Digitized by the Internet Archive in 2015 https://archive.org/details/supplementtotheadave A Z/'i- ' — J /y£j>^ i 't- / v Cf - SUPPLEMENT TO ‘THE AMATEUR’S PERSPECTIVE.’ By RICHARD DAVENPORT, Esq. LONDON: PRINTED FOR THE AUTHOR : AND SOLD BY J. HATCIIARD AND SON, PICCADILLY: EGERTON, WHITEHALL; AND COLNAGIII, COCKSPUR STREET. 1829 . LONDON : PRINTED BY RICHARD TAYLOR, RED HON COURT, FLEET STREET. ADVERTISEMENT TO THE SUPPLEMENT. The former part of this work concluded with an intention of treating further of some parts of the subject which had been but slightly men- tioned; particularly the theory of the Field of Vision, and Point of Distance ; of the height of the Horizon-line ; and the position of the prime vertical line in the picture : but it was proposed that the publication should depend on the reception the foregoing pages should meet with from the Public. Without waiting for the result, the Author has since considered such parts to be essential to the theory, and the work incomplete in its plan without the introduction of them. In a paragraph on mechanical aids, the inventor of the Camera Lucida was alluded to in friendly jocularity. No recollection of him can now occur without lament. A copy of the book was sent to him from the country by the Author, who anticipated a smile at their next meeting; useful criticisms on the treatise, and assistance in the part that remains. Indeed, one motive the Author had for pausing where he did, was the hope of being thus furnished with more concise demon- strations, and happier illustration of his theory. Alas, the days of his friend’s smiles were past, and the hours that remained were too valuable to be employed in the perusal of a work of such minor importance. He is no more. He has vacated a department in the philosophical world, which probably no man living can supply. There may be greater astronomers,— -greater mathematicians, — IV ADVERTISEMENT TO THE SUPPLEMENT. greater chemists,— geologists, — botanists, — more able and practical mechanics, — more experienced physicians ; — but the astronomer, — the mathematician, — the optician, — the botanist, — the chemist, — the phy- sician, — the natural philosopher, — the civil engineer, — the mechanic, (of every description, maker of steam-engines, chronometers, telescopes, barometers, hydrometers,) — the metallurgist, — the framer of every useful invention, down to the manufacturer of caoutchouc-cloth, all derived assistance from him. He stood as interpreter between the sciences, and enabled each one to give its aid to the others. In generalization of knowledge, — minute precision in the observa- tion of phenomena, — in almost undeviating sagacity in investigation, — inexhaustible resource in his adaptation of means, and ingenuity of contrivance, — in quickness and universality in the application of ana- logies, — Who can compete with Wollaston? This help failing, the Author resumes the subject alone ; and will endeavour to methodize and abridge what he had prepared for the desired revision. January, 1829. PREFACE. During the preparation for this additional publication, the Author busied himself in looking over such works as he had not had access to before on the subject, but which time had now given him an oppor- tunity to procure ; and if he had been, from the first, aware of their number, he probably should not have ventured to add to it. Yet he can now deliberatelv refer to his former Preface, and declare that he lias not found the reasons he then gave for his intrusion, removed ; and that he does not repent the having put in his claim to the atten- tion of his fellow amateurs: still believing that those who have wished to be acquainted with the theory of perspective, and have been de- terred from it by the apparent difficulty, will find it capable of being simplified and rendered even amusing. Of the works he has bestowed attention on, the greater part are more or less referred to in the following pages. He has not said much of Malton’s, though it is one frequently referred to by other writers. Mr. Malton favours his readers with nearly as many words as might go to an entire treatise, in discussing the nature of light, and in “ exposing Sir Isaac Newton’s absurdities”!!! and when a reader’s attention is wearied by such means, he is less disposed to attack and follow through a large thick small-printed book, with all the intricacies of its nume- rous plates and references. If the duty of a young artist leads him to the study of them, they will hardly tempt an amateur to work through them ; and the Author confesses he has not had the courage to under- take it. He will say more ; he did not find himself at all repaid by such as he did study. Here he must refer to a mistake he made in his former Preface ; viz. VI PREFACE. in designating Dr. Brook Taylor’s work, as one “somewhat dreaded.” lie had never seen it, nor perhaps can it now be procured ; and the friends whom he had heard speak of the time they had bestowed on it, and the little practical knowledge they had gained by it, meant the publications written in continuation or explanation of it, and which bear the name of Brook Taylor in the title-page. Mention should also be made of a very good book intitled, “Elements of Linear Perspective,” by D. Creswell, A.M. &c. &c. But Mr. Creswell says, “ the first six books, and part of the eleventh, of Euclid’s Elements, are the only books necessary to be read, in order that the whole of what is here delivered may be understood.” His book therefore, however well calculated for the meridian of Cambridge, will not answer the purpose of every tourist ; while the present Author (notwithstanding the confession of disappointment he is about to make) still flatters him- self that the “ Amateur’s Perspective” will sometimes be used on rainy days on the banks of Loch Lomond or the Rhine, and on the Bay of Naples. Mr. Creswell is perfectly aware of, and expresses extremely well, the deficiencies and unnecessary intricacies of most of the books ; and the Preface to the former part of this work might have been ren- dered more concise, had the Author fallen in earlier with Air. C.’s book. He cannot but think, however, that his objection to the introduction of the geometric plan in the theoretic process is unfounded. The reader will long ago have perceived that it is not intended to be used gene- rally in drawing, but is given in illustration of the principle, which assuredly it does facilitate. In fact, the measurements on the base line and on the side lines are all that are wanted; and the geometric plan teaches the student to find the desired points; and the Author will still venture to contend even against Air. Creswell, that the plan is more simple (even for a mathematician) than that of “the Elements” — as generally, applicable, — and as strictlv, demonstrable ; and that it is not “ impossible,” as Air. C. declares it to be, “to put the reader in posses- sion of the principles of perspective without requiring of him the know- ledge of geometry.” Every one knows the meaning and use of lines of longitude and PREFACE. Vll latitude on a map. Every one knows what is the meaning of a hori- zon till ground-plane, or plan, or map. Then if a portion of the picture is laid out as the perspective representation of that ground-plane, the perspective of the lines of latitude and longitude proves even to the beginner, the place in the picture where the desired point is, supposing it to be on the ground-plane : and this is given (in the present system) simply by drawing two lines from the marked points on the base, to marked points on the horizon-line. This requires no previous know- ledge of geometry. Then suppose the point wanted not to be on the visible flat ground, still it must be vertical to some point on that plane ; and all we have to do is, to find that point as before ; and by the measurement on the side-lines, we ascertain the length of that vertical line, which gives the height. Here again no knowledge of geometry is wanted, and the thing is done, — the perspective is right, — the lines are in their places. The rest is the art of the painter ; and to attempt to acquire and practise that, without a previous knowledge of perspective (though many persons do make progress in it, and produce pictures not void of excellence), is just the same thing as to learn music without the pains of learning the notes ; which art likewise some people do so acquire ; at least as far as singing or playing tunes may be satisfactory to them. In a word, any person of education may acquire so much of the theory as will not only correct their own practice, but enable them to comprehend and enjoy the true representation of natural and architectural scenery with far less time and attention than would be sufficient for learning the common rules of arithmetic. The origin of the work was shown in the Dedication. The Author has sometimes seen an incredulous smile when the time there held out as requisite to learn the system was mentioned/or when he attempted to vindicate the promise ; which yet seriously he is not unable to do, claiming only some allowance for additions since made : for, (hoping that the introduction of his justification will not be deemed trifling) he can say, that wherever the request made to friends, to read by the hour-glass, was complied with, those friends (of both sexes) who have Vlll PREFACE. declared they sat down to it quite ignorant of the subject, and unac- quainted with the elements, or even terms of geometry, have reported that the time limited had proved sufficient, not only for reading, but digesting the work, going through all the diagrams and references ; and that they did not need a master to explain and instruct. This morsel of egotism it is hoped will be forgiven ; for if “ simply the writing a book” when the Author has no excuse for it, is a crime, he cannot be much blamed for pressing the excuse he thinks he has. The perception of the truth of the adage Docendo disco is a powerful motive, but a selfish one, and therefore no excuse. It is, to a certain degree, learning at the expense of others. One ground for repentance he has, but no cause of blame. The book grew upon him ; and the multiplication of the Plates has put him to more cost than the price fixed can replace : against that, he will set the gratification of the notice taken of it by individual friends, though “not yet” by the Public. Still he cannot withhold his desire to supply in such degree as is in his power, that which appeared most essential, but with- out attempting to follow up the subject so far as it might lead him. u Liber ibis in urbem July, 1829. SUPPLEMENT CHAPTER I. On the Field of Vision. That the field of vision depends entirely on the distance of the point of sight, as compared with the width of the picture , is obvious : a comparatively distant point of sight contracting the field, a nearer one enlarging it : (see Sect. III.) and this of course may be varied in two ways; i. e. either by widening or narrowing the picture when the point of distance is determined, or by lengthening or shortening the line of distance when the width of the picture (or length of the base) is determined. But it has been seldom or never noticed, that the field of vision relates as much to the extent of the vertical as to that of the horizontal direction of the picture ; to the height of the sides as well as to the length of the base; and this point will be discussed in its place; at present the question will be con- fined to the width. It is commonly said in the books, that “no greater field should be comprehended in the picture than what the eye will take in without moving:” but the eye moves as much from one point of a picture to another, as from one object to another in the field of vision in nature. This rule therefore fails. In others it is said that it should be limited by what the eye will take in without the head being moved. This is a more faulty rule than the other, and needs not much notice. The matter is in truth more intricate than at the first aspect it may appear ; and it is not only difficult to lay down a precise law for the allowable extent of the field, but even the ground of any limit at all (or any much short of the semicircle) is not obvious. Distinct vision extends to but a very small distance wide of the point to which the eye is expressly directed. When the eye is fixed on one point, it may see objects so wide from that point as to comprehend an angle as great as 170 degrees; which is very sensibly felt, if two candles be placed at such a width apart as to form that angle with the eye when it is fixed on an object B 2 On the Field of Vision. in front : but to how very small an angle distinct vision extends, may be proved by the observation that a person looking in a mirror cannot see bis own eyes move. Let him approach or recede from the glass, looking at the pupil of one of his eyes, and finding the distance from which he can most perfectly see the minute divisions of the iris. (Twice the space between his eye and the glass, is his distance of most distinct vision.) Keeping his face perfectly steady, let him, by the motion of his eyes only, inspect the pupil of the other eye. If another person watches the motion of his eyes as he alternates his inspection between his right and left eye in the glass, to such person the motion of his eyes will be perfectly perceptible, but not at all to the spectator himself. Nor can he, while looking at one eye, perceive that the other is more inflected, as it must be, towards tbe bridge of the nose. This shows to how small an angular distance distinct vision extends. We can see strong contrasts of light, and shade, and colour, at a very wide angular distance: but our perception of forms diminishes in an undefined ratio from the very centre of the field of vision ; and if the picture were con- fined to the extent of distinct vision of an eye unmoved, all that could be re- presented would be, a small portrait, or a single countenance on a small scale ; a flower, or other small object, or a distant object such as a telescope will take in. Now since in such landscapes and other pictures as we are accustomed to, the spectator must move his eye from one object to another; and since the magnitudes of spaces in the picture will be always proportional to those in the scene itself, and the perspective of objects that lie wide of the vertical line will be proportionally wide of that line in nature, — why should the picture be limited in width, or the point of sight be prohibited from a near approach ? Why should not the eye approach the pane of glass (Sect. I.), and take in as wide a scene as lies before it? Or at least, why may it not extend to as much of the scene as is visible, though indistinctly, to the eye unmoved in one place ? it being admitted that in viewing either picture or original, the eye changes its direction for distinct sight. One answer obviously presents itself. The size of the picture being limited, the more extensive the field of vision is, the more diminutive must be the several representations of the several parts. The scale becomes too small. This forms some limit, but not the only one. It is true that by some association and habit we do comprehend the per- spective of a picture, though that picture be viewed from different distances and in different directions. With the exception of a few pictures contrived On the Field of Vision. 3 for the purpose, we never fall really into the illusion so as to imagine we see through the picture as a glass, but are distinctly aware that we see a surface on which the scene is delineated : still we refer the point of sight in our ima- gination to some point at a certain distance, or at least to a certain dir ee lion ; viz. to one perpendicular to the plane of the picture. If we see a picture ob- liquely, still we know that the surface represents that which we should see beyond a window in front, and not what we should see through that window in the same oblique direction in which the picture is seen : and on a little consideration it will be found that the nearer that point is to the window, the greater would be found the aberration from it, on changing either distance or direction of the eye of the spectator. Thus let the screen-pole (Sect. I.) be placed at a proper distance from the pane, and directly in front of the centre, and let the spectator observe parti- cularly the objects that are comprehended in the field of vision. Let him remove to a certain distance, and somewhat out of the original direction, and observe the difference of the scene. Let him then place the pole at a less distance, and having made his observation, again remove to a place equally distant from that, and observe how much greater is the comparative variation of the scene caused by the change of place in this shorter distance. Now, to transfer the point of sight in imagination to its true place, under this greater variation, will in fact require a greater effort of mind than habit enables us to use. Our conceptions arise from habits of association ; habits entirely beyond either command or controul : we are even unconscious of them at the very times when they regulate and command our ideas. When a man sees himself in a looking-glass, he imagines a figure in the perspective, of the same size as himself, and at the same distance beyond the glass, at which he stands in front; and he thinks nothing of the surface of the glass. Now suppose that glass to be the picture. His image would be, on that surface, exactly of half his natural size ; and if he will trace it with a little whiting on the glass, he will find it exactly of that measure. Not only does it not give him that idea, but he finds it difficult to believe the fact. lie says, I see that image, in stature equal to mine ; and I see other persons and all the objects in the room, of their natural size and yet he must be aware that the whole surface of the glass is not so large as a single figure. This is the illusion of true perspective. He also knows that if he moves, the relative position of all the objects is changed. If he were looking through a glass into a similar apartment, the effect would be altogether similar ; but if instead of a transparent or reflecting 4 On the Field of Vision. surface a picture is substituted,, the objects do not move with his eye, and the illusion is lost : still his imagination enables him to take in the design of the painter, and to understand the picture as if he viewed it from the true point of sight. In fact it is seldom we do view a picture from its true point of sight, but almost always from a greater distance, and in a less true direction ; and it is reasonable to expect (and experience proves) that the more different that position is from the true one, the worse will be the effect ; and it is obvious that the nearer the perspective point of sight is to the picture, the greater will be the difference between that and the usual distances of the spectators. Besides, distinct vision does not take place within a certain distance in front. The distance is different in different persons ; but in all, distinctness of sight is destroyed by the approach of the eye within some distance of the object : so that if the eye were brought so near to a small picture as to correspond with the perspective point of sight when the line of distance is very short, the picture would be invisible. Suppose a drawing of ten inches wide, and the line of distance to be less than half the length of the base ; few eyes would distinguish the objects at all at that distance. This is a second ground for defining some limit, within which it would be objectionable to place the point of distance of the per- spective. Further, though it will not be admitted (without some qualification at least) that the distortion of the objects which the books object to, takes place, it is yet true that the perspective of objects near the outer extent of the field of vision, differs more from their natural or geometric form, than those nearer to the centre; and this must constitute a difficulty in the conception, and there- fore require a limit : but there is another difficulty which may well be con- ceived to take place, perhaps more generally effectual, though not so obvious, nor so easily and distinctly to be apprehended, nor indeed so palpably to be proved. There is a faculty by which our eyes are able to distinguish distances. Writers on optics, as well as anatomists, have disputed amongst themselves as to the foundation of this faculty ; but of the fact, that we do possess it, all persons are conscious. Now, objects at equal distances from the plane of the picture, are at different distances from the eye. Such as are wide of the central point of view, are further distant than those to which the eye points directly (i. e. perpendicularly) through the plane of the picture, though equally distant from that plane. It is probable then, that the imagination refers them to an interposed curve, rather than a plane surface (there is an 5 On the Field of Vision. apt illustration of this in the species of painting- called Panorama, in which the illusion is in general much more easily elfected than in a flat picture) ; and it is evident that a distant plane surface is much more easily rendered, in the imagination, conformable to a curve, than a near one can be ; circles of larger radius approaching nearer to a right line, than those of a short radius. e A. B. right line. 1.1. arc of circle with long radius. 2. 2. arc of circle with short radius. The dotted lines the radii of the circles. A. B. then may be considered as a horizontal section of the plane of the picture ; 1.1. the large panorama ; 2. 2. the smaller panorama : and it is evi- dent that the picture is more conformable to the larger than to the smaller; which it will be when viewed from the greater point of distance. It will probably now be conceded that this must enter into the estimate of the grounds of limitation of the field of vision (nearness of the point of sight compared with the size of the picture) ; and it is now made evident, that the longer the radius of distance is, the more nearly will it conform to the distance from which the picture is most frequently and most conveniently to be seen : — the less will be the aberration from truth in the various directions in which it is viewed, — and the less will the plane of the picture differ from the curved surface on which the forms of objects would be most truly delineated by their visual rays. Further, the apparent distance of objects seen by one eye from a fixed point, depends on the relative proportions of those of known magnitude ; on the intensity of light, and shade, and colour ; and on their perspective forms as differing from their geometric forms ; equal objects diminishing in the distance as to their parallels of latitude, (Defin. 19.) in a greater ratio than in the direction of their longitudes. (Compare any of the squares of pave- ments, &c. in the foregoing plates.) This elfect it is the office of the painter 6 On the Field of Vision. to imitate ; but not only are there difficulties which require genius, observa- tion, skill and experience, to overcome them, (such as the infinite gradation of light and shade, of absolute colour, of local colour, hue and intensity, of the change of colour by the direction in which it is reflected from the infinitely varying positions of small and irregularly curved surfaces,) but there are some circumstances which insuperably defy imitation, except so far as a transitory illusion to an eye at a fixed point, may be so called. When we look through a glass or into a mirror, we lose (as has been said,) all idea of surface. In a picture we see the surface, and therefore cannot conceive of the forms, as existing beyond that surface ; and it may be made manifest that however much the skill of the painter may do towards the removal of the appearance of surface, the perfect accomplishment of the in- tention is an absolute impossibility. Let a person hold up his finger, or any slender opake object, directly in front of his face, with a lighted candle or any conspicuous object (such as a dark line on light ground, or light on dark) beyond it. If he looks steadily with both eyes on his finger or opake object, he will see that object clear and strong; and he will see two fainter images of the candle or object beyond. If he looks steadily at the candle or remote object, he will see that clear and single; and he will see two fainter images of the near object. If he looks through a window or into a mirror at a strongly visible point somewhat distant, with any intervening spot or line on the surface of the glass, (such as the upright slender frame between two panes,) he will see the distant point plain and single, the nearer spot or line faint and double : and if he fixes both eyes on that spot or line, that will be single and plain, and the distant object will appear faint and double*. Also, if in either of these experiments (that with the finger and candle, or with the spot on the surface of the glass) he fixes both his eyes on the near object, keeping the distant object in the direct line behind, and maintaining steadily that position, covers one eye (the left for example), the distant object will come out towards his right ; and if he removes the covering to the right eye, the same object will come out towards his left. Or if (with the same manoeuvre of removing the covering from one eye to the other) he fixes his eye on the distant point, the nearer one will present the same appearance of removal to the contrary side. * A near-sighted person, or one in whom the foci of the two eyes do not correspond (and there are many who are more near-sighted with one eye than with the other), will not so readily find this effect of the doubled image. On the Field of Vision. 7 . Now if this experiment be made with the picture, relatively to two points, one exactly over the other, but nearly in contact, and intended to represent, the one a distant, the other a near, object in the view, in perfect perspective of place, form, light, colour, &c. it is evident that no such apparent doubling of either object, nor such apparent change of place, will present itself. All this arises from the change of inclination of the axes of the two eyes. They must converge towards the point they look at, near or distant. When the point is very distant, the axes are nearly parallel ; when near, the con- vergence is strong ; but in a picture, the representation of a distant object is not really further from the eye, than that of a near one ; and therefore does not require any change of inclination of the axes of the eyes. Another instance may be given in illustration of the proposition. A near- sighted person sees distinctly objects that are near, but does not see those at a distance without the aid of a concave eye-glass. A far-sighted person the contrary. Either of these would find some point from which they can most distinctly see the picture ; and however well the distance may be expressed in the picture, from that point will they best see every part. Still we may go a step further, and say, that (setting aside the conformable direction of the two axes, and supposing one eye only employed, and at a fixed point of sight,) there is an effort of which we are unconscious, but which careful experiment will convince any one we do make, producing some change in the interior of the eye, and adapting it to the view of distant or near objects, though in the same line of direction. Let one eye, (the other eye being covered), be fixed on some visible point on a transparent surface (pane or mirror), and a distant point in the original be steadfastly observed ; the spectator, scrutinizing his own sensations, will find that he must necessarily make an effort (such an effort as will fatigue him if much repeated) to accommodate his eye to the distinct vision of these two points alternately. The same will be, if by way of experiment he should try to copy on a sheet of paper before him (still using only one eye) part of a large picture on the wall of the other side of his apartment. Whence then arises the fatigue which the eye suffers ? There is a semblance of paradox in the phrase making an effort un- consciously but very many of our habitual actions are composed of such efforts ; who, for instance, when he writes his name, thinks of the muscles on his fore-arm ? Yet every turn of his pen is directed by them, and the effort made in and through them is purely voluntary. This species of effort is equally evident when we contemplate the actions of our eyes. 8 On the Field of Vision. The dilatation and contraction of the pupil of the eye to adapt it to the reception of more or less light, is too much forced upon us to justify the call- ing it, unqualifiedly, an effort : but when we take particular pains to examine very minute objects, we make a painful effort, of the nature of which we are quite unconscious. All know the fatigue of reading small print (or indeed, with insufficient light, any print). Now if the eye were merely passive, what can fatigue it? Mere scarcity of light is rather a relief than otherwise. The eyes, being open, must be filled with rays from every surface on which they are bent, whether the objects are large or minute. The rays from the page give no pain, unless an exertion is made to distinguish them. If this exertion were merely mental, the organ of the eye could not suffer from it. It is a bodily effort, purely voluntary, painfully exercised ; and yet we are entirely unconscious what it is, and know nothing of its nature till the science of the anatomist comes to aid the investigation of it. It is in fact only of late years that the existence of the acting muscles was demonstrated*. Let us imagine the infinite number of visual rays from the landscape in nature passing through a perfectly transparent, and therefore invisible, plane. A perforation of half an inch in diameter in a card held near one eye may represent such a plane ; and such would be of less than a 12,000dth part of an ordinary sized picture by Claude Lorraine ; but would contain in that small space an infinitely finer representation than the skill of a painter could pro- duce on the largest surface he might choose to fill. Let us suppose that plane to arrest those rays in all the perfection of form and hue ; such plane would ( lien be a perfect picture. A larger plane at a proportional distance would represent as perfect a picture, and would give in the eye, or in the hole in the card, a representation equal in size, in all parts similar in form, and equally perfect in colour, &c. Suppose the spectator to view a scene in nature in which some large object (St. Paul’s Cathedral for instance) is at such a distance as to subtend an angle at the eye, of one degree (i. e. the 360th part) of the circle of the horizon ; of whatever magnitude our transparent plane or picture is supposed to be, that object will still subtend an angle of one degree. Thus, let the last-mentioned large plane be supposed to be at the distance of six feet from the spectator ; if he approaches the picture by one-third of that distance (or two feet), the fixed object will subtend an angle of three degrees: but he may walk some hundred times that distance towards the cathedral itself before its enlargement will be perceptible, and many miles before his movement will enlarge the * By Travers, if the Author does not mistake. On the Field of Vision. 9 angle equally with that of the object in the picture. In fact, if the field of vision within the frame were occupied by a transparent plane, the motion of approach of the eye towards it would give a visible expansion of the whole field ; comprehending an additional extent of view, but no sensible enlarge- ment of the parts : but if the forms of objects were depicted on the plane, the approach to it would apparently enlarge the whole picture and every object in it, but would not enlarge the field of vision so as to admit any greater extent of view. In the transparent plane, different effect would be sensible under the slightest motion of approach : and as to direction, the slightest side motion would admit extent of view on one side of the open field of vision, and hide as much of it on the other side ; while in the fixed picture it would produce no change of view at all. Not only then is the skill of the painter inadequate, in degree, to produce on a given surface an appearance imitating that of space (i. e. an appearance of distance between parts which are contiguous on the surface of the picture); but it is plain that the utmost power of execution can do nothing towards satisfying either the mathematical tests which even the slightest variation in the direction of views of nature furnishes us with, or imitating the mysterious functions of the natural organ of sight : and it is plain that the difference between the appearance of space and the appearance of well-painted surface is much less in a picture whose point of sight is distant, than in one with a near point: but it is also evident that the limit of prohibition is subject to no strict line of demarcation, but is only a matter of discretion ; — that the painter may make his distance as short as his skill will enable him to do, consistently with the illusion he desires to produce. A little experimental observation will show the reader that a line of distance, equal only to the axis of an equilateral triangle (the base of the picture forrn- j- ing one side, making an angle of 60°; see Sect. 111. page 5.) borders on the limit of too much difficulty ; and that one equal to the base of the picture is better ; and if he is not anxious to bring in more field of view, a still longer line of distance will have a better effect, as better favouring the illusion. In landscapes with uneven foreground, a larger field may be allowed, than where the forms of objects in the original are regular. There is a difference also between a high and low base , quite distinct from horizon-line. In the former, a shorter line of distance is practically admissible than can be in the latter. This will be discussed in the chapter on the horizon-line, in which place the vertical as well as lateral extent of field of vision will be brought into discussion. c 10 On the Horizon- Line. CHAPTER II. On the Horizon-Line . Lest the assertion in the former part of this work, that “none of the books have given a just theory of the foundation of perspective, and particularly as to the theory of the horizon-line/’ should appear too bold, it may be required that some account of what they do say shall be given. “Pozzo’s Prospettiva,” the “Jesuit’s Perspective,” “Highmore, on Brook Taylor,” amongst the old ; — “Ferguson’s,” the “French Encyclopedic,” and “Chambers’s,” in later times ; — and “Rees’s Encyclopedia,” and the “Bri- tannica,” — Malton, Peter Nicholson, Francis Nicholson, Wood, Brown, Ed- wards, and Charles Taylor, amongst the moderns, — say so little on the subject, that to olfer extracts from them is unnecessary. Kirby, on Brook Taylor, has the following paragraph : “The height of the eye in easel-pictures is left entirely to the discretion of the artist; yet, in general, low horizons have a much better effect than high ones : for which reason the height of the horizontal line should yiexer exceed half the height of the picture : and I believe a little experience will teach any one that if it is made equal to only one-third of the height of the picture, it will be the most proper height of any, — I mean as to easel-pictures : for if the picture be a fixed one, then the height of the horizontal line must be exactly level with the spectator’s eye.” The paragraph is confusedly constructed. The writer must have meant by a fixed picture, one whose base is on the plane of station of the spectator, the foreground on the scale of nature, — and the figures as large as life, and not larger. In fact, the exception has no meaning : and all that remains to be noticed, is, his rule for limiting the height of his horizontal line ; and this rule is now to be examined. Mr. Varley says, (in a sheet intitled “ Practical Treatise,” &c.) “The horizontal line is the proportion of height between the top and bottom of the plane or picture at which the spectator views the same. It would, in most cases, look formal if placed across the middle of the picture so as to divide it in half : therefore Claude Lorraine has generally made it about one- fourth the height of the picture from the ground-line or bottom of the plane On the Horizon-Line. 11 or picture, and which is the most natural appearance for open landscape, where the sky and trees are pre-eminent on the space they occupy. « Caspar Poussin frequently placed his horizontal line about one-third from the top of the picture, which inclined it to a bird’s-eye-view, where the land appears much larger in space than the shy." It goes on to say (as the truth certainly is), “ That in the centre of this line all the direct lines vanish, &c. and all that are oblique vanish in other points of the same line;” and that “this line is the height of the spectator’s eye.” It would follow then from this, that if the painter took his view from the margin of a lake, and introduced a lofty mountain reaching (as it must do) nearly to the top of his picture, such would he “ inclined to a bird’s-eye- view yet if the writer of the paragraph were asked by a scholar the mean- ing of that term, he would say that it signified a scene as viewed by an eye situated (as that of a bird may be supposed to be,) at a great height above. Mr. Hayter says, in his " Dialogues,” “ One-third of the height of the picture is the most general rule for landscape : but it may be sometimes proper to deviate, “ When you take a view from an eminence , you must consequently have a high horizontal line ; and if you make an eminence the object of your view, you must have a low horizontal line. Antique and public statues being on elevated pedestals, must have a low horizontal line ; and whole-length por- traits of distinguished persons : but subjects of familiar life, or less noble characters, are better characterized by a high horizon. The likeness of a dog must have a high horizontal line ; but of a horse or an elephant, low.” Is it then forbidden to put a horse, a dog, and an elephant in the same picture ; or can the artist contrive to produce a picture with three different horizons ?* * As Mr. H.’s book is written in the form of children’s dialogues, it is possible the reader may be led to imagine that it was glanced at in the censure in the Preface to this treatise, on certain 44 books written for children.” Whether the form of dialogue is the best calculated for teaching a science ; whether Mr. H.’s instructions are sufficient and in all respects correct ; whether the easy and perspicuous example of that form of instruction (Mrs. Marcet’s 44 Conversations on Chemistry,” &c. &c.) since imitated by so many writers, has beep by Mr. Hayter, or indeed by any , successfully imitated, — it is not the duty or intention of the author of the present treatise to give an opinion ; but it is no less than justice to both parties, to declare, that the terms of censure alluded to, were by no means intended to be applied (nor can be made applicable) to Mr. Hayter’s book. c 2 12 On the Horizon-Line. It is curious to observe, that the one important line in the picture, where all horizontal distance terminates, — which contains the vanishing points, (and therefore determines the direction and the length ) of all right lines parallel to the ground plane (except such as are also parallel to the plane of the picture, and of these the perspective distance one from the other is determined by it), — the line which in fact determines the perspective of every point in the picture, — the standard, as it were, of measurement and proportion of every picture that can be made, whether of landscape, architecture, portrait, natural object, single or grouped, large or minute, — should for ages have been so scantily noticed by so many writers, and so confusedly and inconsistently described bv others, though all agree in their definitions of the term : — and after all, there is no difficulty in the theory. The Theory of the Horizon- Line. The horizon in nature is the extreme visible line bounding to the eye an indefinitely extended plane, which plane is a tangent to that radius of the earth on which the spectator stands. That plane is the level of the horizon ; and every plane parallel to it is called an horizontal plane: and every line contained in such parallel plane is called an horizontal line. The ocean only marks the real horizon-plane out a lake, or flat land of indefinite extent, of which the boundary becomes invisible by means of its distance, terminates (as far as regards the eye) in the line properly called the horizon in nature. The perspective of this line is, in the technical language of the books, called the principal horizontal line of the picture ; or briefly and more usually the horizontal line. In the present treatise “horizon-line” has been preferred, for avoidance of ambiguity of expression ; because lines parallel to the horizon (or horizontal lines,) are infinite in number; and the words are of necessity and frequently made use of in that sense : and in like manner (and for the same reason) the term “horizon-plane” has been preferred to HORIZONTAL PLANE. Of planes (imaginary or possible) parallel to the horizon-plane, the number is of course infinite : and such planes may be imagined on all levels, above or below the ocean in nature, and above or below the principal plane represented in the picture, and also above or below the eye of the spectator. All visible flat surfaces, table-land, or the surface of a lake on a mountain, the surface of water in a pit, or the area of a pavement in an excavation, the On the Horizon-Line. 13 floor or ceiling of a building, a flat table, &c. &c., — all are planes parallel to the horizon. So is the “ plane of sight,” or the supposed indefinitely extended horizontal plane which passes through the point of sight, which is the place of the eye of the spectator. Now the perspectives of the horizontal planes above or below the plane of sight, tend towards (or as it is technically ex- pressed, “vanish in,”) the horizon-line. (See Sect. XXIV.) In every picture that is drawn from nature or imagination, whether it be the representation of a confined apartment, or of an open and extended view of nature, the delineation of the scene will depend on the altitude from which the scene is supposed to be viewed. Nay, even if it be a portrait, or a study of a head or a hand, or the sketch of an animal, or the delineation of an object on a table or floor, or on a wall or ceiling, the position of the object above or below the eye, and the greater or lesser distance of it from the eye, will deter- mine its whole form and relative proportions, and the direction of all the lines of which the drawing is composed. The imaginary plane in which the eye is placed, terminates, as has been said, in the horizon-line of the perspective : therefore that line must be marked or supposed in every picture; and on its position the whole of the perspective depends. Now the books say, “the best proportion of a picture is when this line is at one-fourth or one-third (or some other proportional part) of the height of the picture above the base line that “it must never exceed such a height,” and so forth : and the author of this treatise has maintained that the two pro- portions are independent of each other. A picture may possess a high horizon (i. e. be truly drawn as viewed from an elevation high above the scene represented), and yet the horizon-line may be near the base of the picture ; or it may possess a low horizon (i. c. as viewed from a low level) when the horizon-line is considerably above the base line. Suppose a person placed at any greater or lesser elevation, casting his eye over a plane of great extent, (the surface of the sea will furnish the most con- venient illustration,) — the line which divides that plane from the sky, is his horizon-line : and it will in the real scene appear to be, and therefore in a picture must be supposed to be, exactly on a level with his eye ; i. e. in the plane of his vision. If he rises to a higher eminence, or descends to a lower station, this line will appear to rise or sink with him. To begin with a station on a shore nearly flat. He looks over along the surface of the sea, and sees a tall-masted vessel floating light on the water. 14 On the Horizon-Line. (The deck of this vessel is supposed to be higher above the water than the eye of the spectator is.) Then the extreme line of the sea will cut the sides of the ship ; as in fig. 1. No. I. and the gun-whale of the ship, as well as the masts, will intercept a part of the sky. Let the spectator now rise to a higher station. He sees the platform of the deck itself. He sees the surface of the sea beyond it ; and the line which divides sea from sky (his horizon-line) has risen with his eye, and now cuts the mast instead of the side of the ship. * Let him again ascend, and he will see the surface of the sea clear over the mast of the ship ; and his horizon-line no longer cuts any part of it, but leaves a space, which must be represented in the picture between the utmost height On the Horizon-Line. 15 of the mast, and the line that divides sea from sky ; — the line in question, — the horizon-line of the picture. Now what becomes of the limitations in the books ? If the horizon is high, it must be represented as high. It is above the mast of the ship, and it must be drawn as it is. The scene is viewed from a high level, and the horizon-line is, according to all definitions, a part of that level. Now it would be absurd to say that a painter must not represent any scene in nature viewed from an eminence ! May he not take a sketch from a high fortress, a cliff, or a mountain ? Say, “ that it is difficult,” and the observation is just. The cause of the difficulty will be considered presently. A skilful artist, however, will overcome it in practice, and will not yield to the unnecessary prohibition. What is seen and admired, it is desirable to represent. What can be seen at one view through a transparent plane upright and directly before the eye, may be represented on a similar opaque plane (the plane or face of the picture). The image on the glass may be copied, and that copy would be a picture. In the original landscape, water furnishes us with a constant level. The horizon-line must be above the furthest edge of any water beyond which flat land is, or may be seen ; or at that furthest edge, if bounded by the sky. A spectator looking at Diag. I. is supposed to stand on a fiat sea-shore. He sees the figure of a man standing on the same ground plane with himself, whose head reaches the horizon-line. The same line cuts the hull of the ship. In Diag. II. he is supposed to view the scene from an elevation ; and figures are seen in the picture on the same level with the spectator, whose heads also reach the line, which now cuts the mast of the ship ; and in Diag. III. where the elevation is still greater, there is an expanse of sea above the mast, and no ship or object touches the horizon-line. 16 On the Horizon- Line. In all, a distant cliff and mountains might be put in beyond. In the first of the diagrams, (1.) the line of mountain would be low; and in the last, (III.) much higher: but in none of them would the perspective be disturbed, or the height of the horizon-line altered, by the introduction of high land beyond. The most distant visible line of sea would still represent it*. A space of flat shore might also be introduced in the picture between the eye and the sea, by lowering the base line for the purpose. Neither would this affect the relative height of the mast, and the upper edge of the sea-line ; neither will their relative heights be at all altered by cutting off the bottom of the picture, nor by raising or lowering the upper part, and thus cutting off, or adding to, the ski/. Yet by such adding to, or taking off, the proportion which the height the horizon bears to that of the height of the picture, or to its width, will be entirely changed. No. IV. * Suppose two cliffs of exactly equal height, with a channel of sea between them. The curvature of the surface of the sea would intercept from the eye of the spectator, on either of them, a por- tion of the upright cliff opposite ; and on the supposition that it barely left visible the extreme height of it, the extreme visible line of sea would be exactly half way across the channel ; but would appear to be distant by the whole width, and to touch the opposite land. (The refractive On the Horizon- Line. 17 This change of proportion, though it does not remove the relation of the horizon-line to the position of objects in the view, does greatly alter the effect of the picture. The increase of the space of foreground below the horizon, if well managed, gives the idea of greater expanse ; (particularly if the repre- sentation of water touches the base line :) and, if ill managed, destroys the appearance of level, and gives the water, and objects on a flat, an appearance of rising like a ladder before the eye. Thus a picture with a very high horizon as to perspective may leave, below the horizon-line, a very small space compared with either its height or width : and on the other hand, a picture may have a very low horizon, and yet there may be a large space of foreground below the horizon-line. What then constitutes high horizon, as distinct from low base, or space below the horizon-line? Answer. — When the eye of the spectator in the reality is high above the level of the principal horizontal plane represented, (whether the representa- tion be of the distant part only of that plane, or of the nearer part only, or of both,) that is a picture with high horizon. When the eye of the spectator is low, and near the level land or water, (whether the painter introduces much or little ground-plane below the horizon, i. e. near his feet or the point of station,) that is a picture with low horizon. The high horizon is, when the station is high ; the low base, when the near part of the scene is introduced ; and this may take place on a perfect flat. To recur to our pane of glass (Sect. I.) A man may stand on the plane himself, and by attempting to bring into his picture the ground near his feet, power of the atmosphere is not here taken into account, but only the mathematical direction of the visual rays. The bending of the rays by atmospheric refraction will be noticed afterwards.) But if the relative heights of the two cliffs be unequal, the line of sea intercepting any part of one bank from the eye of the spectator on the other, will be nearer to the spectator on the opposite cliff, if his is the higher ; and further from him if it be lower. He has no means of estimating this distance, unless he knows either the relative heights, or the height of one, and the length of distance. The same will be, if he stands on some height equal to that of the mast of a distant ship, and can just distinguish the end of the top. mast over the line of sea. Then that horizon-line is half way between him and the ship. Another ship on that line would be visible in its whole vertical, from its water-line to the vane of the top-mast ; and the small angle which that vertical line of ship and mast would subtend at the eye, is the difference between the height of the horizon-line, and that of the plane of the spectator’s eye. It would be imperceptible in a picture, (as said in Sect. V . page 7) , not exceeding the thickness of a pencilled line in a drawing, or perhaps a thread or two of the canvass in a moderately sized easel-picture. If the surface of the ocean, or of an extended plain of land, were really flat, the distance would vanish imperceptibly, and no boundary between earth and sky would be visible. D IS On the Horizon- Line. he may produce in his picture all the bad (because unintelligible) effect of an extraordinary and ill managed high horizon ; but he cannot bring in any ob- ject higher than himself, of which the upper part will not be above the horizon-line ; whereas., when his base of station is high, high objects (such as the ships in Diag. III.) will be below the horizon, whether they be near or distant. In the first of the two cases, cutting off the bottom (or raising the base line) will bring the picture into ordinary perspective; in the second case it will only shut out so much of the representation, and alter the relative proportions of the height and width of the picture in its frame. It will now appear, that the height of the horizon has no more to do with the height or width of the picture, than it has with the thickness of the wood frame in which the picture may be intended to be put. It may be placed at any height in the picture ; nay, it may be supposed out of the picture ; above the top, or below the base : but in the first case, the picture must be placed low, and viewed from above ; in the latter, it must be hung high above the eve, and viewed near, and from below. The perspective will be violent, (as the phrase is,) but it may be made intelligible. Instances will be given of these cases. The low base, however, must have its limit in degree and manner perfectl) analogous to that of the field of vision (see page 9.); to which head it in fact belongs, though the discussion of it could not be introduced before the theory of the horizon-line was given ; and it must still be postponed until a few words have been given concerning the position of the prime vertical line. The field of vision is circular, it is the base of the cone of visual rays*, and the most regular and comprehensive form of a picture would be, a circle, of which the vertical diameter is the prime vertical line of the picture, and the horizontal diameter is the horizon-line. In this case the zero point will be the centre of that circle. But such form of pictures is neither pleasing nor convenient, and therefore not usual. The painter then selects a part of it, generally quadrangular, and leaves out the rest : he cuts off a part of the top and bottom, and of each side. Whether his quadrangular frame shall be square, or oblong either way, is a matter of indifference as to perspective, but will be decided by his taste or convenience, and adapted to the view he means to present ; but which portion of the circle (the base of the cone of visual rays) he will inclose in his quadrangle, is a question belonging to our subject — Perspective. * The eye is directed perpendicularly on the plane of the picture ; and the sight comprehends a circle round that point. The visual rays from all parts of the circle and its contents meet in the eye ? and thus form a cone; of which the apex is at the eye. This is called the cone of visual rays , On the Horizon-Line. 19 The part of the view in nature, to which he directs his eye, must be the point here called the zero point; it is where the prime vertical intersects the horizon-line : and, according- to the system here insisted on, it should intersect at the centre of that line. On that head, it has been already said, some authorities are against us ; and the dispute shall presently be entered into: but for the present it may be said, only, that the intersection is not neces- sarily, nor usually, in the centre of the prime vertical. A term is wanting to express the low base ; but before we propose such term, the predicament itself shall be more closely defined. It is, when the painter will delineate ground-plane near him, carrying down, as it were, the whole frame of his picture, and showing more of the lower than of the upper part of the circular base of the cone of visual rays. The lower he brings it, the more different will be the perspective form of the objects and spaces in the foreground, from their true forms in nature; — the more violent and less intelligible the perspective will be : and therefore the judicious painter will avoid carrying it to a degree beyond his power of making it explain itself. The difficulty is exactly analogous to (indeed it is the same with) that pointed out in the chapter on the Field of Vision. He has enlarged too much the vertical field of vision by bringing the plane of the picture too near the point of sight ; even though the lateral field of vision be at the same time narrowed by cutting off (or not extending) the lateral width of the frame. But a paradox presents itself here. The extent of the field of vision consists in the nearness of the point of sight to the plane of the picture : and as the line of distance is perpendicular to that plane, it must measure from the nearest part of it ; and this measure cannot be affected by relative proportion of width and height of the picture, or by the height of the horizon-line, or the lowness of the base. How then can it be said that the point of sight is too near, with respect to the lateral field, and not with respect to the vertical field ; or, vice versa, too near to the latter, and not to the former ? It is answered, that with respect to the central part of the circular base of the cone of visual rays, the lengthening or shortening of the line of distance has very little effect on the perspective. Look through a pane of glass, on a house or other object at a distance. Observe the magnitude and proportion of the figure it forms on the glass. Withdraw to a greater distance, keeping the object in the same part of the glass ; — little or no difference will be per- ceptible, Withdrawing from, or approaching towards the glass (lengthening or shortening the line of distance), will exclude or admit other objects, but d 2 20 On the Horizon-Line. will cause little or no difference in the appearance of the distant objects in or near the centre ; but with respect to such as are wide of it, the magnitudes and proportions will be affected by the nearness, as has appeared in all the preceding problems and diagrams. Now, to lengthen or shorten the line of distance, and to enlarge or diminish the picture from a fixed point of distance, is the same thing. A small plane near, is the same thing as a larger one proportionably distant. It presents to the eye, not only proportional, but equal objects ; the picture formed within the eye, is in both cases equal in magnitude, — not similar, but identical. Therefore, the lowering of the base of the picture merely admits objects in that direction in addition to the former field, not varying the perspective of it. The widening of the sides would in like manner admit additional objects in that direction, still not altering the perspective of the central parts. There- fore, on determining the point of sight, we do not estimate the length of the line by actual, but by relative, distance ; the proportion of the line of distance to the height or width (or height and width, both, or either) of the picture ; to the length of the prime vertical line admitted within the supposed frame, or to that of the horizon-line within the same ; to the portion of the circular base of the cone of visual rays selected by the painter, and admitted into his qua- drangular picture, whether it be high and narrow, or low and wide. As a term is wanting to express this low base, we shall venture to propose, "a broad sub-horizon and thus it will have been proved, that a picture may have a high horizon, and low base, (or broad sub-horizon) or the contrary. Diagrams IV. and V. (page 16.) are instances ; and some further examples will be given in the succeeding plates. We now want a term to denote that part of the prime vertical which is above the horizon-line, which may there- fore be called “the super-horizon and the picture may have a high or low super -horizon, whether the horizon-line be high or low. The high or low horizon, — the broad or narrow swi-horizon, — or the broad or narrow swper-horizon, — are three predicaments, each existing by itself, independent of the others. It will be observed, though perhaps the reason may not be so obvious, that a high swper-horizon is not so objectionable as a broad sw&-horizon. The cause will be noticed in a following page, when we have to consider why, (when it is admitted that the zero point may be placed above or below the central part of the prime vertical line,) it is insisted that it must be placed in the centre of the horizon-line. Of the Position of the Zero Point. 21 CHAPTER III. Of the Position of the Zero Point. That point to which in the present treatise the term zero has been given, is in some called the point of sight; and in some “the centre of the picture;” and in some “the principal vanishing point.” A reason has been given for refusing to adopt the first; as to the second, the vanishing points are infinite, and the word principal not evidently applicable to any one ; and the third term is inappropriate, as the point is very rarely placed in the centre of the prime vertical ; and though it has been here contended that it ought to be placed in the centre of the horizon-line , that is by some denied. At any rate, the point in question, is, the intersection of the prime vertical line with the horizon-line ; and the question resolves itself into this : — Must the prime vertical line be placed equally distant between the two sides of the picture, so as to cut the horizon-line in two equal parts ? A considerable degree of latitude is allowed in this respect by some writers and by some painters. It is said by some writers,. that though this “principal vanishing point” is called the centre of the picture, it is not always necessary to place it there ; that it must be in the horizontal line, but may be nearer to one side of the picture than the other ; and in fact, very many painters do so place it. The principal reason given for it, is, that the centre of the picture will not always be the centre of the scene the painter chooses to represent ; that the placing the centre of the scene in the centre of the picture would oblige the painter either to introduce, on one side, objects that are not picturesque, to the exclusion from the other side, of such as he wishes to introduce ; or else, to enlarge his field more than is convenient; and instances are given of the practice of some old masters of high repute. With respect to the last reason, it may be put out of the question ; for authority has no place in geometry. They may refer to example, and maintain that, notwithstanding the irregu- larity, the etfect of the picture is fine ; but still if it is irregular, however beautiful the picture may be, it is not perspective. It may be said that a certain known picture by Angelica Kauffman, in which (the legs of the figures being all naked, with open-sandalled feet,) one of the principal 22 Of the Position of the Zero Point. figures has two right legs, is a fine picture : but it will not therefore be con- tended that it is allowable” to draw a man with that deformity, because the painter thinks it will put his group into better form, and then quote the au- thority of that painter. What is a picture ? It is a representation of what the painter sees or conceives. It is designed to communicate to the spectator, that scene, whether real or imagined, so that the idea of the artist and of the spectator may be the same. If the painting is supposed to be that delineation on surface which would be described by visual rays passing through that surface to an eye placed in a given spot, and bent in a given direction, that spot and direction must be supposed and agreed upon. Without this convention, the painter has no means of securing the correspondence of the conceptions of the spectator with his own. It must be agreed and understood, that in plane perspective the line of view' is perpendicular to the plane : and it must be agreed (or in some way ex- plained,) on what point in the perspective plane that perpendicular falls. Mr. Varley illustrates this very well. 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