figure. Also, it is at the same time a perspective and a geometrical figure, and can therefore be measured with the compasses. Or in other words, we can touch the square _fj_, because it is on the surface of the picture, but we cannot touch the square _ghmb_ at the other end of the cube and can only measure it by the rules of perspective. II THE POINT OF SIGHT, THE HORIZON, AND THE POINT OF DISTANCE There are three things to be considered and understood before we can begin a perspective drawing. First, the position of the eye in front of the picture, which is called the +Station-point+, and of course is not in the picture itself, but its position is indicated by a point on the picture which is exactly opposite the eye of the spectator, and is called the +Point of Sight+, or +Principal Point+, or +Centre of Vision+, but we will keep to the first of these. [Illustration: Fig. 9.] [Illustration: Fig. 10.] If our picture plane is a sheet of glass, and is so placed that we can see the landscape behind it or a sea-view, we shall find that the distant line of the horizon passes through that point of sight, and we therefore draw a line on our picture which exactly corresponds with it, and which we call the +Horizontal-line+ or +Horizon+.[3] The height of the horizon then depends entirely upon the position of the eye of the spectator: if he rises, so does the horizon; if he stoops or descends to lower ground, so does the horizon follow his movements. You may sit in a boat on a calm sea, and the horizon will be as low down as you are, or you may go to the top of a high cliff, and still the horizon will be on the same level as your eye. [Footnote 3: In a sea-view, owing to the rotundity of the earth, the real horizontal line is slightly below the sea line, which is noted in Chapter I.] This is an important line for the draughtsman to consider, for the effect of his picture greatly depends upon the position of the horizon. If you wish to give height and dignity to a mountain or a building, the horizon should be low down, so that these things may appear to tower above you. If you wish to show a wide expanse of landscape, then you must survey it from a height. In a composition of figures, you select your horizon according to the subject, and with a view to help the grouping. Again, in portraits and decorative work to be placed high up, a low horizon is desirable, but I have already spoken of this subject in the chapter on the necessity of the study of perspective. III POINT OF DISTANCE Fig. 11. The distance of the spectator from the picture is of great importance; as the distortions and disproportions arising from too near a view are to be avoided, the object of drawing being to make things look natural; thus, the floor should look level, and not as if it were running up hill--the top of a table flat, and not on a slant, as if cups and what not, placed upon it, would fall off. In this figure we have a geometrical or ground plan of two squares at different distances from the picture, which is represented by the line _KK_. The spectator is first at _A_, the corner of the near square _Acd_. If from _A_ we draw a diagonal of that square and produce it to the line _KK_ (which may represent the horizontal-line in the picture), where it intersects that line at _A·_ marks the distance that the spectator is from the point of sight _S_. For it will be seen that line _SA_ equals line _SA·_. In like manner, if the spectator is at _B_, his distance from the point _S_ is also found on the horizon by means of the diagonal _BB´_, so that all lines or diagonals at 45° are drawn to the point of distance (see Rule 6). Figs. 12 and 13. In these two figures the difference is shown between the effect of the short-distance point _A·_ and the long-distance point _B·_; the first, _Acd_, does not appear to lie so flat on the ground as the second square, _Bef_. From this it will be seen how important it is to choose the right point of distance: if we take it too near the point of sight, as in Fig. 12, the square looks unnatural and distorted. This, I may note, is a common fault with photographs taken with a wide-angle lens, which throws everything out of proportion, and will make the east end of a church or a cathedral appear higher than the steeple or tower; but as soon as we make our line of distance sufficiently long, as at Fig. 13, objects take their right proportions and no distortion is noticeable. [Illustration: Fig. 11.] [Illustration: Fig. 12.] [Illustration: Fig. 13.] In some books on perspective we are told to make the angle of vision 60°, so that the distance _SD_ (Fig. 14) is to be rather less than the length or height of the picture, as at _A_. The French recommend an angle of 28°, and to make the distance about double the length of the picture, as at _B_ (Fig. 15), which is far more agreeable. For we must remember that the distance-point is not only the point from which we are supposed to make our tracing on the vertical transparent plane, or a point transferred to the horizon to make our measurements by, but it is also the point in front of the canvas that we view the picture from, called the station-point. It is ridiculous, then, to have it so close that we must almost touch the canvas with our noses before we can see its perspective properly. [Illustration: Fig. 14.] Now a picture should look right from whatever distance we view it, even across the room or gallery, and of course in decorative work and in scene-painting a long distance is necessary. [Illustration: Fig. 15.] We need not, however, tie ourselves down to any hard and fast rule, but should choose our distance according to the impression of space we wish to convey: if we have to represent a domestic scene in a small room, as in many Dutch pictures, we must not make our distance-point too far off, as it would exaggerate the size of the room. [Illustration: Fig. 16. Cattle. By Paul Potter.] The height of the horizon is also an important consideration in the composition of a picture, and so also is the position of the point of sight, as we shall see farther on. In landscape and cattle pictures a low horizon often gives space and air, as in this sketch from a picture by Paul Potter--where the horizontal-line is placed at one quarter the height of the canvas. Indeed, a judicious use of the laws of perspective is a great aid to composition, and no picture ever looks right unless these laws are attended to. At the present time too little attention is paid to them; the consequence is that much of the art of the day reflects in a great measure the monotony of the snap-shot camera, with its everyday and wearisome commonplace. IV PERSPECTIVE OF A POINT, VISUAL RAYS, &C. We perceive objects by means of the visual rays, which are imaginary straight lines drawn from the eye to the various points of the thing we are looking at. As those rays proceed from the pupil of the eye, which is a circular opening, they form themselves into a cone called the +Optic Cone+, the base of which increases in proportion to its distance from the eye, so that the larger the view which we wish to take in, the farther must we be removed from it. The diameter of the base of this cone, with the visual rays drawn from each of its extremities to the eye, form the angle of vision, which is wider or narrower according to the distance of this diameter. Now let us suppose a visual ray _EA_ to be directed to some small object on the floor, say the head of a nail, _A_ (Fig. 17). If we interpose between this nail and our eye a sheet of glass, _K_, placed vertically on the floor, we continue to see the nail through the glass, and it is easily understood that its perspective appearance thereon is the point _a_, where the visual ray passes through it. If now we trace on the floor a line _AB_ from the nail to the spot _B_, just under the eye, and from the point _o_, where this line passes through or under the glass, we raise a perpendicular _oS_, that perpendicular passes through the precise point that the visual ray passes through. The line _AB_ traced on the floor is the horizontal trace of the visual ray, and it will be seen that the point _a_ is situated on the vertical raised from this horizontal trace. [Illustration: Fig. 17.] V TRACE AND PROJECTION If from any line _A_ or _B_ or _C_ (Fig. 18), &c., we drop perpendiculars from different points of those lines on to a horizontal plane, the intersections of those verticals with the plane will be on a line called the horizontal trace or projection of the original line. We may liken these projections to sun-shadows when the sun is in the meridian, for it will be remarked that the trace does not represent the length of the original line, but only so much of it as would be embraced by the verticals dropped from each end of it, and although line _A_ is the same length as line _B_ its horizontal trace is longer than that of the other; that the projection of a curve (_C_) in this upright position is a straight line, that of a horizontal line (_D_) is equal to it, and the projection of a perpendicular or vertical (_E_) is a point only. The projections of lines or points can likewise be shown on a vertical plane, but in that case we draw lines parallel to the horizontal plane, and by this means we can get the position of a point in space; and by the assistance of perspective, as will be shown farther on, we can carry out the most difficult propositions of descriptive geometry and of the geometry of planes and solids. [Illustration: Fig. 18.] The position of a point in space is given by its projection on a vertical and a horizontal plane-- [Illustration: Fig. 19.] Thus _e·_ is the projection of _E_ on the vertical plane _K_, and _e··_ is the projection of _E_ on the horizontal plane; _fe··_ is the horizontal trace of the plane _fE_, and _e·f_ is the trace of the same plane on the vertical plane _K_. VI SCIENTIFIC DEFINITION OF PERSPECTIVE The projections of the extremities of a right line which passes through a vertical plane being given, one on
{'title': 'The Theory and Practice of Perspective by G. A. Storey', 'source': 'Project Gutenberg', 'lang': 'en'}