If-, % 4' Use ft ^^^^ 4nr^ , y far* 8% Digitized by the Internet Archive in 2014 https://archive.org/details/scienceofvisionoOOpars OF VISION; OR, PERSPECTIVE! CONTAINING THE TRUE LANGUAGE OF THE EYE, NECESSARY IN COMMON OBSERVATION, EDUCATION, ART AND SCIENCE ; CONSTITUTING THE BASIS OF THE ART OF DESIGN, WITH PRACTICAL METHODS FOR FORESHORTENING AND CONVERGING IN EVERY BRANCH OF ART, THE NEW ELLIPTICAL OR CONIC SECTIONS, LAWS OF SHADOWS, UNIVERSAL VANISHING POINTS, AND THE NEW OPTICAL LAWS OF THE CAMERA OBSCURA, OR DAGUERREOTYPE, ALSO, THE PHYSIOLOGY OF THE HUMAN EYE, EXPLAINING THE SEAT OF VISION TO BE THE IRIS AND NOT THE RETINA. SECOND EDITION OF THE ORIGINAL WORK, ENTITLED " PERSPECTIVE RECTIFIED," WITH CORRECTIONS AND MANY ADDITIONS. WHTTIS W WISSJ'E"2' = JF®WIR, 3F Ha A IP 35 Si. By ARTHUR PARSEY, Memher of the British Association for the Advancement of Science, ttc. ijr. SCIENCE NATURAL LONDON: LONGMAN & Co., PATERNOSTER ROW. MDCCCXL. " If the reader keep in view that God is the creator ; that nature, in the general sense, means the world he has made, and, in a more limited sense, means the particular consti- tution which he has bestowed on any special object of which we may be treating ; and that a law of nature means the established mode in which the actions and phenomena of any creation or object exhibit themselves, and the obligation thereby imposed on intelligent beings to attend to it, he will be in no danger of mistaking my meaning." — Combe on Natural Laws. USE OF THE SENSES. " To bring man into communion with external objects, and to enable us to enjoy them." — Combe. APPLICATION OF THE SENSES. "The leading object should always be to find out the relationship of every object of our nature — organic, animal, moral, and intellectual, — and to keep that relationship habitually in mind, so as to render our acquirements directly gratifying to our various faculties. The reward of this conduct would be an incalculable increase of pleasure, in the very act of acquiring a knowledge of the real properties of external objects, together with a great accession of power in reaping ulterior advantages.'' — Combe. WILLIAM HENRY COX, 0, Great Queen Street, Lincoln's Inn Fields. INTRODUCTION. The first edition of this work was published under the title of " Perspective Rectified," in February, 1836. The scope of Natural Perspective extending far beyond the limited pro- fessional purposes of linear art, I have given to this edition the title of "The Science of Vision," a science that has never before adorned literature. This edition contains many altera- tions, corrections, and additions to the former work. Optics, in the present state of that science, only explains the laws of refraction and reflection of light; and the popular theory of perspective being only an artificial system, no production has hitherto taught the natural language of the eye. The optical principles of the projection of light and ocular appearances being resolvable to the same common laws, the linear science of vision will constitute the practical manual of optics. I think I am justified in saying, that this work contains a new knowledge, with which no one has been acquainted, or, at least, thoroughly understood. I am the more emboldened to make such remarks, from the experience I have had of men of the first character and learning for the last five years, none of whom have I found, with all the advantages of art and science, to possess full, clear, or defined notions of visual phenomena. I do not make these observations with any intention of underrating such talented men, or of presump- tuously pronouncing the superiority of my knowledge, or the advantages the deep study of these matters has given me, but to shew the true state of information on vision up to the present iv INTRODUCTION. time. If the matters of which I treat had been known, or if the natural principles of the sight had been denned in optical science, we should find men of learning to agree upon general points, as we do upon other important questions ; we should find artists pursuing the fine arts upon rules simple, consistent, and satisfactory ; and, in conversing with intelligent and intel- lectual people, we should find a common understanding and just conception of the language of the eye ; but such is not the case. The task I have performed, and which I believe will prove of no small value in general education, art, and science, would not have fallen into my hands, if the knowledge had been defined ; I could have wished it had fallen into abler hands, or that I had had the advantages of the assistance of able and disinterested scholars in bringing this valuable know- ledge to perfection. I have been stimulated by the common impulse of talent, under the impression of doing mankind a benefit, and of improving the fine arts and literature of my country. On taking a review of past times, it will be perceived, that philosophy, in the pursuit of so many things, has never turned its enquiries seriously and deeply into the nature of vision, particularly as relates to the basis of the knowledge or linear outline of external objects as seen by the eye, although such created outlines are so far more numerous and peculiar than the geometrical outlines of abstract nature. The effects of the sight are the first intellectual food. As ideas cannot exist in the human mind, but under the similitudes of some material or visible form, and as geometrical similitudes are very limited compared with the multifold and incessant changes of visual similitudes, it is of the greatest importance to the understanding to be acquainted with their existence as well as their principles and natural mode of production, or the mind will be judging of visual effects by the nature of the geometrical ; which has unquestionably become a common practice from the want of INTRODUCTION. V a clear exposition of visual phenomena. This science will teach the necessary common knowledge of how and what we see. Who, on looking at the moon, can say they see a sphere 4 ? — it undoubtedly looks a flat round surface ; how we come to know it to be a sphere is not by the evidence of sight. So also with the starry vault, as it is called — who sees a concave hemisphere ? If some stars did not appear larger and brighter, how should we distinguish that they are not all equally far off"? If any one lies down on his back on a starry night, and does not revolve the head, how can he judge of the circumambient sky "? On looking at an orange, we look towards a spherical form, but we certainly do not see a sphere, — we see a circle some- what less than the diameter of the orange ; we know it to be spherical by handling it, and from the effect of light and shade, but we certainly do not see what we know as to form. We never see the form of any thing ; the form and the effect seen are never alike. If I look at a triangular pyramid, in unseen form or geometrically, it has four equilateral triangles, but I can only see one equilateral, or two and three scaline triangles, according to position; I know it has four equilateral triangles, but I do not see what I know. It is the same with all other things at which I look ; what I see is not what I look at. Voltaire says, "I see a small round tower in the distance, I approach near to it, and lo! I see and touch a hugh square building, which assuredly is not what I saw. Relatively, therefore, to ourselves, the measurable and tangible object is one thing — the visible another." Without understanding these things, we see by knowledge, as it is called, and that sort of knowledge constantly lies or deludes the judgment. Mankind are ever judging of the • perspective phenomena that play incessantly before their eyes ; the major part of whom, however, are not at all aware that such phenomena exist. vi INTRODUCTION. Let us now enquire into the import of pictures ; in general they are looked upon only as luxuries or ornaments, produc- tions more for pleasure than for any instructive benefit ; but if we consider an importance that really belongs to them, and the influence works of art have in forming our notions or ideas of external nature, from the first picture-book put into our infant hands till we become men of taste and connoisseurs in art and science, we shall not fail to see that if these productions be not the natural language of the eye, and do not communicate what they ought to do, that it were better pictorial art had never been known. Pictures purport to be, and are generally considered, true representatives of what is seen ; it will not take much pains to expose and prove this to be a delusion ; for, let any one consider his own knowledge and experience, and then revert to the standard character of drawing, and he will see at once that both theory and art have always falsified nature in one particular, which blunder has prevented the rest of the subject from being correct. For instance, on looking up to any lofty parallel surface, as a tower of a church, &c, every one has perceived in his own vision that the top appears narrower than the same breadth at the bottom, which is the infallible and constant effect of seeing ; and yet there is not a picture in the world that has that effect, and consequently no picture (prior to my own) has been drawn as mankind see objects. If every artifice be tried, nothing can destroy this natural effect — it must be seen ; neither can any artifice be resorted to, to enable the eye to see natural objects as they have been delineated. Parallel perpendicular lines, or all the upright lines of buildings, have always been drawn so, whether seen on lofty eminences or down below in valleys. Lines of buildings, running in horizontal directions, Art, how- ever, has always converged, with which the public eye is quite familiar; the natural effect of this direction has not been correct, in consequence of the lines in the perpendicular direc- INTRODUCTION. vii tion not having their proper effect given to them ; in short, Art has always represented objects geometrically, or as they cannot be seen in the perpendicular, and visually, or as they can be seen in the horizontal direction. On drawing the attention of any one to a parallel surface, they instantly acknowledge the perpendicular effect to be the same as the horizontal, and though perhaps unacquainted with art or science, can give the reason, " because one end is further than the other from the eye." The first picture ever drawn with optical accuracy I exhibited in the Royal Academy in 1837, and forms the frontis- piece of this work. The following year, my pupil, Mr. George Mallock, exhibited another there. Having stated wherein the general character of pictures is false, and that the theory of perspective, as laid down by Dr. Brook Taylor and others, is only an artificial system, it will be necessary to explain the present method of art, and to shew good grounds for denouncing that theory which ought to have been the guide of art. When a youth shews a talent for drawing, or his inclina- tions urge him to the study, with such information as the present system of education may give him, either of himself or under a master, he copies and copies from drawings and casts, till such time as habit — mere habit — has given him sufficient manual skill to enable him to commence making his living. During the course of this drudgery, he has guessed at every thing he imitated, nor has he found in books, nor has his master given him so much as an idea, that his profession dis- tinctly calls for an accurate representation of what he sees, and to do that with propriety, he must understand his own eye-sight. The master certainly could not tell him what he did not know himself, and was not aware of. If any part of his pictures, or the branch of art he pursues, should be archi- tectural, perspective works would be consulted as a linear art, and not as the language of the eye; from these works he will viii INTRODUCTION. learn to draw a horizontal line ; — use, but never understand vanishing points, &c. ; — find the theory produce many distor- tions, which no rule would remedy, and so put in many parts by guess, or thumb rule, as draughtsmen call it, to make it look tolerably natural. It is rather curious to hear of persons speaking of what is natural and of what is unnatural, when a knowledge or natural standard in drawing has not been known. I have no hesitation in stating the fact, that not one artist in a hundred ever troubles himself about any rules of the kind. They draw by skill or by eye, as it is termed. I do not mean these observations as a censure upon art and artists, but merely to point out that the mode of study and the practice pursued, are not what they ought to be. There is no doubt, if the ele- ments of visual knowledge had been discovered a century since, and the science of seeing reduced to simple practical rules, the study of art would have been established upon its legitimate basis, and no such loose doctrines or pro- miscuous practice would have been to be complained of at this time. With respect to the popular theory of perspective, as laid down by Dr. Brook Taylor and other learned men, if it were true, and of any value, it would be in general use. The only parties who make any use of it are architectural draughtsmen ; they however, as I said before, are obliged to make many allowances for its inaccuracies and deficiencies. The system, nevertheless, is considered by learned men to be perfectly correct, because it is based in the immutable principles of mathe- matics; but we shall be able to shew, notwithstanding the immutability of mathematical principles, that there may be a misapplication of them ; which, though it may not invalidate the principles, must surely destroy the purpose in view. If we take any case in perspective on Dr. Brook Taylor's system, the general, and the whole drift of the rules is to find the image or figure of the section of the visual rays that pro- INTRODUCTION. ix ceed from an object, or certain number of objects, to an eye, under some fixed or given data ; the section being invariably that at right angles or perpendicular to the ground; it is, however, made conditional, that the same section, in the trans- verse direction or horizontally, shall be at right angles to the axis of vision ; now, be it observed, that unless the eye be placed exactly in half the width and half the height of the object or objects viewed (which is the only true case in the old system), that is, so that the axis of vision or centre ray fall on the centre of the mass, the section stated will be at right angles to the axis of vision horizontally, but it will be oblique to the same axis perpendicularly. This obliquity in the transverse direction of the section is fatal to the optical truth of the section ; for, as will be seen by the illustrations of this work, the eye admits of no geometrical obliquity, but equalizes its rays in both directions about its axis, and the law for one direction is common to both. The figure produced from the vertical section of any form or pencilling of visual rays, is unquestionably a true mathematical figure, and so would any other figure in any other section of the same rays, as well as that, be a true mathematical figure ; but it is not the purpose of the art of perspective to find the abstract figures of an infinite number of sections that may be imagined or conceived to exist in a given form of rays, for the object of the science or art is to delineate the figure seen by the eye, while forming that given pencilling, or form of rays, which can have but one, and not an indefinite number of effects ; again, witli fixed data as to object, distance, and place of the eye, every mathematical section of the rays would appear alike, and similar to the image seen. The question then is, does the section perpendicular to the ground give, in all cases, the image seen by the eye *? The mathematical system provides for the production of the figure of no other section, and its rules are useless for drawing any o ther ; this then, must have been con- X INTRODUCTION. sidered the visual section, or image seen by the eye. In answer to the question, it must be evident to every mathema- tician, that these mathematical sections are not, and cannot be made optical sections, and that but one optical section can exist in the same rays ; now, if the eye be placed oblique to a width horizontally, that is, not perpendicular to its centre, that width diminishes in appearance, or foreshortens. Is it the horizontal position that causes this '? In a perpendicular posi- tion, when we call the same length a height, would not the same effect take place % Is it not the position, or obliquity, in any direction that makes it foreshorten % Or, has Nature two laws, one for seeing upright, and another for seeing sideways % The question is then answered, that no section, however mathe- matically true in conception or abstract science, is a true or useful figure in visual science, or can be seen, except that from a central point of view as above described, when that mathe- matical section is the same as the optical, and then only. As any pyramidical form of rays is totally dissipated the moment the eye is removed from the point of observation, the optical image is destroyed, and, as we have shown, all the mathema- tical images appear like it, and can only be seen (when made), of those diversified shapes (like the optical one), from points opposite to each centre, which points are all in different vertices to the optical or common vertex ; it is quite absurd, and con- trary to mathematical reasoning, to pronounce these artificial and non-existent shapes, to be perspectives of objects as seen by the eye. If the rays could be solidified, such sections might be made, and the surfaces placed to be seen of their natural or geometrical form, and the eye assume the positions of the different vertices. The principles of the optical section, and the simple rules of this work for finding it, are common to the production of any of the mathematical sections, the legitimate use of which is, in applying them in the art of light and shade, in solid geometry , or in practical mechanical purposes. An INTRODUCTION. interposed transparent medium, such as a pane of glass, when placed in any of the mathematical sections of rays, will contain such an image, but it must be made on it for us to see it; when, in reality, it becomes not an optical image, but a material interposed form, which makes in our eye, from that position, an optical image, and hides the form and similar image behind the glass. It is very necessary to avoid the delusions of images upon transparent mediums, for when they are turned, or looked at from the natural points of observation, they no longer inform us what we saw when they occupied the mathematical sections of a visual pyramidical form of rays. The images of objects seen through the upright panes of glass of a window, are illustrated in most works on perspective, to convey to students the notion of the plane of the picture or image seen. The explanations I have just given, and a study of the rules of this treatise, will, I trust, counteract this delu- sion for the future. In the production of the present species of delineation, the art depends on a geometrical adjustment of the horizontal line or level of the eye, vanishing points peculiar to that section only, and other technicalities, which cannot be understood without practical study. For the production of the section usually represented, the rules of Dr. Brook Taylor, if strictly followed, will be found to be mathematically correct, but no artist could venture to offer pictures made by them to the public judgment, the distortions of common appearances would be too monstrous. For the representation of objects as they are seen, or for the repre- sentation of any of the unseen sections, the base and horizontal lines require novel adjustments, on account of the introduction of the natural foreshortening and converging of perpendiculars, a new disposition of vanishing points of each section peculiar to the inclination of it; an increased number of lines of pro- jection, and the altogether new method of delineating without Xll INTRODUCTION. vanishing points, which are features of importance and useful novelty. I should have been glad to have recorded that the solution of the problem of perspective, so well known to be a deside- ratum of art, had not met with the usual prej udices, which oppose discoveries that rectify previous imperfections, or develop new but indisputable truths. On the first introduction of my system, Dr. Birkbeck, seconding my desire to explain the subject in public lectures, presided as chairman on the deli- very of a trial lecture, at the Mechanics' Institution, Southamp- ton Buildings, on the 13th April, 1836. He passed many eulogiums on my debut ; but there were individuals controling that institution, who, finding the natural principles to be, not only undeniable but subversive of the popular doctrines, declined any further enlightenment of their members. Subse- quently, on writing to the learned doctor, soliciting his patronage, and sending him the illustration of the natural pro- duction of the trapezium {Fig. 41 of this work), I never received an answer. Notwithstanding the first check of pre- judice, which I had never for a moment entertained a thought of, I commenced the delivery of lectures at my own residence, and offered my gratuitous services to many institution's. They were accepted, and I explained and illustrated the subject by diagrams and models to the members of the Western, the Marylebone, the West London, and the Westminster Literary and Scientific Institutions, from all of which societies I received most satisfactory and complimentary testimonials. I afterwards was engaged and delivered a course of six lectures in the Mechanics' Institution, Manchester, and was invited to the Manchester Architectural Society.* The latter society not only expressed their satisfaction to me personally, but after- * The lecture I delivered, and the acknowledgment of that Society, are inserted at the end of this introduction. INTRODUCTION. xiii wards investigated the subject by a series of papers brought forward by Mr. Hance, and unanimously agreed that my theory was " the true system of finding the plane of the picture," which they reported in the Manchester papers, and in The Architectural Magazine, The Civil Engineer and Architects Journal, &c. I also illustrated this subject before a full meeting of the members of the London Royal Institution, the Earl Stanhope presiding ; again I delivered a course of lectures in the Polytechnic Institution ; and, lastly, I explained the natural principles to the mathematical section of the British Association for the Advancement of Science at Birmingham in 1839 ; at the conclusion of which illustration, Professor Forbes was pleased to put a stop to any discussion, by rising and saying, "he thought enough had been said on the subject, for he felt sure every one had thoroughly understood me, and every one must he perfectly satisfied with the truth of my principles." It would be far from interesting to my readers to follow all the instances of non replies to letters addressed to influential scholars, and the apathy and prejudices that have opposed the dissemination of this theory, notwithstanding so much publicity has been given to it, and so much satisfaction expressed, but in justice to myself, and in justice to the present generation, particularly our youthful students, I must give an account of the reception my application met with, to give a full and gratuitous explanation to the Royal Institute of British Architects. The subject being one so intimately and inseparably con- nected with architecture, and so necessary to the practical purposes of the profession, with the view of gaining the patronage of this chartered establishment, I proposed giving a thorough exposition of the art of representation. The reply I received runs thus : — xiv INTRODUCTION. " 19th Dec, 1836. " The council, having submitted your paper to a competent quarter for an opinion upon it, are advised that it is a subject which it would not be expedient to bring before the notice of the members. " I am, &c, "Thomas L. Donaldson, Hon. Sec." Not comprehending the term "expedient," I wrote to the honourable secretary for an explanation, to which he replied: — * 22d December. " I regret my letter should have been expressed in terms to mislead you. I do not recollect saying ' that it is advised that perspectivq is a subject which it would not be expedient to bring before the notice of the members.' I merely meant to inform you, that the council, from the opinion with which they have been favoured by a very competent judge, are not satisfied that your system is either sufficiently original or correct to justify them in bringing it under the notice of the members. You must be aware that a certain character attaches to every subject, which has so much of the sanction of the Institute as to have been submitted to the consideration of the members and visitors at one of the meetings ; this sanction the council do not deem it prudent to afford on the present occasion. " I have the honour to be, &c. "Thomas L. Donaldson." After my success at Manchester, and the acknowledgment of the Architectural Society of that place, I renewed my offer to the Institute, to which I received in reply : — INTRODUCTION. XV 3d October, 1838. " Sir, — The first meeting of the council, since the receipt of your letter of the 6th September, was held last evening. I laid it before the members, and am directed to inform you, that they are unwilling to enter upon a subject which they already have declined to entertain in their reply to your application made in December, 1836. I am, at the same time, instructed to thank you for the courtesy of your offer, and am, &c. "Thomas L Donaldson, Hon. Sec, " Corresponding Member of the Institute of France." On the 6th of February, 1837, the members of the Institute assembled, Earl de Grey president, in the chair, who then addressed the meeting, and presented the charter; after which, the address of the council was read. Among other things, after expressing that being " recognized, as this body has been, by the first great source of authority and power, it is hoped that the future existence of this Institute will meet with no other rivalry than that of a generous contest to effect the utmost good ; and that it may pursue its course of usefulness by cultivating its many branches of science, &c." The address concludes with, " the Charter is not the ultimate point of our hopes ; it is but the threshold of an enlarged field of action : it should serve as a stimulus to our continued progress onwards, and to a gradual increase of attainments and know- ledge, until the science which directs us shall be as well defined, and as accurately laid down, as astronomy now is, by which the mechanism of unnumbered worlds has been brought within the grasp of the human understanding ; and until the region of taste, the music of the eye, as it has been aptly termed by Aristotle, shall have been thoroughly investi- gated, its effects resolved to their first principles, and its laws be as well understood, and as universally recognised, as the XVI INTRODUCTION. exquisite beauties, which, in literature, distinguish the produc- tions of a Homer, a Dante, and a Shakspeare." Entertaining so high an opinion of the yet unknown music of the eye, and the necessity of investigating and recognising the first principles of it, as the Royal Institute publicly expresses, can anything shew prejudice, or inconsistence of pro- fession and practice, more plainly, than that the council and members should refuse me permission to pass their threshold, to demonstrate to them the very accomplishment of the music, or as I term it, the language of the eye. Investigation was all I asked ; I did not want recognition without it, or sanction without merit. It is but due to some of the members to acknowledge that the course pursued was not unanimously approved. Those members who understand any- thing of the subject know, as well as the very competent judge, that the ,common theory and practice of perspective will not stand investigation ; and nothing more is required to prove that it is not comme il faut, than the concluding flourish of the Royal Institute of British Architects. If I have not defined and laid down accurately the natural laws of vision, I hope this learned body will set me right. I challenge all the members of all the colleges, schools of art (not excepting the Royal Academy) to justify the common theory of perspective by the laws of vision. I trust, after what has been said, that our learned and disin- terested critics will impartially examine the question at issue, and give their verdicts on the side of truth. The chemical discoveries of Mr. Fox Talbot and M. Daguerre, in "fixing" the images of the Camera Obscura, have most singularly con- firmed and fortunately substantiated the truth of my theory. The " natural images " of that instrument differ from the promiscuous outlines of artists, as well as from those made by the unpractised theory of perspective. Here then are three different delineations of the same thing — which is right or INTRODUCTION. XVII natural ? France has given M. Daguerre 4000 francs per annum for his discovery of "fixing;" and Arago, the great French scholar and philosopher, unhesitatingly pronounces the images of the Daguerreotype to be "natural," and says "they shew how far the pencil of the draughtsman has been from the truth," and " that there must be new laws of light, and shade, and optics ;" and also " that the sciences of chemistry and optics, in their present state, are inadequate to give even a plausible explanation of those phenomena." Without knowing of the endeavours to " fix " the images of the camera, I first pro- nounced them to be natural, in corroborative evidence of the truth of my theory, in my lectures at the Marylebone Institution, August, 1837. Notwithstanding all that has been said and published of the chemical discovery, and the unusual outlines of the Daguerreotype drawings in converging perpendicular lines, not one of my countrymen has opened his mouth upon this point; may I ask why? Is it for fear of the public knowing science and art to be at fault ? Why does not our Royal Academy or our artists take this matter up, and support their reputations, by showing the images of the Daguerreotype to be unnatural ? — the dignity of the profession demands it. Why has the renowned Turner resigned, and the Academy suspended the professorship of perspective ? Why is the Academy without a professor or lecturer on the basis of the fine arts ? I should not be able to put these questions, if per- spective were plain, intelligible, and communicable in its present state; nor would it be proper or necessary to do so, if a ready, candid, and impartial enquiry had taken place on the first introduction of the science of vision. I crave the pardon of my readers for dwelling so long on these points, but I have conceived it necessary to make known the difficulties I have encountered thus far, and to draw attention to a question in which all are equally interested with myself; if it should prove that I have done a benefit to the literature and fine arts 1) xviii INTRODUCTION. of my country, I hope I may have the satisfaction of being acknowledged. The delineations of objects naturally, or as they are seen (which will be similar to the productions of the Camera Obscura), will appear very strange and irreconcilable to the public eye after the undisturbed familiarization of inaccurate drawing in all ages and countries. To eradicate the impression now so deeply made, it will take the united efforts of all men of science, artists, lecturers, and teachers, to explain and satisfy the present adult race of the new effects, and perhaps this will be the most arduous and unsatisfactory part of the undertaking ; but as this must have been the case with other discoveries which have changed the order of belief, the duty of promoting this useful knowledge must not be shrunk from on the score of difficulty. The benefit of the change, I should hope, will be a stimulus to all men of intelligence and real lovers of the fine arts to join at once in the promotion of the art of design. However slow the conviction of the public in general may be, whose general pursuits or want of classical attainments may disqualify them for judging exclusively of such matters, if this, as it is said, be an enlightened, liberal, and improved age, I may live to see general and united efforts in this herculean task of turning the general ideas of things, and the commencement of training the rising generation in those just notions which sight and reason seem to me to be united in man, to elicit from the exhaustless appearances and effects of nature. The mere cor- rection of the lines of pictures would not be of so much conse- quence, were it not that art is the standard of visual impres- sions ; the public, and indeed all persons, thinking they see things as they are commonly drawn, some reasons might be advanced for not disturbing the general belief of effects and satisfaction in eminent works of art. The benefit does not, however, rest with putting all the lines of pictures together with optical accuracy, but it has ulterior claims in bringing the aberrations of our ideas to a just and natural verification, cor- INTRODUCTION. xix recting educational and doubtful theories, and bringing important branches of practical science into physical demon- stration. I am not so vain or thoughtless, as to suppose that I can, single-handed, or even with the assistance of those I have and may myself instruct, be able to do what time alone will do, in bringing the theory into general practice, for, as Candidus said in the Architectural Magazine, "I have undertaken a task greater than all the labors of Hercules put together." It is impossible to dilate upon all the topics affected by the introduction of the linear science of vision, or to point out what may be the future benefits of it ; but I may safely say, in pro- moting the study, and for the improvement of practical design, so desirable to the manufactories of this country, nothing can be brought forward more advantageous or beneficial to that object, than defining the elements, and establishing an universal system of imitating the geometrical and visual varieties of material nature. This knowledge and true basis of art alone, I am aware, will not insure a multiplicity of first-rate designers and draughtsmen ; the gifts of Almighty God must 1 e bestowed on the intellects, and the happy genius must have the advantages of sound education, opportunities of gaining gene- ral knowledge and practical experience, to give his manual skill sources of invention or design ; without such qualifications, many may learn to copy well, but can never be expected to have a creative imagination, or to become good designers for tin- purposes of trade or the higher branches of the fine arts. On the loose and systemless custom of the present schools of art, where pupils attend to learn and not to be taught, the object desired will never be satisfactorily attained. By adopting the laws of nature, the British school of art need not look to those of Berlin, Lyons, or any other sources of improvement, but those places we now emulate will have to look to us. In the linear science of vision will be found the principles and rules b 2 XX INTRODUCTION. for drawing with accuracy the human figure, the animal, floral, and every class of animate and inanimate nature. Everything we see is seen in perspective ; as no objects can he seen geometrically in one view, so they cannot be represented but in perspective in one picture ; — .no branch of the arts can be exempted from the governing influence of the science of vision, although it is so common to think it is only applicable to architectural drawing. When the principles of nature shall be generally applied, and to historical pictures especially, that epic class of painting will no longer contain defects that have so seriously depreciated many of the best productions ; as an instance, the great picture of the Raising of Lazarus, by Sebastian del Piombo, in our National Gallery, in tone, arrangement of colour, and skillful application of materials, deserves the highest praise ; notwithstanding its perfections, as respects the natural distribution of the figures upon the canvas, equal commendation cannot be bestowed. Overlooking some imperfections of the principal, or foreground group, if notice be taken of the group of six or seven little figures on the right-hand, over the heads of the supporters of Lazarus, and of the seven over the head of St. John and the uplifted hand of our blessed Saviour, on comparing these two groups, the first, which is on the nearer plane or distance, is composed of figures much smaller than the latter at a greater distance. This inconsistency reminds me of the satirical perspective of Ho- garth, wherein he puts the smallest sheep nearest, and as the flock encreases in distance, they get larger and larger ! If we have any rational ideas of a ground plane, we may ask, on what does the latter group stand in Sebastian's picture, to be elevated so high above the head of St. John*? — if the foreground figures were removed, perhaps we should discover a pedestal ! The old masters may be justified for these things, on the score of the former state of visual science ; but nothing will justify future masters in errors of the same sort. Till a pure INTRODUCTION. XXI system of representation adorns the Fine Arts of advanced and enlightened Europe, we have no right to make contemptuous observations on Asiatic and Chinese perspective. In architecture, I may point out a remedy in linear visual science, for the present lamented deficiency of architectural taste, instancing the Royal Institute as the head source of that lament. From the difficulties of making them, and the unsatisfactory effects of perspective drawings, it has been the custom of the profession to design by geometrical ideas, and to judge of them chiefly by geometrical drawings ; few architects of latter times have studied the theory of perspective deeply, many not at all, and the most part have depended on a sub- ordinate draughtsman in their employ to put their designs into a pleasing shape, when required to submit perspectives with their geometrical drawings and plans ; now herefrom arises one cause of deficiency of taste. The public, who is the judge of edifices, and whose approbation is the stimulus of talent, forms its opinions by visual effects, or the natural perspectives of them. If then the architect were to design to what he must be judged by, would not this w music of the eye" bring together a satisfactory coincidence of ideas between the profession and the public. How often does it happen that the drawings of proposed buildings look admirable on paper, but how disappointed are people on seeing them when erected ; the reason is, neither the geometrical nor the perspective drawings coincide with the appearances of real buildings. The omission of the " foreshortening " in perpendiculars (to say nothing of leaving out vertical convergence) has greatly misled the judgment of the architect, for when the eye reduces those lengths, the geometrical proportions of the design are not preserved, and has been a leading cause of the exclama- tion — " how different it looks to the drawings ! " He should xxii INTRODUCTION. design to the visual quantities, for the public, as well as him- self, cannot see anything else, and however beautiful the geometrical distribution of parts may be in professional con- ception, it might as well never be studied for, as it cannot be shown ; and as it cannot be seen, how can the architect expect the public admiration and approbation of what is not per- ceptible. After an architect has well considered the purposes and fitness of a proposed structure, and concluded on the external character he will give to it, being aware of the peculiar site it will occupy, and the distances and approaches from which the public will obtain views of it, not forgetting that nearness of inspection is necessary to discover the details, he should put his design into perspective accordingly, to see if the proposed combination of geometrical proportions produces equally favour- able impressions from those points ; but this he can only do by the natural principles of the vision ; any artificial system will not direct him, and better the geometrical design, in forming a judgment and taste. By a just method, he will be able to be beforehand with the public, and satisfy his own judgment before he submits his ideas to them. If this had been done, would the expensive alterations of Buckingham- palace have taken place. This subject might be descanted upon at great length, sufficient, I trust, has been said to shew, that as greatness in architecture may be summed up in the effect produced, taste demands the eye ever to be kept in view, and that the architect should design to it as he will be judged by it. I shall only add, on this head, that such things as set the public wondering — as sticking up an effigy of the Duke of Wellington on horse- back at Hyde Park Corner, or of erecting a boarding of the plinth of the Nelson Testimonial, to try the visual effects, and to ascertain the necessary proportions of the parts, — would not INTRODUCTION. xxiii be necessary to the architect or sculptor, if the science of vision were known, whereby such effects might be mathe- matically ascertained in his studio. The elliptical sections, or production of visual ellipses, the principles of which will affect the present theory of the conic sections, and most likely Keplars Laws, the Principia of Newton, and some of the present astronomical calculations, especially such as are made by the present rules of perspective, will form an interesting part of my work, especially to those learned and popular scholars who devote their studies to the celestial hemispheres. In taking the magnitudes of the moon, its facial appearance, or visual magnitude, which determines the angles of observation, will be less than the base of the tan- gential rays of its spherical body, and still less than the diameter which cannot be seen ; these circumstances are necessary to be observed in the calculations of the real mag- nitudes of planetary and distant spherical bodies. It never can produce accurate results, to consider rays to proceed to a point of observation by parallel projection, however distant the object may be ; for however infinitely the imagination may be stretched, the sphericity of a body will ever obscure the diameter of it from projecting its magnitude. I may just say, although I expect I shall be deemed presumptuous in antici- pating so much from the science of vision, I conceive it will prove that the orbits of planetary bodies are perfectly circular and not eccentric or oval ; that the radius vector sweeps over equal areas in equal times, and also equal distances ; that the velocities of planets are equal throughout their orbits ; and that when the geometrical quantities shall be judged of by the just knowledge of the perspective quantities, they will prove to be equal in time and space. I humbly solicit pardon and indulgence for advancing these hypotheses, but I have con- sidered them well, and having stated my reasonings to others, capable of setting me right, who however assent to them, 1 risk xxiv INTRODUCTION. the announcement, hoping I may be right for my credit's sake, and trusting, if I am hereafter proved to be wrong, that I may be freely pardoned on account of my zeal for the advancement of art and science. With respect to my announcement of the Iris being the seat of vision. In the year 1837, I first published an article in the Sunday Times, describing it to be the seat and not the retina ; and in my public lectures in London and Manchester, I have repeatedly explained my views on this head, and illustrated it by diagrams of the eye — reports of which were published in the Manchester Guardian and Times in 1838. I have enlarged on the subject in this volume, with the view of removing the notion that we see straight lines as curves, because of the concave form of the retina ; and at the same time to give a reasonable explanation for seeing things the right way upwards, or in their natural order, instead of inverted, as they are in the eye. With respect to the works that have been published, and the articles that have appeared in periodicals since the introduction of the natural and universal principles of perspective, I can but observe, that the authors being well acquainted with the imper- fections of the theory, assume an unjustifiable authority and influence over public opinion, and abuse public confidence, in obstinately maintaining the popular character given to the art by Dr. Brook Taylor. They well know, from experience, investigation is by no means a common proceeding, and that in a general way they will be more readily credited than any one who attempts to correct their dogmas ; therefore, regardless of any benefit or interest but their own, they persist in disseminating what they term orthodox principles. Among those that have appeared, the work entitled Geometry as Applied to the Arts, by Dr. Lardner, so far from being what the title implies, very few artists know of the existence of such principles, and those that do INTRODUCTION. XXV make but a very partial use of them. Let rne ask, does that volume, any more than those of the same character, contain geometry as it ought to be applied to the arts? The press, the free press of this country, could never do a more beneficial service to the present and the rising generation than by arousing public discernment and judgment on this topic. It introduces a new and a necessary general knowledge, in which every one is interested ; and the public would do well, for their own sakes, as well as doing justice to me, by shewing to future times, that the power of bigotry and superstition was non-existent in the present day, and that pride, prejudice, and self-interest were alike impotent in their endeavours to deprive the present generation of the benefit of a valuable discovery. As an author of a system that corrects existing theories, I am bound to speak boldly and plainly, particularly as I have not met with that liberality and candor which might have been expected in bringing forward a subject of this nature, and establishing a science on a foundation that can never be subverted. I cannot pretend to form an estimate of the time when a general adoption of the natural and universal principles of perspective may take place in the arts ; I have no doubt, public judgment, in process of time, will compel artists to keep pace with it, if they should defer following the laws of nature. The productions of the old masters and modern painters, down to the present time, though faulty on account of the imperfect state of the theory and absence of visual science, will, nevertheless, be entitled to the eminent rank they now hold. The exquisite productions of Canaletti, Raphael, Michael Angelo, Claude, Rubens, Corregio, Vandyke, Reynolds, &c, abounding in high conceptions, judicious arrangements, harmony of colouring, and masterly handling, will ever place them in the first order of art. Whatever may be the merit of the productions of artists after this epoch, remarkable for the discovery of the true basis xxvi INTRODUCTION. of pictorial art, the imputation of inaccuracy of outline, and the wilful commission of errors, neither consistent with geome- trical nor visual science, will be sufficient to counterbalance other points of merit, and spoil the finest reputation. In conclusion, I solicit a candid investigation of this subject, and beg to remark, that investigation into the theories of education, art, and science, may be productive of more solid benefits than denouments of popular novelties in their present state: — " Trace science, then, with modesty thy guide, First strip off all the equipage of pride; Deduct hut what is vanity or dress, Or learning's luxury, or idleness, Or tricks to shew the stretch of human hrain, Mere curious pleasure, or ingenious pain : Expunge the whole, or lop th' excrescent parts Of all our vices have created arts ; Then see how little the remaining sum, Which served the past, and must the time to come." — Pope. THE AUTHOR. London, 1*/ of October, 1840. xxvii MANCHESTER ARCHITECTURAL SOCIETY'S CONVERSAZIONE. Mr. Parsey's Lecture. — On March 7, the members of the Manchester Architectural Society held their periodical conversazione in the Society's rooms Mosley-street, at which Mr. Parsey was present by invitation, and a good attendance of members. After the members had adjourned to the library, and Mr. A. Hall had taken the chair, they proceeded to the election of trustees to the Society, when the choice fell upon the following gentlemen : — Mr. Richard Lane, Mr. James Heywood, Mr. J. Fraser, Mr. George Peel, Mr. A. Hall, and Mr. James Adshead. Mr. Parsey, of London, was then called upon, and proceeded to deliver a short lecture on his new principles of perspective. In opening his address, he said — " That the problem of perspective has not been solved requires no argument, from the known existence of so many opinions on the subject. Opinion always implies doubt ; and, where we find diversities of it, at most there can only be one in the right. The theory, as it has been promulgated, after the labour of its acquirement, has always left on the mind of the practitioner many questions of its truth. It is universally confessed, that judgment disallows a strict adherence to its rules. To obviate any future conflict of opinion, the lovers of the fine arts, and the promoters of sound and useful knowledge, must test the existing theories of vision by the unerring laws of nature, from whence only we can hope to discover a standard of taste. First, then, we must discover the laws of nature, whose unerring principles only can be the legitimate guide of practice. We must throw aside all prejudices, naturalised, as it were, by preceding custom ; and, for the sake of truth, and the happiness and fruitfulness it produces, not only enjoy its benefits ourselves, but transmit its valuable influence to future generations. No practice can be good or safe unless it is founded on permanent principles. The future satisfaction and improvement of art and science depend altogether on this investigation, and the establishment of a practical science of vision. As respects the purposes of art, the science of perspective proposes to define the images of external objects as seen by the eye. It would be ridiculous to append " as seen by the eye," to the definition of the art, as nothing can be seen but by the eye, were it not to distinguish optical effects (upon which our natural ideas depend) from those shapes which in abstract science may be required for solutions unconnected with vision. It will be evident that, whether we require the practical skill of drawing the appearances of objects or not, the understanding loses a necessary and valuable power, in not being capable of apprehending natural effects ; hence the principles of visual science are not less valuable to common knowledge than to the draughtsman and the refined and cultivated mind. " It is only to the theory of perspective that society can look for information on this head; and how few there arc, even among the practitioners of art, who are in any degree versed in this knowledge, imperfect as it is ! And why ? xxviii MANCHESTER ARCHITECTURAL SOCIETY. because of its unintelligibility, and its mandates clouding the purer con- ception. The practice at present consents to the following leading laws : — Vanishing points produced by parallels to the base lines of the object, from the point of station, cutting the line of projection through the nearest point of the object; the adjustment of the horizontal line (on which the vanishing points are fixed) at the height of the draughtsman's or spectator's eye from the base line of the elevation ; a vertical section of the visual rays proceeding from objects to the eye, that is, a section perpendicular to the ground plane, or natural horizon ; and the invariable erection of the geometrical altitudes of perpendiculars in all elevations or depressions of the point of view. On these leading features of the old system are established the consequent minor details of the art. Writers have introduced various methods to facilitate the practice, but a strict adherence to these fundamental rules has been observed by all ; so that in contrasting mine, it is not necessary to particularise any author's system. I will now explain these rules by my models and diagrams, after which I will lay before you my new theory ; or, I should have said, the principles I have perceived to be the causes of unalterable and unavoidable optical effects." Mr. Parsey then explained that, in the old system, he held the only true case to be when the horizontal line passes through half the altitude of the object with equidistant vanishing points. He then entered into an explanation of his own system, in which he held that the lateral plan exhibits the true plane of the picture, which demands an optical placing of the vanishing points, a natural adjustment of the horizontal line, the visual reduction of altitudes to agree with reduced horizontals in width and depth, with the consequent minor details of the visual science. This formed the principal feature in the explanatory part of his lecture. He continued : — " The effects, and the practical principles I have laid down for producing them, I have not defined by ingenuity, or on any peculiar views of my own ; they are not a contrivance to gain popularity for novelty's sake ; but they are the natural causes of the infinite, unavoidable, and incessant influences of external nature on the vision of all mankind. To these, then, we must consent ; by these we must be guided in our theories, and by these only can we produce ideas, and pursue our practices on rational grounds. Before my theory and its adoption can be opposed, it must be shown that these are not the elementary laws of nature ; and some justification must be given to the world for persisting in a system at variance with truth and nature, and with the present professions of societies and individuals for the advancement of science : wilful and obstinate, indeed, will be the continuation of erroneous practice ; and wicked, I may say, will be the dissemination of doctrines known to be suppressive of a right understanding of that faculty, by which, if we make a right use of the divine boon, we may ' look from nature up to nature's God.'" Amongst his testimonials, Mr. Parsey mentioned those of the Rev. J. B. Reade, nephew of the late Professor Farish, author of Isometrical Projec- MANCHESTER ARCHITECTURAL SOCIETY. xxix tion; Ft. R. Reinagle, Esq. ; R. A. ; the late John Constable, Esq., R. A., William Etty, Esq., R. A., &c. He went on to say : — " It is said on all sides that my theory is correct; but that it would be absurd to put it into practice. The admission of the truth of my principles at once does away with any absurdity in adopting them ; for it would be tantamount to insanity to argue, that practice may be justly pursued on false principles. It is the perfection of human efforts to combine principles and practice. " Deem me not presumptuous or arrogant in calling upon this learned and influential Society to set the example of public recognition ; and as Manchester is a point from which so many improvements in art, science, and manufacture emanate, to claim to ourselves the distinction of being the first public body to acknowledge the accomplishment of this desideratum. Lay the foundation stone of the temple of taste, unfurl the standard, and place the British school of art on a proud pre-eminence. Deter not merit from struggling for the universal good, and let the persevering see that their efforts will not be in vain. The art of design, in all its branches, must be feeble till its root be cultivated and nourished. A perfect theory of perspective has been anxiously sought by the refined of all polished nations. Hail, then, the accomplish- ment as a British achievement, and let our native talent first reap the advan- tages of an improved practice." At the conclusion of the lecture, Mr. Parsey entered into conversation of nearly one hour's length, freely discussing with the members his new prin- ciples, meeting any objections that were suggested, and more familiarly illustrating his views. A vote of thanks was then proposed to him, which was instantly carried by acclamation. Mr. Hance addressed the members, and stated that he had been decidedly prejudiced against the new system ; but, from instructions received of Mr. Parsey, he was a decided convert. The members separated at a late hour, after one of the most gratifying meetings they have had since the establishment of their Society, which now bids fair to take root and rear its head amongst the permanent institutions of the town. — Manchester Times, March 10, 1838. MANCHESTER ARCHITECTURAL SOCIETY. On Wednesday Evening, 5th September, the Seventeenth General Meeting of the Society was held in their Rooms in Mosley -street. Mr. J. W. Hance, the secretary, read the first of a series of papers inves- tigating the principles of a new system of perspective, which has created much sensation, invented by Mr. Parsey, of London, who, it will no doubt be remembered, delivered a course of lectures on the art in this town, in the early part of the present year. After a few prefatory remarks on the necessity XXX MANCHESTER ARCHITECTURAL SOCIETY. of a knowledge of perspective to all who wished to attain even a tolerable pro- ficiency in drawing, Mr. Hance proceeded to compare the principles of Mr. Parsey's system with those of the usual one, pointing out their discrepancies. Assuming as his data — 1st, That for any art or science to be of practical utility, it must be based on sound principles, invariable and immutable ; 2nd, That of two systems relating to art, that must be the better which is the more simple in practice, and whose results are more in accordance with natural effects ; 3rd, That any practice, even if sanctioned by long custom, which can be proved to be founded on false principles, is unworthy of support, and should be discarded by those who are anxious to follow the truth. Mr. Hance remarked that perspective was generally defined as a section or cutting, by the plane of delineation or picture, of the rays supposed to proceed from the object viewed to the eye of the observer, and was often familiarly illustrated by supposing a window, plate of glass, or other transparent plane, to be inter- posed between the eye and the object ; the figure generated on the glass, &c, by the rays, would be the perspective representation of the object ; and to perform this upon an opaque surface, such as paper or canvas, by mathe- matical rules, is the science of perspective. Upon the placing of the picture, or plane of delineation, the whole operation depends ; and this was the point to which he should confine the present investigation. Great diversity of opinion prevailed about the mode of fixing this plane ; but he thought he should be able to prove that Mr. Parsey's assertion was correct, " That we cannot choose the plane, but that Nature herself marked it out." All we have under our control in viewing an object is, to fix the position of our eye relative to it ; which being once fixed, only one image or figure could possibly be impressed on the mind. There must, therefore, be only one fixed invariable natural plane intersecting the rays of vision in the same manner under all circumstances and in all cases ; and if this were transposed into a sensible, tangible plane, such as a picture, &c, no alteration would take place in the image seen. Now he would prove, by a small diagram, this natural plane to be, as in Mr. Parsey's system, at right angles to the axis of vision, or centre of the system of rays, which is always in the centre of the object viewed — for in this way only can we obtain the same result in all cases ; and as it would be obvious that by the usual system it was possible to obtain two or more repre- sentations of the original object with the same given data, it must be manifest that it is erroneous, and cannot be depended on as affording satisfactory results. After Mr. Hance had concluded his remarks, which were listened to with much interest, an animated discussion took place ; and it was the unani- mous opinion of the meeting, " That Mr. Parsey's mode of finding the plane of delineation is the correct one." — Manchester Guardian. ANALYTICAL TABLE OF CONTENTS Page Introduction ....... iv Manchester Architectural Society's Conversazione . . xxvii Investigation and Acknowledgment . . . xxviii Definitions and Geometry necessary for the Study of the Science of Vision ........ 1 Physiology of the Human Eye ..... 26 Rectilinear Perspective : — Elementary and Practical Rules of Visual Science . 37 Foreshortening . . . . . . .39 The Perspectronometer ..... 44 Convergence . . • • • • .46 The Sectional or Lateral Plan . ... 50 The Method of putting a Plane Surface into Perspective without Vanishing Points . . . . . .52 Another Method hy the True Visual Vanishing Points . 53 Variation of Appearances from a Fixed Point of View through the Interposition of other Objects . . . .55 The Method of putting a Quadrilateral Surface into Perspective from a Point of View within the Figure seen 57 The Method of putting a Square into Perspective, producing a Trapezoid . . ... . . .59 To find any Abstract Section of the Rays, or Section of a similar Pyramidical Solid . . . . . 61 To put a Square or Rectangular Surface into Perspective, Viewed Oblique to its Sides, producing a Trapezium . . 62 The Old System or General Practice of Perspective . 64 The Methods of Drawing Solids in Perspective . . .67 The Cube. — When one of the Edges only is projected Geo- metrically . . . . . ib. When all the Edges seen are in Oblique Perspective, the Eye being level with the Height of the Object . 68 When all the Edges seen are in Oblique Positions, the Eye being above the Altitude of the Cube . . .69 When all the Sides Foreshorten and Converge . . 70 The Methods of putting Pyramids into Perspective: — The Method of putting a Pyramid into Perspective, opposite one Edge, Inclined directly from the Spectator . . 72 xxxii CONTENTS. Page The Method of putting a Pyramid into Perspective Oblique to the Edges ....... 73 The Line of Projection . . . . . 74 The Method of putting a Building into Perspective . . 80 How to Make a Perspective Drawing of an Increased or Decreased Size from the same Ground Plan . . 85 How to Represent Parallel Ordinates, or Rows of Parallel Lines, Equal Heights of Figures, &c. . . . ib.. How to put a Horizontal Line and a Perpendicular into Perspective 90 How to put a Human Figure into Perspective, so that Every Limb may be Optically Foreshortened . . . .93 New Practical Catoptrical Illustrations — The Horizontorium, Reflections of Light, &c. . . . . 95 New Laws and Rules of Shadows . . . .101 Vanishing Points and Horizontal Lines Explained . . 108 . for Superficies . . . . .110 for Solids . . Ill Curvilinear Perspective : — The Elliptical Sections, with an Enquiry into the Nature of the Conic Sections . . . . . .113 New Method of Producing the Visual Ellipse . . 118 How to Find the Distance of the Point of View, and the Originating Circle of an Ellipse . . . . . .121 How to Find the Image of any Section of a Cone . . 122 How to Draw a Perspective of a Cylinder . . .124 Method for Correcting the Drawing of Circular Buildings . 126 How to Represent Circular Columns as we see them . .129 The Axis of Vision and Plane of the Picture explained . 131 Remarks. — Convergence of Small Objects, Appearances Altered by the Motion of the Head, Landscapes, and Distance of Station . 142 THE SCIENCE OF VISION ; NATURAL PERSPECTIVE. Perspective is the art of representing by lines any form or number of forms combined, as they would appear to the eye, from any chosen position, or fixed point of view. The term perspective is generally described as being derived from per, through, and specio, seeing, or seeing through ; but it seems (o me that the proper derivation is from per, by, and spectrum, the image, or seeing by the natural image. Perspective is the science of visual phenomena and representation. Ainsworth gives an excellent definition of the art in his dictionary, although it must have appeared paradoxical to the general reader: — " Ea pars optices que res objectas oculis.aliter qutim re ipsa sunt represcntat? — " That part of optics by which things seen by the eye are represented different to the thing itself." Although it is the representative art, and the only guide to the practical draughtsman, the knowledge is not less essential to the community at large ; for it is evident every one ought to know the true impressions made on the sight, as well for their own infor- mation and pleasure, as for the pow 7 er of judging and reflecting on the effects of the works of nature and art. Perspective is the science of seeing, the language of the eye, and the only guide to the knowledge of what we see. B 2 $ THE SCIENCE OF VISION ; OR, There can be no perspective, but in the eye of a spectator. It is the eye only that gives it creation, or wherein it exists. We reason on or represent the appearances of objects, conceived to be or actually seen from certain constrained or chosen points of view, with the head fixed, but the eye revolving on its axis. The fixture of the head is a necessary condition ; for it would be absurd to reason upon, or to attempt to represent, in one picture, a succession of changing delineations produced on the eye by the motion or revolution of the head. Perspective is divided into two classes, rectilinear and cur- vilineal; the first refers to straight lines and the latter to circular lines. The art teaches the treatment of lines according to their natural appearances in objects, which are distinguished by their edges or contours. A natural appearance is the uniform impression on all minds from identical positions of object and sight, with equal powers of vision. Some authors speak of aerial perspective, which is simply giving distinctness or obscurity to the outline and colour according to the quantity and quality of intervening atmosphere between the objects and the eye; but this is more properly to be referred to the art of light and shade. As the attainment of perspective depends on the right under- standing of the geometrical nature of lines, before any rules are advanced for their application in visual science, it will be necessary to introduce an explanation of the undeviating laws, arising from the connexion of lines in bodies, which are familiarly given in geometry — the science of quantity, exten- sion, or magnitude, independent of vision. As practical per- spective can only be performed by geometrical rules, it would be useless for the student to attempt to proceed without ac- quiring the technicalities or, at least, so much of that art as applies to construction. I have endeavoured to give these elements as abbreviated a » natural perspective. 3 form as possible, knowing the usual dread and reluctance to engage in the study — the value of time to many, and the uncon- trolable causes which exclude others from diving deeply into it, if neglected in early education. The value of geometry, as a preliminary study of art, is not generally known. It does not seem to the general reader to have any relation to drawing, and students in art have little or no conception how it can further them in their studies. The general view is, that persevering practice and doing a great deal of work, will ensure skill ; but this sort of drudgery often proves little better than a waste of time, from the want of that propriety which the knowledge of geometry would ensure. Excellence can only be attained by the principles of geometry, for it may be taken for granted, that any one who has arrived at eminence in the profession, even if he be unacquainted with the popular rules of geometry, has most assuredly fortunately adopted modes of his own, which, if scrutinized, will be found to be strictly geometrical; considering this fact, then, it will be seen how advantageous it will be to set out with this help. As this knowledge is a constituent part of experience, to have it at the beginning of the study of art will most surely facilitate the practice of the draughtsman, and give propriety to all his efforts. DEFINITIONS IN GEOMETRY. Definitions are the fixed names for the variety of forms. The first three are not forms, but the properties in all forms; the rest are divided into two sorts — planes and solids. A plane is called a surface. A solid is a form having four or more surfaces. Surfaces are regular or irregular. Regular — when the lines are equal or parallel. Irregular — when the lines are unequal and angular. B 2 4 THE SCIENCE OF VISION ; OR, The first three definitions are — a point, a line, a super- ficies. 1. A point is that which has position, but no magnitude nor dimensions ; neither length, breadth, nor thickness. 2. A line is length, without breadth or thickness. 3. A superficies is an extension of two dimensions — length and breadth, but without thickness. We can only describe these three by words, as they are not definitions of any figure. 4. A body, or solid, is a figure of three dimensions ; namely, length, breadth, and thickness. {Fig. 1, Plate 1.) Polygons are figures having a number of sides : they are called regular when the sides are equal, and irregular when the sides are unequal. The regular polygons are called triangles, squares, penta- gons, sexagons, septagons, octagons, &c. A triangle, with two sides equal and the third unequal, is an isosceles. A scaline triangle is that whose three sides are unequal. A right-angled triangle has one right angle. The following are irregular figures of four sides. A rhomboid is an oblique-angled parallelogram. {Fig. 2, Plate 1.) A rhombus is an equilateral rhomboid, having all its sides equal, but its angles unequal. A trapezium is a quadrilateral, which has not its opposite sides parallel. {Fig. 3, Plate 1.) A trapezoid has only one pair of opposite sides parallel. (Fig. 4, Plate 1.) A diagonal is a right line joining any two opposite angles of a quadrilateral. {Fig. 5, Plate 1.) The rest of the definitions I shall explain in a description of the circle, from which all the terms for lines and figures are derived ; and those persons who are altogether unacquainted N AT U 11 A L P E RSPECTIVE. 5 with geometry must acquire practically this indispensable introduction to perspective. The reader will observe that these definitions are merely the technical terms for various shapes or distinctions of geometrical forms. These names were given by the earliest geometers in reference to their abstract forms, independent of the changes such fixed shapes undergo when viewed from different positions ; but as these geometrical shapes raise, in the vision of all mankind, appearances or shapes different to the shapes looked at, such created forms being similar to the geometrical, the definitions apply to both, so that the student will not lose sight of the two origins or purposes of the definitions of geometry. Hitherto, the abstract form has only been taught, and the natural visual production of them has not been considered. It is more than probable (although nothing has been said to justify me in the supposition), that the first geometers perceived these visual figures to be optical creations of geometrical figures, which natural origin may account for the permanency of those technical terms, which we cannot conceive to have been a matter of chance or an accidental and ingenious adoption of figures coinciding with the practical operations of the sight. In illustrating the visual production of the shapes called tra- pezoids and trapeziums : if a square board be viewed imme- diately over the centre, then not over the centre, but in a line parallel to the sides, passing through the centre, and again in any position or line oblique to the sides, passing through the centre or not, in the first case this geometrical square will appear a square, in the second a trapezoid, and in the third a trapezium, although what we look at is in every position a square board. By peculiar circumstances of lines of objects and position with each other, such geometrical lines will produce in the eye the appearances of all the definitions. The infinite variety of shapes created by the eye, of which, for the want of visual knowledge, the greater part of mankind are quite uncon- 6 THE SCIENCE OF VISION; OH, scious, gives alone legitimate form to our ideas of external nature, which would be poor indeed if it only entertained the sight with the geometrical form of things. These creations of appearances from a single form are not a creation of the fancy, but are the operations of a faculty, which in man has not only the animal uses, but is the source of the highest intellectual enjoyments. To teach mankind how to use the eye-sight to the full extent of its purposes, will, I trust, not be considered an unimportant effort of philosophy. In the first study of geometry, if the visual creation of the defined figures be introduced, it will take off much of the dryness commonly complained of, and make it more agreeable to the natural inqui- sitiveness of youth ; besides, it will give a necessary distinction to the abstract or general principles of geometry and the prac- tical principles of visual geometry. The juvenile reader will understand that abstract principles or shapes are such as we consider, without using the eye-sight, and distinguish by the sense of touch, or such as we reason on in the mind by memory ; but practical effects can only be determined by understanding the creations or language of eye. A geometrical square must be seen, or have been seen, to give an idea of that shape. To no other sense than the sight can it become a square, and solid forms are still more obscured from the understanding, if submitted to the touch only. To persons who have never seen, the touch conveys to the mind only four extensions, but no figure, and with solids more, but no optical figure ; as the mind cannot form — that faculty must originate in sight. With a sudden gift of sight, it has been proved that shape and geome- trical form cannot be recognised from the former habits of touch. The perspectives or natural images of the vision alone give legitimate form to our ideas, and constitute their rational outline. In every useful action of the mind, a blindness is never implied ; the intelligence of the eye is always a con- ditional basis of our ideas ; and if our thoughts extend NATURAL PERSPECTIVE. 7 almost to infinite space, that thought itself is the penetration of vision THE CIRCLE. (See Fig. 6, Plate 1.) The centre of a circle is a point. The radius o, a, is a right line from the centre to the cir- cumference, or the length between two points. A circumference is a line which is always deviating from the right or straight line, and joins its extremes at one point. There cannot be a centre without its being the centre of a circle, which has all its radii equal. When we speak of the centre of a square or other figure, the mind refers to the circle out of which it is formed ; the length or radius from the centre o, to the four corners, e, f,g, h, being equal to all the radii of the originating circle. The same principle applies to solids. A circle is generated by a line or radius ; that is, length between two points ; by revolving one point around the other, called a centre, the revolving point producing a circumference ; hence the properties of a circle are, a centre, a radius, and a circumference. The established division of a circle is into 360 degrees or divisions ; half a circle, or a semi-circle, has therefore only 180, and a quarter of a circle 90 degrees. The lesser divisions are angles of smaller dimensions, and may be divided again and again. The diagram is set out in sixteen divisions of 22^ degrees each, to avoid complication. The pupil may readily supply the intermedial radii in his own mind. Two radii of equal length, a o, o c, lying in the same direc- tion, form a diameter, which is the longest line that can be drawn within a circle. There can be but one perpendicular, b d, and one horizontal 8 THE SCIENCE OF VISION ; OR, diameter, a c, in a circle ; all the rest must be angular ; hence all lines are either perpendicular, horizontal, or angular. No two radii are ever parallel. An angle is two lines, e o, a o, meeting at the point o. Parallel lines, f e, g h, never meet each other at either end. A right angle is one line perpendicular to another, as b o is to o a. Every right angle contains 90 degrees, because there are that number on any circumference circumscribed through the expanded ends of two lines, as a and b, the point of angu- larity being the centre o. An acute angle is any two lines within or less than a right angle, as e o, a o. An obtuse angle is any two lines containing a greater number of degrees than a right angle, as /* o, a o, equal to 120 degrees. Two lines only denote the number of degrees between them, and do not describe any figure till bounded by a third, either straight or curved. A right line makes them a triangle, a curved line a section of a circle. A Triangle is 3 "\ £ c [3 A Square . . 4 J g I 4 = ef, g h, A Pentagon. .51 2 is 1 5 \ \ points of a circumference. A Sexagon ..6 1 g | 1 6 A Septagon..7 1 l 7 An Octagon. .8 J V.8 A parallelogram is two horizontal and two perpendicular parallels, ef, g h. An arc, or arch, is a part of a circumference, as a e, a b, and a f, &c. A segment is an arc, e h, bounded by a chord, h e, which is a straight line from the two points or ends of the arc, e h. A tangent is a line parallel to any radius touching but not cutting the circle, as i a. A chord is a line drawn within the circle from any two points or degrees, the diameter being the longest chord NATURAL PERSPECTIVE. 9 A diagonal is a line from opposite corners of figures of four sides. The diagonal, e g, is the longest line of the right-angled triangle, e f, g f, that figure being only half of a square, ef\ g h. These are the principal definitions, and refer to planes and solids, solids being composed of a number of planes. A prism is a solid whose ends are parallel, equal and like plane figures ; and its sides, connecting those ends, are paral- lelograms. {Fig. 7, Plate 1.) A prism takes particular names according to the figure of its base or ends, whether triangular, square, rectangular, pen- tagonal, hexagonal, &c. An upright prism is that which has the planes of the sides perpendicular to the planes of the ends or base. A parallelopiped is a prism bounded by six parallelograms, every opposite two of which are equal alike and parallel. (Fig 8, Plate 1.) A cube is a square prism, being bounded by six equal square sides or faces, and are perpendicular to each other. (Fig. 1, Plate 1.) A cylinder is a round prism, having circles for its ends. Fig. 9, Plate 1.) The axis of a cylinder is the right line, joining the centres of the two parallel circles, about which the figure is described. A pyramid is a solid, whose base is any right-lined plane figure, and its sides triangles, having all their vertices meeting together in a point above the base, called the vertex of the pyramid. A pyramid, like the prism, takes particular names from the figure of the base. A cone is a round pyramid, having a circular base. ( Fig. 10; Plate 1.) The axis of a cone is the right line joining the vertex, or fixed point, and the centre of the circle about which the figure is described. 10 THE SCIENCE OF VISION ; OR, I have selected the following problems, being the most useful to artists. To bisect a given line, AB, that is, to divide it into two equal parts. {Fig. 11.) From the centres A and B, with any radius, describe two arcs intersecting each other in C and D, and draw the line CD, which will bisect the line AB in the point E, as required. N.B. The two ends of the line, AB, are called centres, being made so to draw the arcs, the intersections of which being equally distant from the two ends, a line from C to D must pass through the centre of the line and divide it equally. To bisect a given angle, BAC. (Fig. 12.) Draw two lines, B A, CA, forming any angle at A ; then from the centre A, with any radius, describe an arc, DE, and from the centres D and E, describe arcs intersecting in F ; draw AF, which will bisect or equally divide the angle A. Pupils practising these problems, will find them very easy if they follow the order laid down for constructing them. At a given point, C, in a given line, AB, to erect a per- pendicular. (Fig. 13.) From the given point, C, cut off equal parts, CD, CE, on the given line. Then, making D and E centres, describe arcs, intersecting in F. Then join CF, which will be perpendicular, as required. Otherwise — When the point C is near the end of the line. (Fig. 14.) Draw the line AB, and mark a point, C, near the end of the line. NATURAL PERSPECTIVE. 11 From a point, D, assumed above the line for a centre, describe a circle, passing through C, and cutting the line at E. Draw a line from E through the centre D, and cutting the circle at F. Join CF, which will be a perpendicular. From a point, A, to let fall a perpendicular on a line, BC. {Fig. 15.) Draw the line BC, and choose a point, A, above it. From the point A, with a convenient radius, describe an arc, cutting the given line at the two points, D E. Then, with any radius, describe two arcs, intersecting at F, and draw AF through G, which will be the perpendicular required. Otherwise. — When the point is nearly opposite to the end of the line. {Fig. 16.) Draw the line BC, and fix the point A near the end of the line. From any point, D, in the line BC, as a centre, describe the arc of a circle through the point A, cutting BC in E. Now, from the centre E, with the length EA, describe another arc below the line, cutting the first arc at F. Draw AGF, which will be the perpendicular to BC, as required. To describe the circumference of a circle through three given points, A, B, C. {Fig. 17.) Make three points in any position, and mark them A, B, C. From the middle point B, draw to each of the other points, A and C. Bisect these lines, BA, BC, perpendicularly by lines meeting in O, which will be the centre. 12 THE SCIENCE OF VISION ; OR, Then from the centre O, with the distance of any one of the points, as OA, describe a circle through the two other points, B and C. To find the centre of a circle. {Fig. 18.) Describe a circle. Draw a chord, AB, and bisect it perpendicularly with the line, CD, which will be a diameter. Bisect this diameter in O, which will give the centre as required. To make a square on any line, AB. {Fig. 19.) Draw a line, and mark the length AB on it, for the proposed square. By the third problem raise two perpendiculars on the points, AB. Mark AD, BC, each equal to AB ; on them join DC, which will be the square sought. To inscribe a square in a given circle. {Fig. 20.) Describe a circle. Draw the two diameters, AC, BD, crossing at right angles in the centre, E. Then join the four extremities, A, B, C, D, with right lines, to form the inscribed square. To describe regular pentagons in a circle. {Fig. 21.) Divide the circle into as many equally distant radii as the pentagon has sides; join the extremities, and it will give the pentagon required. NATURAL PERSPECTIVE. 13 To measure angles. All angles are measured by a circle, the centre of which is at the point where the two lines meet. Draw two lines, forming the angle proposed to he measured. (See Fig. 22.) Then with the radius GO marked on the scale of chords, describe an arc, cutting the two lines equally. Take the distance between A and 13, with a pair of compasses, apply them to the same scale, which will give the measurement of the angles sought. In this example AB is equal to 30 degrees on the scale, which is the measure of the angle C. On mathematical rules are scored a scale of chords, and may be known by a C or Clio, marked before the degrees, up to 90. By taking the length, from 1 to 60, with a pair of com- passes, and describing a circle, the length, from 1 to 90, quarters the circle ; and any lesser angle may be measured from the scale. Sixty degrees (the length of the radius) mark on the circumference six equally distant points, which, when united by lines, form a sexagon. By dividing the 360 degrees into equal parts, and measuring them from a scale, a polygon of any number of sides may be formed. It is scarcely necessary to enforce the necessity of being e tact in these operations. The construction of figures, on geometrical principles, is the principal object of the draughtsman ; the contents of figures are shewn by mathematical calculations, which, being a distinct science from perspective, cannot aid the practical operations of the artist. Trigonometry, or the measurement of triangles, gives a con- prehension of the dependance of the length of lines on the expanse of angles : the most useful points to the artist I shall briefly illustrate, and those who have leisure and opportunity will find themselves amply rewarded by a deeper study. 14 THE SCIENCE OF VISION ; OR, whether it can be brought into immediate practical use or not ; for the art of perspective presents difficulties to the mind which can only be surmounted by mathematical skill. Every triangle contains 180 degrees in the three angles. In an equilateral triangle the sides are equal in length, and the angles are equal. For if each point be made a centre of a circle, as in the diagram, each angle forms a sixth of the circle, or 60 degrees, and their sum 180 degrees. {Fig. 23.) In a right-angled triangle, if the corners be made centres and circles described, it will be seen the right angle is a quarter of a circle, or 90 degrees ; the vertical angle a sixth, or 60 degrees ; and the acute angle a 12th, or 30 degrees ; and the sum of the whole 180 degrees. {Fig. 24.) Observe, the perpendicular or shortest line (1) is opposite to the smallest angle (30 degrees). The base (2) is opposite to the greater angle (60), and the hypothenuse or diagonal (3) the longest line, and opposite to the largest angle, or 90 degrees, and are in proportion to their angles. In trigonometry the calculations are made similar to the rule of three ; viz. as the logarithm for the angle 30 is to the logarithm for the length of the side 1, so is the logarithm for the right angle to the logarithm for the hypothenuse. So that having two angles of a triangle, the compliment of 180 degrees will be the third, &c. All the preceding elements must be practised and repeated till thoroughly understood; reading them only will not be sufficient to enable students to apply the rules to practical purposes ; the object they have in view will be defeated, if they follow the common practice of slighting a material part of a work from an eagerness to get at the conclusion, which is too frequently the cause of instructive works failing to supply the knowledge sought. Before I enter into an explanation of the principles of con- nected lines, I consider it necessary to discuss the first three definitions of geometry, there being many controversies about NATURAL PERSPECTIVE. 15 their true meaning ; and it is essential for the artist to distin- guish the symbols from the ideas they represent. They are thus defined in mathematical works. " A point is that which has position, but no magnitude nor dimensions ; neither length, breadth, nor thickness." " A line is length without breadth or thickness." " A surface, or superficies, is an extension or a figure of two dimensions — length and breadth — but without thickness." Every thing in nature, from the animalcule to the hugest mass, has length, breadth, and thickness ; hence any idea that wants these properties of form, must be out of nature, in fact no-thing. A mathematical point, therefore, cannot be made visible, for the smallest touch of a pencil has the three proper- ties. It can only be an idea, a mental point or place, where we conceive succession or length to commence or end. A point therefore is the position from which two or more lines diverge, but which point has not the least conceivable part either of length, breadth, or thickness, which is sometimes defined as the meaning of a mathematical point. The diameter of a circle gives us no idea of its being shortened by passing through a centre, because we cannot assign any dimensions to a point which only bisects and makes one line into two equal radii. It is an axiom that all the parts are equal to the whole : the two radii are equal to the whole diameter; therefore, a mathematical point is truly said to have only position. A line is also a mathematical idea, and is a symbol of exten- sion, commonly called length. It is the shortest distance between two points, but cannot be the representative of any quantity. If a line were any thing but an idea or symbol of length, a pencil line would represent some object in nature, which it does not : a point has no dimension ; a line has one (length), but without three properties it is formless. A surface or superficies is called " a figure of two properties, length and breadth, but without thickness." As every figure, 16 THE SCIENCE OF VISION ; OR, real or imaginary, must have the three properties, there must be some error in this definition. I conceive it exists in confounding the terms " surface " with " superficies." A surface is the tangible side of a solid, which less than three lines will not represent, as a triangle. A A superficies is the dimensions of a surface — the abstract idea of its length and breadth — which two properties of quantity can only properly be shown by symbol thus,n, is no figure. A surface may be touched, a superficies can only be conceived. Although the first three definitions are only terms for defining the ideas of solid or imaginary extension in length only, in length and breadth, or in length, breadth, and thickness ; or, in other words, the three unseen properties of all natural forms; these mathematical nothings, although they cannot be made tangible may nevertheless be made evident to the sense of sight, which I usually exhibit in my lectures to make the nature of these terms obvious to the students of visual science. It has been said, that it is impossible to conceive nothing or a nothingness. Now, as these terms express no quantity of tangible matter, it is evident they signify nothing; but to convey the true meaning of these mathematical terms, interpose a square piece of board or paper between the flame of a candle and a wall ; on the latter a shadow will be made, presenting to the eye extension in length and breadth, without thickness or substance ; the corners of the shadow shew the position of the points, the edge shews the line or extension between two points, and the whole shews the superficies, which being only a negation of light, and wanting the third property of all things —thickness, is nothing. A shadow consisting of no materialism, although visible, can occupy no space. Nothing can occupy space that has not extension in three rectangular directions, by which alone solid forms are bounded, without these, they are only airy nothings. The elucidation of terms prevents a confusion of ideas, and NATURAL PERSPECTIVE. 17 every one who wishes to master an art like perspective, which imperatively calls for distinct ideas, must cease to follow the common acceptation, and reduce them in his own mind to a critical definition. Superficies is derived from supra, above, and fades, a face, that is, a plane on which the extent of any surface is computed by length and breadth ; but as it literally is not intended to convey any idea of solidity, it does not include thickness. An imaginary square in atmosphere is the same as a superficies in contact with the plane of a solid, but is not so distinct to persons who have never trained their minds by thinking mathematically. It is necessary for the artist, whose drawings are symbols of realities, to know the difference between a mathematical point, which exists only in idea, from the point of a needle or the corner of a door. The point of a needle is the vertex of a circular cone, though much smaller than a sugar loaf. The point of a door is the vertex of a triangular pyramid, which we cannot touch without feeling one or all three of its sides or surfaces, which gradually diminishing, form a vertex. The point of union is represented by a drawing point, and the edges of these surfaces by lines. A right-lined pyramidical point cannot be produced with less than three surfaces. The union of two surfaces makes an edge, to represent which artists must draw a line ; but it should be remembered, if we touch the edge, we feel one or both the surfaces, and not a line. We cannot feel the symbol. This may explain the common saying, that there are no lines in nature. Drawings represent the quantity and quality of visible objects. Let the quantity of the material be whatever it may, every thing has length, breadth, and thickness, which, like height, width, and depth, are only terms for length or extension. By breadth we mean length, lying at a right angle to another length ; and by thickness, a rectangular length c 18 THE SCIENCE OF VISION; OR, to breadth, there existing but three rectangular positions. (%• 25.) Axiom. Every thing in nature has length, breadth, and thickness, or parts lying in those connected and inseparable positions. The properties of form are palpable to the touch as well as to the eye-sight, and the student is recommended to pass his hand over the edges of a book, &c, by which his mind will be impressed with the abstract idea of forms that, when introduced to the eye, originate appearances hereafter treated upon. An object has but one form, but it may have an infinite number of appearances, when introduced to the eye-sight. In teaching, I have found almost every one confound the abstract form of a thing with its appearances ; for instance, conscious of a cube having six equal and perfectly square sides, which is its abstract and only form, — even while looking at it, and their attention being drawn to the alteration of these squares in appearance, they fancy they see squares ; so delusive is the eye, or rather their knowledge, in confounding form with its appearances. The cube represented in Fig. 43, has no one side a perfect square, and no two sides identical, and yet it accurately repre- sents one appearance from a fixed point of view. If more than one side of a cube is shewn in a drawing, none of the sides can be made perfectly square. Perspective expounds this seeming mystery. To prepare the mind for definite rules, the pupil must know, that appearances are the effect of an object on the mind through the medium of the eye ; and that a picture is a representation of that effect on the artist's mind, from some fixed spot, and at a particular time. The object, the eye, and the mind, are inseparably con- nected; for if we take away the object, the eye has nothing to NATURAL PERSPECTIVE. 19 convey to the mind, — and the same result follows the removal of the eye or mind. As the object, the eye, and the mind, have a fixed relative position at the time of making the drawing, the eye being at a certain distance from the object, and above, level with, or below it, the distance in the plane of the eye is commonly expressed as the point of view, which, without con- sideration, does not embrace the connexion of eye, distance, and thing. These connected positions are spontaneous, and are the causes of various appearances, and originate the principles of perspective. As all drawings are not the actual representations of nature, but are sometimes the composition of artists, the foregoing ob- servations may not, at first sight, seem applicable ; but as the mind can only conceive objects similar to those it has been impressed with, they may be properly termed actual represen- tations of the mind, or reminiscences of sight ; and the same propriety must be observed as though they were made from nature. In composition we must imagine a fixed position and distance for the eye and its objects. The faculty of sight ought to be enquired into by every draughtsman and by every person who comments on works of art. Seeing, and comprehending what we see, are distinct ideas ; the first is a simple impression on the organ of sight, common to all animal nature, for the purposes of necessity and life. The latter is an intelligence super added to the human mind, for the higher purposes of reason and reflection. The eye is one of the five organs of sense, and the leading faculty; by it we derive more knowledge than by either of the others ; the situation and action are peculiar; it is immediately connected with the brain ; its spherical form revolves with slow- ness or velocity in its socket unfelt, through which the mind receives impressions from whatever it is directed to or revolves upon. This placid action causes it to escape a general enquiry c 2 20 THE SCIENCE OF VISION; OR, into its properties by the possessors. The lenses of the eye, like an artificial lens, concentrate and cast on the hyaloid a spot only of the object viewed, and this direct sight is termed a visual ray. Although indirect rays enter the sight, this concentrated spot is the whole space we truly see at one moment; but by the imperceptible movement and velocity over a surface, it is gene- rally supposed that we see or embrace a much larger portion of it than we actually do. In reading, the eye embraces letter after letter so rapidly, that the whole word is instantly conveyed to the mind; word follows word in instant succession through this beautiful and delicate construction. The rays diverge from the pupil, and form a system of rays; the centre ray is the only direct one, all the rest are indirect and scatter only an imperfect or faint impression ; and to trace a form, the direct ray must be passed over the whole outline. The nature and motion of this faculty may be fully understood and slightly felt, by fixing the head and directing the eye along an edge or over a considerable surface, and should be tried by every one who desires to acquire perspective thoroughly, or to have a clear comprehension of this useful medium. It is well to fix the head and study the appearances of all the edges of forms before us, and retaining the impression, to change the position of the eye, and compare the changes, and endeavour to perceive the natural cause. This experiment will cost but little time, will assist the comprehension, and convince every one that the principles laid down in this treatise are founded on nature. It is well to adopt this mode of observation in the daily walk, much difficulty will be removed by it, and it is highly amusing. As we proceed, the apparent movement which takes place in sur- rounding objects naturally draws us to enquire into the cause, which the simple and easy principles of perspective at once explain In most of the effects of nature, the cause seems to be put NATURAL PERSPECTIVE. 21 beyond the reach of human intellect, but this is not the case with this instructive art; for artists, connoisseurs, &c, derive from it a knowledge of the form (cause) and a comprehension of the appearances (effect) which motion or life adds to this other- wise inanimate museum. Perspective, which is but another name for the principles of drawing, causes form to be so deeply scrutinized, that the imitator cannot fail of knowing the principles of all, and the particulars of whatever class of objects he may select for his profession. The imagination is put in motion by this study ; the beauties of nature are disclosed, and the genius enabled to display them with accuracy. It has been stated that the eye embraces only a small spot by direct vision. From this spot, in a direct line to the eye, is termed a visual ray. As the eye moves, these rays are infinitely multiplied along a line, and, to represent them, we must join them or shade the whole area between the eye and line ; but in our future explanations, only the two rays from the extremes of a line will be given ; but the mind of the student must always supply the rest. (See Fig. 26.) The line drawn between two points must be considered a symbol of these successive and multiplied rays of sight. The rays take a different course on coming to the end of every line — the place where the change of direction occurs is termed a point, being the union of two lines coining from different direc- tions, but no part of either. As a line is formed by passing the eye from one extreme of an edge to the other, so a form is made in the mind by adding a number together successively, exactly as the pencil visibly begins at a point, passes along and forms the line, changes its course, and adds successive lines till the proposed form is pro- duced. This train of thinking and familiar knowledge of optics can alone lead to a comprehension of the general terms used in perspective. 22 THE SCIENCE OF VISION ; OK, Terms used in Perspective. Point of sight. Point of station. Point of view. Horizontal lines. Vanishing lines. Planes. Vanishing point. A Point of Sight is a single visual ray from any spectator, extending forward till the sight rests on something level with it. Lines of buildings parallel with this ray appear to tend towards one point in a drawing, which is the point the sight rests upon in nature, and hence called the point of sight. The eye of the artist is opposite to this point on taking the view, and it is distinctly recognized in drawings of interiors, streets, &c, wherein ranges of parallel buildings to the right and left are represented to the right and left of the centre of the picture, by lines tending to a common vanishing point in the picture. In drawings of objects on an angle, by which the sides vanish both ways, that is, converge to points to the right and left out of the picture, then there is no point of sight to mark the place of the draughtsman. The level of the eye or its height above the ground can only be seen by the horizontal line on which those vanishing points may be found beyond the margin of the picture. In short, the point of sight is only an interior or central vanishing point, and possesses no other importance, although by other writers the governance of the plane of the picture is assigned to it, over which, however, it will be shewn it has no control. When draughtsmen shall adopt natural representation, the point of sight may then be known in a picture by the centre point of the perspective horizontal line. The Point of Station is the place a person stands upon to make the drawing, and represents the distance from the objects portrayed, and can only be shewn in the ground plans. According to the greater or lesser distance, the angles of vision contract or expand, and the vanishing lines become more or NATURAL PERSPECTIVE. 23 less acute. The point of station can only be conceived in a drawing by the place of the point of sight or vanishing point if it be in the picture, which being always opposite to and level with the point of view, and the point of view being over the point of station, the connexion readily explains them. A picture cannot point out the distance between the objects re- presented and the point of station, because it shews only the effect of seeing, and not the connecting circumstances which produce that effect ; a point of distance has been a technical term in perspective, which has not been meant to describe the distance between the objects seen and the eye as here spoken of, but the distance between the eye and the objects in the visual rays where an image might be found of the size of the artist's picture, or a proportional to the great picture at the distance of the objects. I perhaps may be better understood by some, by explaining this distance to be that of the frame of the picture from the eye if held before it, and the objects painted in it seen at a greater distance through it. This intervening distance of the artist's picture has been called the point of distance, and much trouble has been taken to explain it. I disuse the term, because I see no practical use in it. It is of no consequence at what distance the reduced appearance intervenes, so long as the proportions be true. The distance cannot, and is not, required to be shewn any more than the eye that sees, or the rays by which we see. It is a matter of mere mathematical enquiry. In mathematics there are many sections of the rays or differences to be found ; but it is a curious fact, that in the vision there are no differ- ences of sizes of images to be perceived in the same system of rays, for the eye being a centre of the rays diverging from it to all the points of any object, the angles of those rays are the same at all distances, and every sized picture interposed will cover the objects that make the picture, and to the eye will appear equal, whether near or far from it. 24 THE SCIENCE OF VISION ; OR, A Vanishing Point. — The lines of widths and depths appear horizontal and parallel in one view only, in every other they appear diagonal, and seem to tend or converge to a point. When the horizontal lines of buildings are not parallel with the ray from the point of view to the point of sight, they com- mand a vanishing point according to their deviation from it. Vanishing points are always found on the Horizontal Line, which is a line drawn across the paper, to signify the perspective level of the eye, and to distinguish things that are above, from those below the sight. The geometrical level of the eye can only be drawn geometrically when it is midway in the perpendicular height of the object, which is a new feature in this art. A perpendicular, through the point of view, divides nature by a transverse plane about us. It is well to distinguish all other horizontals from the horizontal line or plane of the eye ; this we will call the horizontal, and others a horizontal line. A Plane. — The meaning of a plane is twofold — real and imaginary. A real plane is an extended level surface, and an imaginary plane is a continuation of the idea of that level to the fullest extent of our conception. Without reference to any form, we can conceive planes in or through the atmosphere in the direction of every radii of a sphere, on some of which the bases and sections of solids may exist, when they are said to be on particular planes, of which the real planes or bases form defined figures on the indefinitely bounded planes. All objects have a base which must be above, below, or level with the horizontal imaginary circular plane, of which the eye is the centre. Every form differing from another, piled one on the other, has its own base, agreeing with its form; and each base is a figure on different planes. When we say things are on the same plane, it signifies that NATURAL PERSPECTIVE 25 they are level with each other, although they may not be hori- zontally level. The surface of the earth is the general ground plane or base of objects — the extended circumference is considered a level, at least within the reach of the sight. If the vertical point of a cone or pyramid be considered the plane of the eye ; the base the superficial form of an object; and the outer form, visual rays, any section on any particular plane, being similar to the base, will be parallel, and in geometrical proportion to it. A picture is a section of the visual rays (cutting the outer rays equal, vertically and horizontally, at right angles, to the axis of the system), which can be chosen on any proportion from the vertex, till the section comes in contact with the real dimensions. As buildings, trees, and many other objects are larger than is convenient for pictures, they must be drawn on a scale of reduced proportion, and it is not difficult to conceive equally reduced proportions, if the student will refer his ideas to a conceived section of his visual rays, equal to the dimensions of the drawing he proposes to make. Finally, a real plane is a surface of limited length and breadth ; an imaginary plane is an unlimited superficies. The terms of the art will be better understood by practising the diagrams, whereby their precise meaning can alone be gained. THE PHYSIOLOGY OF THE EYE. With a Diagram, Plate 3. In consequence of many conflicting opinions in linear science, arising from the discordance of its theories with the con- struction and action of the eye, as well as the practice of art, I shall offer the result of my observations and experi- ments on it, with the view of removing those anomalies. As the cornea is a plano-convex, the crystalline a double convex lens, and the retina an expansion of the optic nerve over the greater portion of the concave surface of a sphere, it is hence inferred that the right lines of objects, being refracted by the former and received on the latter in circular lines, must be so seen. The theory of delineation and the practice of art differ from this conclusion, and the images of objects are projected in right or curved lines, according to the nature of the object seen, with certain modifications of foreshortening and con- verging ; hence much mystery has enveloped the doctrines of perspective. The difficult point is to associate the natural evidence of effects with the refractive media and construction of the eye ; by experiment, we have the inverted and invariably curved figure of right lined as well as circular objects on the retina (according to physiology), it is a question then how we shall reconcile the rules and practice of visual science with the sense, so as to have no discordance between them. If the hand touch a straight, round, angular, or elliptical form, by the sense of feeling we determine and are satisfied with its evidence as to those properties, and it would be deemed an aberration of common knowledge to deny such conclusions. NATURAL PERSPECTIVE. 27 If we see a straight, round, angular, or elliptical form, we are satisfied with the evidence of that sense, without the corroborative testimony of the touch, which we can bring in support of its truth ; and it would be deemed an aberration of sound intellect to dispute general conclusions in practical observation. It is by the senses we form the understanding and gain knowledge. Nothing improves the understanding, or is in reality knowledge, but what is derived from them and from a comprehension of natural phenomena — hence any theory is unworthy our entertainment, that cannot be reconciled with the principles of physical nature. In the first place, it is necessary to explain the structure of the eye. (See Plate 3, Fig. 30.) A. The outer case of the eye is named the Sclerotic- Coat, and is an opaque substance impervious to light. B. The Cornea, is part of the same coat, but is transpa- rent, to admit the rays of light to enter the eye. C. The Choroid coat, lining the sclerotic coat ; a delicate membrane which immediately contains the retina. It secretes in the human eye a black mucus, which is spread all over it, called the pigmentum nigrum ; this black mucus has the effect of absorbing the rays of light on reaching the retina, where an inverted image is made. D. The Retina, or optic nerve, is expanded over the choroid coat; it is a delicate net-work, serving as a lining to the choroid, between which and the expanded retina, the black mucus is contained. E. The Hyaloid membrane is the capsule which contains the vitreous humour and the crystalline lens; passing round the humour ; on approaching the margin of the lens, it splits into two layers, one of which passes behind the lens and adheres to its capsule, the other passes over the fore part of the lens, identifying itself with its capsule. F. The Vitreous Humour. 28 THE SCIENCE OF VISION; OR, G. The Crystalline Lens. H. The Canal of Petit, an empty channel around the crystalline, formed by the splitting of the hyaloid membrane. I. The Iris, in the centre of which is the transparent pupil to admit light into the eye ; it is united to the horns of the choroid coat, at the margin of the cornea. The pigmentum nigrum, or black mucus, lines the posterior surface of the iris, which being placed at a small distance from the fore part of the crystalline, forms a dark chamber. K. The Aqueous Humour contained between the curved transparent cornea, and the anterior plane surface of the Iris, forming a piano convex. L. Muscles of the Eye. M. Optic Artery. If a ray of light proceeds from O, it passes through the cornea, the aqueous humour, the pupil, the crystalline lens, and vitreous humour, and impinges the vertical point N, on the hyaloid membrane. If an object, PQ, transmit its image through these media, the end, P, will impinge the point of the hyaloid membrane, R, and the end, Q, the point S inverting the image, which may be distinctly seen by scraping the sclerotic coat of a sheep's or bullock's eye, and holding a light to the cornea. Now the right line, QP, sectionally becomes a curve RS, on the membrane, although we are not sensible of any curvature, or of any invertion of the image. By an attentive inspection of the diagram or section of the eye, it will be seen that so much of the case is spherical as contains the inner portion of the media, which, for uniform vision, should suffer no derangement of that form ; but the fore part protrudes to admit of various adjustments to modify the power of light on the other parts, &.c. The muscles, LL, of the eye, which turn it on its axes in all directions, attach to the margin of the cornea, which is adjacent to the termination of the choroid and its attachment to the Iris. By reason of the protruding NATURAL PERSPECTIVE. 29 portion of the eye, on turning the eye on its axes, or what is termed indirect vision, the curve of the cornea and the aqueous humour alters the form, Fig. 31 ; the muscle opposite to the direction of the eye compresses the sclerotica, hyaloid membrane, and margin of the Iris upon the cavity H, while the opposite muscle relaxes, and the Iris preserves the same adjustment or parallel as in direct vision, by which means the retina is impinged in as many points as are transmitted vertically from the object. But for this alteration of the anterior media, in every direction of the eye we should impinge the same point N ; for as the spherical case with its contents revolve together on its axes, it is evident, while the adjustment is preserved, the impingement of the same point must follow. This would not be the case if the coats of the eye were attached to the bony socket, and the humours revolved on their own axes; then, direct and indirect vision would impinge the various points on the fixed membrane. Now on opening the eyelids, whatever objects present themselves to the sight, the media instantly and involuntarily describes an image on the hyaloid membrane; precisely as objects would on a concave mirror. Supposing the head to be fixed, and the sight directed to a fixed point, that point will be distinct, and all the points around to the extent of the field of view will be less distinct the more distant they are from the centre point. It would be difficult, nay impossible, to define any object at a small distance from the centre, without moving the axis, so that it appears necessary that the eye should be directed to every point of a figure successively for us to distinguish the minutiae of the objects, or, as we may truly say, to see them. The eye then actually traces every line or edge of involuntarily made appearances, and in this operation of the sense it is necessary ; the direction of the eye to new and successive points should not produce as many involuntary images, but that the first image in the whole field should be retained till it be as it were traced off ; for this purpose, if the head be fixed, and the eye revolved 30 THE SCIENCE OF VISION; OR, in its socket, within the field of view, the image is described on the hyaloid membrane or the retina inverted from its natural position. The posterior surface of the crystalline lens embraces the image on all the incidental points, and refracts the image upon the posterior plane surface of the Iris in its natural or external position. It is well known that the images of all objects act upon the surfaces of lenses. Now it is impossible to conceive that the surfaces of the crystalline are an exception in nature, or that it is placed in the eye without an office to perform ; and as we know an image in form, colour, &c, like that in nature, is made on the hyaloid membrane, we must suppose it will be reflected on the posterior surface of the crys- talline, and that by the natural laws of refraction it will project that image on the dark field of the posterior surface of the iris, being a natural action of the sense over which we have no control. In nature, where there is action, there is always re-action — the eye is not an exception to this rule. The rays of light act upon the hyaloid membrane, the re-action (of which we are always sensible) is on the Iris, consequently that is the seat of vision. According to the present conclusions of science, it is deemed requisite that the rays of light should undergo no reflection after reaching the retina; but as such conclusion, considering the structure and nature of the media, is contrary to a common law, we can but infer that it is erroneous or com- pulsorily formed to agree with conclusions on the nervous system. As the knowledge of the nervous phenomena is merely conjectural, or at least not thoroughly understood, we may perhaps be more fairly justified in forming conclusions on the construction and action of those parts of the eye by natural laws, which admit of demonstration. It is known that the greatest sensibility is in the termination of the nerves, as, for instance, in the ends of the fingers; so, as the expansion of the optic nerve terminates in the Iris, we may conclude on the great sensibility of that part, particularly if we consider that that NATURAL PERSPECTIVE. 31 is the only portion of the human body undefended from the re-action of the rays of light by a superimposed expan- sion of nerve, or epidermis, or skin ; it is exposed to all the refractive power of the crystalline. We know when a slight graze removes the epidermis or superficial skin from the hand or any part of the body, that the rete mucosum is very painful if touched. The rete mucosum, or pigmentum nigrum, as it is called, is a tenacious moisture between the epidermis and the cutis, or true skin, resembling the pigmentum nigrum in the eye ; it is described to diffuse itself in water, communicating a turbid cloud to the fluid, subsiding as an impalpable powder to the bottom, and that the rete mucosum admits of being detached as a coherent membrane, the side next the cutis appearing of a deeper colour ; the choroid is covered with a thin layer of it, but over this is spread the expansion of the optic nerve or retina, on which the inverted rays are said first to act ; but the final image produced by the crystalline is made by impingements on this excessively irritable seat of vision. As the advancement of this theory of vision is new to science, a familiar account of experiments which have led me to that conclusion will best convey my views to the reader. Considering the anterior portion of the eye to admit of various adjustments, I examined the eye of a living subject by a powerful double convex lens, causing the person to roll the eye inwardly, outwardly, upwards, and downwards, keeping the head fixed, when in each opposite direction the B trained muscle evidently compressed the iris, and notwithstanding the oblique direction of the axis, it was retained in a direction parallel to that of direct vision, or nearly so. Again, 1 opened the sclerotica of a bullock's eye, without removing the hyaloid membrane ; on presenting the flame of a candle to the cornea, an inverted image presented itself on the membrane, as it would have done on it, had the retina, &c, not been removed. I then removed the membrane, and holding a sheet of paper 32 THE SCIENCE OF VISION ; OR, before the aperture, received on it the inverted image of the flame ; then I presented the flame at a short distance from the aperture, holding the sheet of paper before the cornea, when I likewise received an inverted image ; but as the flame was held at a greater distance than the natural place on the hyaloid or retina, I held the flame close to the humour, when the focal power of the crystalline did not project an image on the paper through the cornea, but illuminated the dark chamber of the Iris with remarkable splendour ; from which we may conclude an image was made on that part as on the paper, and that the crystalline deals with an image on the retina or hyaloid pre- cisely as with the flame. By entertaining the idea of the Iris being the seat of vision, we not only account for the natural order of seeing things, but remove many difficulties. It is acknowledged by good writers, that " the cause of squinting is obscure," and that although it sometimes happens that the eye which squints has an imperfect vision, caused, no doubt, from neglecting its use, yet in most cases vision with either eye is equally good, and can be used singly, but cannot prevent the other from turning away from the object of vision. The cause is, that one of the muscles of the squint eye has not the flexion of the rest, and therefore the eye cannot turn freely on its axis like the other, neither can the Iris form a parallel adjustment with the other, which takes place when the muscles are perfect and in free action. If the finger be slightly pressed on the margin of the Iris, instantly we see two images of the same thing, because we have disturbed the anterior portion of the media and the parallel adjustment of the Iris by compression, as is the case with the contracted muscle of a squint eye. Squint eyed children see double images of every thing, and are often troubled, from these being mixed, to learn their lessons, but at last, by disregarding one, they accustom themselves to see with the other eye only. On opening the sclerotic coat, and removing the choroid and NATURAL PERSPECTIVE. 33 the retina, no image is projected through the hyaloid mem- brane, which surrounding the vitreous humour may justly he regarded as a concave mirror, and the retentive surface of the inverted image. The retina, as a part of the nervous system, is no doubt affected by the rays of light which form the image over it, and may be the regulator of the quantity of blood necessary to be excited in the optic artery for the various degrees of sensation caused by strong or faint impressions. The beautiful choroid which lies beneath the retina is highly reflective ; over which is spread the black mucus, or pigmentum nigrum, and together may be the means of preserving the natural colours of the image, and of absorbing so much of the rays as may prevent the illumination of the vitreous humour, that the crystalline may take up the perfect image to be refracted on the Iris. In eyes wanting the pigmentum nigrum, they cannot see with strong light, because of the illumination of the inner chamber of the eye, which counteracts the purpose of the crystalline. As the posterior surface of the Iris has no membrane over it, the pigmentum nigrum may altogether absorb the rays from the crystalline, and no actual image may be made there. The sensation of these pencilling of rays on the unde- fended and irritable surface, may communicate the again inverted image of the hyaloid membrane to the sensorium, if that be the mind. The hyaloid is more likely to be the seat of the inverted image than the retina, which expansion of nerve by no means seems calculated to sustain a figure. The trans- parent membrane, like the surface of a lens, will form and retain an image so long as the object be present, besides, as the membrane lies immediately upon the retina, there is no distance between them to project an image beyond the mem- brane. If the finger be held seven or eight inches from the eye, and any object be in the line beyond it, as a candle flame, and the sight be fixed on the flame, two fingers will appear one on either side the flame ; then, if the sight be fixed on the D 34 THE SCIENCE OF VISION; OR, finger, two flames, one on either side the finger will appear ; the reason is, to whichever the sight is directed, the parallel adjustment of the Iris gives the same figure, and two of the other, or rather, the impingement of the object looked at is on similar points, and of the other in dissimilar points in each eye. The Iris never grows, but is the same in the infant as at an adult age. The similarity of action of the camera obscura to that of the human eye, upon which construction it is formed as nearly as it is possible, remarkably coincides with my physiological ex- planation of the eye. The camera obscura is an instrument known to the public for the purpose of exhibiting views. It is sold as a toy also, for the amusement of children. It consists of a box having a convex lens inserted vertically in one side, which inverts the image or view on a plane reflector, whence the image is transmitted in its natural position to a receiving surface in a dark chamber of the box. As near as human ingenuity can contrive it, this instrument is in imitation of the eye ; the con- vex lens answers for the lenses of the eye, the plane reflector for the retina or hyaloid membrane, and the dark chamber of the camera for the dark chamber or irritable posterior surface of the Iris. In my lectures at the Marylebone Literary Insti- tution, on the 14th of August, 1837, and since, in all my public lectures, I informed my audiences of this optical adjust- ment, and, moreover, was the first to assert that the images produced by the camera obscura were the " natural images." I did so for the purpose of proving my hypothesis, of the Iris being the seat of vision, as well as to substantiate by ocular evidence the infallible truth of my new theory of Perspec- tive ; having that year exhibited in the Royal Academy a specimen of a building, delineated by the new principles, being the first picture ever drawn as it would appear to the eye. The subsequent introductions of photogenic drawing by Mr. Fox Talbot, and the Daguerreotype by M. Daguerre, still NATURAL PERSPECTIVE. 35 further confirm the truth of my discovery. I had never heard of the attempts at fixing the images of the camera obscura, till the latter end of 1838. I believe I am the first person that ever pronounced the images of the camera to be natural, and I know of no theory but my own upon which to rest that assertion, or by which they can be demonstrated to be so. Previous to the introduction of rectified perspective, those images were always called distortions of nature, and the instru- ment was rejected as a practical draAving instrument. Notwithstanding the curves which exist on the concave sur- faces of the media of the eye geometrically, on viewing a form, if we consider the pencilling of rays from each right line that forms them, we shall perceive that the curved line in the eye is the base of a plane sector of a circle, and those of a curved line in an object a curved spherical sector. The effect perceived is not the base, but the right or curved character of the sector. Likewise, as the points of impingements that describe the terminations of lines in objects upon a concave surface must necessarily be at unequal distances from the common centre of these sectors, a common base cannot be taken from them, which is a common law in vision ; so that if we reason with mathe- matical strictness, the right base of the axis of the pencillings of rays is the legitimate figure. The actual or abstract figure on the concave surface of the hyaloid membrane, or the retina, would not coincide with the mathematical dimensions of the object, nor the impinged points be at corresponding distances from the common apex of the sectors in the eye to those of the points in the object from their common centre or apex out of the eye ; and no mathematical analogy can be obtained ; it is not required, because the effects arc not geometrical, but optical, and we are not treating of the abstract principles of the materials which produce them, but of the principles of those effects themselves. If we saw the organic figure, that is, if we saw every thing on curves, and on curves only, then the image n 2 36 THE SCIENCE OF VISION. on the hyaloid, or retina, might be mathematically demonstrated, and there would be no laws of optics at all. Such effects as foreshortening and convergence would not exist in nature, and humanity would be endowed with mundane omnipresence. As it is, the eye is a centre to each person, and this beautiful function plays with and transforms the geometrical forms of nature into figures peculiarly its own, levelling all distances, heights, and widths to a common plane, both in and out of the eye. Sight is always focal, the same as light. The effect produced, or what we see, is always the optical right base of that focal projection, which is to be found in the eye, as well as the curved geometrical base, or the irregular base or bases of a multiform object, out 'of the eye. We therefore cannot hesitate to con- clude on which of these to found our visual deductions. Our knowledge is artificial, or misapplied, if we confound the one with the other. THE ELEMENTARY AND PRACTICAL RULES OF VISUAL SCIENCE. The three properties of form are computed by inches, feet, yards, miles, &c, and are drawn on scales of proportion, as the 8th or 4th of an inch, or more, to a foot, yard, &c, as may be convenient for a drawing. In the study of perspective, it is adviseable to set out the ground plan, distance from the object, height of the point of view, &c, of each diagram, by some convenient scale ; the larger the better. The pages of a publication necessarily limit the sizes of the examples. There are two sorts of drawings, geometrical and perspec- tive. A Geometrical Drawing only represents length and breadth ; when thickness is required to be shewn, the rules of perspective are necessary to adjust the lines, and instead of their geometrical length, to give them only the length they appear to the eye. A geometrical drawing has no reference to a spectator, and is not designed to convey an appearance, but only purposes to exhibit the abstract measurement of the sur- faces of some projected or proposed structure, in length and breadth, superficially. It is geometrical, because it is drawn on a scale of proportion to its real dimensions, without refer- ence to the sight. A Perspective Drawing represents a structure or object as it would appear to a spectator from some fixed or chosen point of view, which, from an involuntary action of the eye, gives to real dimensions a fictitious length. 38 THE SCIENCE OF VISION; OR Rule I. A length or line appears so and is represented geometrically when the eye sees it from a point opposite to its centre, and the visual rays from each end are equal in extent (See Fig. 26, Plate 2) : because any line drawn parallel to the line seen would be in some geometrical proportion to it. N.B. Only one surface of a solid can be represented geo- metrically, and that must be from a point opposite its centre ; if more than one side be seen, then all its surfaces, according to its position and nature of the form, must appear in perspec- tive, because they will be oblique to the axis of the eye. Rule II. A length or line in perspective being only a fictitious or optical length of a geometrical line, is reduced according to the angle which the position of the eye may fix in relation with it, as Fig. 27, Plate 2. The line A B appears only the length B C from the point or place of the eye of the diagram ; B C being the greatest distance between the equalized rays, and also the right base or regular subtense of the angle. General Rules. Every line that is geometrically represented has the two outer visual rays equal, and the eye opposite the centre. Every line that is perspectively represented is seen from a point, from which the two outer visual rays are unequal, and may be known by drawing a line between two points in those rays, each distant from the eye equal to the shorter ray, or between points parallel to those nearer to the eye as the proportion may require. NATURAL PEllS^iiCTlVK. 39 FORESHORTENING. The first step in practical perspective is the acquirement of the laws, by which lines appear less in length hy position (independent of distance), or foreshorten. By the rules just given, and a reference to the diagram, it will he seen that the appearance of any length always forms the base of an isosceles triangle with the extreme rays, or, in other words, that the image seen by the eye always lies in the visual rays at right angles to the axis of vision, which, the student will understand and perceive by the diagram, is the centre ray or line which bisects the angle formed by the whole object or objects. This is the fundamental principle of foreshortening, or natural effect of viewing oblique lines. That the equalization of the extreme rays of the triangular system of rays produced from a line lying obliquely to the sight is the natural length seen (Fig. 27); by referring to Fig. 2G, it will be seen, that when the line projects itself geometrically, the outer rays are equal ; the centre ray bisects the angle as well as the base line also, that the plane of the image is in the plane of the originat- ing line itself and at right angles to the axis of vision, forming an isosceles triangle. These simple geometrical laws are preserved in every appearance ; for when the line is placed obliquely it forms a geometrical oblique triangle, as in Fig. 27 ; on equalizing the rays, the obliquity is, as it were, cut off by the right base, 13 C ; and the appearance, B C, reduces the geometrical triangle to an isosceles or visual triangle, the centre ray bisecting the angle as well as the base or appear- ance, and the plane of the image, B C, is at right angles to the axis of vision. Thus, the principles of the natural effect of foreshortening are resolved to simple geometrical rules, deter- minable by the few lines of the diagrams. A little reflection and practical observation will prove the truth of the rule of equalizing the visual rays:— Let it be 40 THE SCIENCE OF VISION J OR, borne in mind, that a visual ray is only a point in our own eye, however far off an object may be, because we look, as it were, through that distance the same as if we looked through a very small pipe or tube, observing the spot without being able to judge of its length or extension in direct line before us. By way of ocular proof, place very small shot in the direction A B, or in the curved line, on a level surface or table, cut a small hole in a piece of card-paper, placing the hole next the edge of the table, on applying the eye to this small aperture, the shot on either line will appear to the eye to range on the equalizing right line, B C, or chord of the arc of the circle described by the radius of the shorter ray. For this reason, a ray being only an unperceived extension of a point, the marginal rays from the two extreme shots give the extremes ; and the intermediate rays give the intermediate points in the same right line or plane. In a similar manner this effect may be evidenced by observing a number of lights in a harbour' or on any still water ; such lights, though placed at different distances appear to range on a chord line of the arc described by the shortest distance or nearest light. It is only by our judging of their various strengths of light by another faculty that we conclude on their different distances from us. The reader will find it to be a common rule, in all the treatises on perspective, to take this section of the rays horizontally, although but few of the diagrams adhere to the rules of the works, by cutting the line of projection at right angles to the axis of vision. The same rule ought to have been given for cutting the rays perpendicularly, to be consistent with the nature of the art ; but it has been a standing rule, and an invariable practice, to take sections of visual rays perpendicular to the ground plane, or supposed level of the earth. No writer has ever swerved from this maxim ; for instance, if the ray A be parallel with the ground plane, the section E B perpendicular to it has been pro- NATURAL PERSPECTIVE. 41 duced by all draughtsmen for the apparent length of the line A B. Now, by turning the diagram, and considering the ray B to be parallel with the ground line, the section B F, perpen- dicular to ray B, has been produced for the apparenriength of the line AB. By various inclinations of the rays, in reference to a horizontal ground line, an infinity of perpendicular sections or apparent lengths with the same given data, it may be seen, may be produced, which is absurd. It is, therefore, evi- dent the common practice is unnatural, and contrary to the science of vision, in which only owe image can be seen or represented with fixed data. A line seen in any direction is subject to the same permanent and universal rule of equalization. Remarks. — Lines vary in appearance from three causes: obliquity of position, distance, and comparison. Thus : 1st. If the line A B be placed more oblique, the length B C, or equalization, becomes less from the same distance. 2nd. If the rays be decreased or increased in length, by a greater or lesser distance, the equalization expands or contracts according to the distance of the eye. 3rd. If a line be viewed alone, it forms its appearance on the former rules ; but viewed in combination with another inter- posed, it then varies from its isolated appearance, and appears comparatively smaller. Thus : if the line F 2, Fig. 28, was viewed alone from the point of view B, the natural appearance would be F f t B /" being equal to B F ; but if E 1 be interposed, its appearance will be D E, and be a primary object, and the appearance F/ will become 2 2 on the plane D E, where, by comparison, we determine its relative extension. The rays of the primary line, it will be observed, are equalized, but not the rays proceeding from the other lines ; their apparent lengths are determined by the intersections on the primary 42 THE SCIENCE OF VISION; OR, plane, as many objects can be viewed only on one plane at the same time. The rays from the secondary and inferior lines, 2 and 3, forming different triangles to the primary line ; the triangles formed by their intersections on the projecting plane D E, and the vertical point B, will be different. If the three perpendiculars, E 1, E 2, G 3, were viewed from the distance AE, with the eye raised to H — A H, being equal to half E 1, this primary line and its rays would make the isosceles 1 H E, the secondary 2 H F, and the inferior 3 H G, and the inter- sections on E 1, and the point H — three isosceles triangles, because the originating triangles are similar. In the foregoing observations, the reader will observe that the ideas are directed to the line without reference to breadth or thickness, taking into consideration the abstract length only to explain simply the manner in which we see lines reduced in length, or foreshorten from position, distance, or comparison; but as every object having length has also width as well as depth, in addition to the unavoidable action of foreshortening in length, there also follows an equally unavoidable and inse- parable effect of convergence in width on the organs of vision ; where the one takes place, the other joins in as a matter of course. The effect is always perceptible to the cultivated eye, whether adequately or inadequately impressed on the sense, to remind us of this natural phenomenon. If more than one line engage our sight, the plane of their appearance will be the line which reduces all the geometrical triangles to a visual isosceles triangle. Thus if two lines, a b, b c, Fig. 32, engage the sight, with the eye at e, the two geo- metrical triangles, a e b, b e c, are reduced to the isosceles triangle, a, e, c 2, of which a c 2 is the base line or plane of the images ; a b 2 being the perspective of a 6, and 6 2, c 2, the perspective of b c, dh the same plane. But if the eye take in the additional line c d, the system of rays is increased, and NATURAL PERSPECTIVE. 43 the three geometrical triangles are reduced to the visual isosceles, ae,d 3 — a e being equal to d 3, e and a b 3, c 3, d 3, the base line or plane of the appearance of the three lines. The equalization of the two extreme rays of the geometrical triangles alters the plane of the image on the addition of each line, and the rule is simply to draw the line or chord between the equalized points, through the point of contact of the shortest ray, which in Fig. 32 is the point a. If the three lines be placed as in Fig. 33, the equalization will be through the nearest point b, that coming first in contact with the eye, in the plane of which point the image is made in nature. Any section cut intermediately and parallel to that plane will be true in proportion. Throughout perspective, the plane of projection or appearance must conform to this rule, which is not invented but discovered by me to exist in nature. It may be well here to impress upon the student the fact, that if lines be thus placed in a practical model, and viewed from the fixed point e, all the mathematical sections which may be cut otherwise than parallel with the base line of the isosceles will appear to the eye the same as the perspective length in the optical section or base a d 3, Fig. 32, or a 2, d 2, in Fig, 33. He will perceive the difference between the mathematical sections or oblique triangles, and the optical section or isosceles triangle, and see the necessity of strict observance of this rule to avoid the former inconsistency of confounding mathematical with optical principles. In every surface there may be conceived to be many parallel lines or narrow stripes in transverse directions. All these parallels will conform to the general rules of the single line, subject to modifications which will be readily understood on practising the representation of surfaces and solids in a future part of this treatise. 44 THE SCIENCE OF VISION ; OR, THE PERSPECTRONOMETER. To illustrate the principle of foreshortening lines, I have invented an instrument which I have termed the Perspec- tronometer, as shewn by the annexed wood cut. \ \ Fig. 1. . 2. Fig. 1 represents the instrument, c b is a brass bar revolv- ing on a centre at c ; over which is a steel wire of the same length, with a cock at c ; ad and a e are two thin brass tubes, to represent two visual rays expanding from the point a, or NATURAL PERSPECTIVE. 45 plane of an eye. The brass bar I call the object bar, and the steel wire the index of the appearance of that bar, in any angle of view. If the object bar be placed as in Fig. 1, so that b a, c a, are equal in length, the line of the object will form the base of an isosceles triangle, and appear of its geometrical length as indicated by the steel wire. If the object bar be revolved on the centre c, and placed in the inclination a c d, Fig. 2, the index shews the apparent length in that angle to be f c, and the quantity lost to sight in this foreshortening is projected through the cock at c. The apparent length,/ c, forms the base of an isosceles triangle, with the rays f a, c a, as b a, c a, did before, but the angle b a c is reduced to f a c. By continuing the revolution of the object bar, the apparent quan- tity always forms a base of an isosceles triangle in any angle, till on bringing the bar in a line with a c (Fig. 3), when the angles cease from a union of the rays, and the whole of the index wire is projected through the cock. I have also invented an instrument which I term the Deflectometer, which exhibits the combined effects of converg- ing and foreshortening. A rectangular form is made to revolve on the line a b, Fig. 39, Plate 5. Four fine threads are attached to the four corners, and brought to a point s, or place of an eye. A frame made to contract in width between the upper ponts c and d is inserted in those threads. A slit is cut through the board or platform, between a and b. When the rectangular form forms laterally an isosceles triangle, that is, when both ends are equally distant from the eye ; the index frame inserted in the threads coincides with the objeel frame, but on erecting it, say to the angles//*, Fig. 39. the index form sinks down the slit a b ; the parallel sides become deflectors, or convergent lines, a k, b I ; and the breadth, c d, becomes k I, while the geometrical length, f g, becomes fore- shortened to the length fi,=fh, thus giving ocular evidence of the 46 THE SCIENCE OF VISION ; OR, ever combined effects of the elementary principles of the science of vision. The rule given by Dr. Brook Taylor, and others, for drawing the line of projection in the ground rays, at right angles to the axis of vision, is only given as a rule unsupported by any reason for so doing, and which rule he does not observe verti- cally. I give a reason for doing so, namely — that the eye equalizes distances or extensions of visual rays ; not only in a horizontal direction, but in every direction. CONVERGENCE. The laws of visual convergence of upright parallel lines in surfaces, and a simple method of delineation being unknown to art and science, some explanations will be given to prepare the student for the practical operations of the art. This effect of nature launched incessantly upon the vision of mankind, as well from perpendicular as from horizontal surfaces, has never been recognised by theorists, neither is it to be found in works of art. It has evidently been a sheer omission. To this over- sight may be attributed the mystery and unintelligibility of the theories, and the slow advancement to perfection. The necessity of adopting this principle for the future in the visual sciences, as well as in representative art, will require no urging, so soon as this truth and its consequences shall dawn upon the un- biased intelligence of the world. From the influencing maxims and practices of art throughout all preceding time, the little thought that has been bestowed on vision by the public in general, and the reluctance of practitioners to adopt new cus- toms, I know it will be a difficult task, and take some time to dissipate the misguided notions that have become naturalized. The immutable mathematical principles upon which the laws of foreshortening and converging are founded, cannot fail to carry conviction with them, and the errors and inconsistences NATURAL PERSPECTIVE. 47 of former practices cannot fail to strike the unprejudiced reader, and secure the ready consent of the enlightened. The popular maxim, that all objects appear less the further or higher they are from the eye, is a persuasion so common and powerful, that it would be impossible to disturb the impression. Notwithstanding this feeling has always existed, the theory and practices of art have never coincided with it in regard to perpendiculars, we therefore see in all works of art parallel perpendiculars so represented, whether seen below, level with, or above them. Although the common observer has not de- tected the slight impressions of sense in objects of ordinary altitude, it is somewhat singular that the philosophic observer and able draughtsman should not have been struck with the many extreme cases of daily observation, and have resolved the principles to a common law. The fact is, another faculty has antagonized and refused consent to the influence of sense. What is called knowledge, grounded on no principle, and vul- garly conceived to be superior to sense, has been confided in, instead of the latter being the guide of the former. No small por- tion of this feeling has arisen from the systems of education instilling abstract principles disconnected from the practical pur- poses of learning. True and valuable as are the abstract laws of science, they have been most falsely applied in reference to visual science. Conception of form in abstract is quite another knowledge to that of viewing things practically. It is well known that one abstract mathematical law applies to many practical purposes. It becomes the scholar not to misapply them. In heights and distances, a part of the study of trigo- nometry by the laws of sines and angles, abstract dimensions are sought and found, but in visual science the purpose is not to find abstract heights and lengths, or one of the legs of a triangle ; but from these data to define the practical effect or apparent extension. The omission of associating the practical purposes with the principles of education, induces scholars to 48 THE SCIENCE OF VISION ; OR contemplate nature as though they had no eyes. Being habituated to study things in this way, and knowing how firmly abstract mathematics may be depended on, the theorist unacquainted with practical art has never discovered the mis- application. Foreshortening and convergence are effects inse- parable from the eye, except when lines project themselves geometrically. The convergence of a surface is thus performed : — If a rectangular superficies, or parallel palaster, 1 2 3 4, Fig. 48, be viewed from the point V, so that ray V 2, be twice the dis- tance V 1, the top breadth 2 3*, equal to 2 3, will form the triangle 2 V 3*, in the eye ; and the bottom breadth 1 6, equal to 1 4, will form the triangle 17 6; the latter being double the angle produced from the top ; consequently, that more distant end will appear only half the width of the nearer end. For equalize the rays laterally and vertically to the vision by the line 1 5 ; from the point 5, intersect the rays of the greater triangle, and the breadth 8, will be half 1 6 — therefore 1 5 will be the foreshortened length of the surface 1 9 the con- vergence of each side, and 19 4, the converged figure produced to the eye of a spectator, by the rectangular form 1 2 3 4. This rectangular figure can only form the parallel shape in the eye, from a point opposite its centre, in which case the lateral plan of the rays would make 1 V equal to 2 V. Remarks : — The tyro will find it advantageous to his pro- gress, to reflect on the visual production of the trapezoid 19 4, from a rectangular figure. The comprehension of the meaning of the lines of a diagram goes a long way towards acquiring the knowledge of the action of the eye. As we have only a flat surface to describe upon, the palaster is shewn (to use a common expression), as it is, or geometrically; but as the person stands in front to see it, unless we model on the paper, the distance of the eye over it cannot be shewn, so that we are obliged to imagine, and draw the same thing sideways ; thus NATURAL PERSPECTIVE. 49 the line 1 2 represents the front of the palaster edgeways. — 1 V shews the distance of the eye, and V must be supposed to be our eye. Now as in this sideway proceeding we cannot shew depth geometrically on a flat surface, but by detached plans of the parts, the two lines, V 2, V 1, convey the idea of four lines — two from the top corners and two from the bottom corners — which make the two triangles 2 V 3* and 17 6. At equal distances from the eye V in these triangles, the extreme widths of the trapezoid is seen ; the equalizing line, 1 5, points out these two dimensions, the lower point shewing the width, 1 6, and the upper point the width of the line 8, which is the same in the triangle 1 7 6 as the width at 5 in the triangle 2 V 3*. A play of the imagination must be courted in this study, and as much as we can to indulge in the idea, or conceive ourselves to be in an actual survey, instead of merely looking abstractedly at the dry lines of a diagram. If the width of any other part between the rays forming the lateral triangle, 1 V 2, and the two triangles, 2 V 3* and 17 6 should be required to be known: draw the proposed sectional line a b parallel to 1 5. Then the line b and the line a in the triangle 17 6, give the bottom and top breadths of that section, in the same manner as before. Equalizing sections, parallel to the plane of the picture, are all optical sections, proportioned to the first which touches the object. Other sections will not be optical or visual sections, but produce abstract or mathematical shapes ; because they produce bases oblique to the axis, which is the cause of fore- shortening. For any abstract purpose, any section may be found by the means just pointed out, as the top and bottom of any line in the lateral triangle will shew the widths of the top and bottom in the two detached triangles, as in optical sections. Of course the sectional line is the perpendicular length of the E 50 THE SCIENCE OF VISION ; OR, figure, as the line of projection at right angles to the axis is the perspective width horizontally. The Sectional or Lateral Plan of the Visual Bays. As the images in the eye are made involuntarily to ourselves on an interposing plane at right angles to the axis of the eye, or direct vision ; to explain the manner in which appearances of external ohjects are created, and to give a simple method of delineating them naturally and accurately, I have introduced the sectional or lateral plan of the rays. By this means the vertical fore-shortening, and the true quantity of convergence, is readily found, without vanishing points. I question if many pro- blems of science could be solved without the assistance of this plan, unless by a very tedious and unsatisfactory process. The lateral direction of the rays has been explained to pupils in most works on perspective, but that plan of the vision has never been employed for the purposes above men- tioned. A picture being an isolated representation of what has been seen by the eye of an artist under fixed data, no trace of the spectator, nor his rays of vision connected with the objects, can be manifested in it. To shew this connexion, which is the art of perceiving or delineating : all the perpendi- culars must be raised from a ground plan, and ranged at their proper distances from each other, placing the person at the chosen distance from the nearest, as it were, in a conceived side-view or parallel projection ; and from this sectional geome- trical diagram, to produce the exact apparent lengths vertically, as we find the exact apparent widths horizontally, by the usual ground plan of the rays. Example. — Let E F G [Plate 2, Fig. 28) be three perpen- diculars, viewed from B, at the distance A E, the three perpen- diculars would be seen as in Fig. 29, of which Fig. 28 is the NATURAL PERSPECTIVE. 51 lateral plan or transverse section of the rays of that view. This sectional drawing explains under one view, — the ground plane A G — the point of station A — the point of view B — the point of sight C, or ray parallel with the ground — the horizontal line B C or level of the eye — the vertical angles of the rays 1 B E, 2 B F, 3 B G, and the equalization or vertical plane of delinea- tion D E, including the intersections of the apparent altitudes. The eye of every individual is a centre (B) to himself inde- pendent of others, around which nature is circumscribed ; consequently, the objects E 1, F 2, G 3, affect the visual circumference between the points D and E, and the chord of that arc becomes the natural right plane of vision or plane of the picture ; thus we see from a curve, but on a right plane. Without the use of this process, the draughtsman has no means of discovering more than the horizontal apparent widths of objects, which they obtain from the ground plan and the ground rays, drawn to the point of station ; which horizontal expansion of the rays, by rule, ought always to have been cut by the line of projection at right angles to the axis of vision. I have before observed that this rule of all writers has not been attended to, even in their own publications, and among draughtsmen, as with authors, the horizontal line of projection is usually cut parallel to the top of the paper. With regard to the rays, no reason can justify a deviation from their natural equalization. This line, if cut correctly, will project the widths of the parts of an object; but as the flat surface of the paper cannot shew the two other dimensions, depth and height, these effects have been determinable only by the use of vanishing points : but have been incorrectly determined, because the leading perpendicular has been erected geo- metrically, in consequence of which, the vanishing lines have intersected falsely ; as those intersections have been on parallel perpendiculars instead of convergent perpen- diculars. E 2 52 THE SCIENCE OF VISION ; OR, By the addition of the lateral plan, the apparent horizontal depths and perpendicular heights are found as simply as the widths from a ground plan. The lateral plan is the same in principle as the ground plan, and is only a transverse plan of the plane of the image seen ; in short, these two plans do all that is wanted, and all the apparent dimensions can be gathered from them without any of the complicated details of the former methods. Simplicity, elegance, and truth are the results of the method produced by the combination of the two plans. The representation of depth in a picture must be between points, in a perpendicular direction on the paper or canvas as well as heights, while widths are represented between points transversely or horizontally. The latter are produced by the ground rays to the point of station, in the diagrams of planes and solids. Depths are produced by the intersections of the rays proceeding from ground points, in lateral plans ; thus the depths or distances E F, F G, are distinctly marked by the intersections 2 1, 1 E, and heights are as distinctly marked between pairs of intersections as D E, 2 2, 3 3, Fig. 28, and shewn in the elevation or picture, Fig. 29. The Method of Putting a Plane Surface into Per- spective, without Vanishing Points. Let A, B, C, D, E ( Fig. 34, Plate 4: J be a square surface, divided into sixteen equal compartments, to be represented as seen from the point F, at the distance E /, with the eye raised about the level of the square to the height of f F. Draw the square, and divide it into sixteen equal squares, as a ground plan. Draw the ground rays from all the points on the side A, and also from the line E, to the point of station S. Draw the lateral plan A F, B F, C F, D F, E F. NATURAL PERSPECTIVE. 53 Equalize the rays A F and E F, by placing one leg of the dividers on F, and cutting off F G equal to F E with the other. Draw E G, which produce to H. Now draw the base line E equal to A E for the picture or image seen, Fig. 35, which divide into four equal parts. Draw lines D, C,B, A, Fig. 35, parallel to this, at the distances of the intersections on E G, Fig. 34. Cut off m I on A, equal to L M in the ground plan, with its intersections. The line LM must be in the plane of G. Join the points on E, Fig. 35, with the points on A, and the perspective of the sixteen compartments is obtained. Another Method by the True Visual Vanishing Points. Draw the square, and divide it as before, in ground plan. Draw ground line A,B, C, D, E /, Fig. 34. Draw E / equal to distance, and /F equal to height of eye, as before. Draw the rays A F, B F, C F, D F, E F. Equalize A F, E F, and draw the line E G, which produce to H, intersecting F H, drawn parallel to ground line A E f. Now for the production of the figure, draw the base line E, Fig. 35, which divide equal to A, B, C, D, E of the ground plan. Erect perpendicular on E, as the view is central. Cut off E F, Fig. 35, equal to E H, Fig. 34, Draw horizontals parallel to E, Fig. 35, at the distances of the intersections on G E, Fig. 34. Join the five points on E, Fig. 35, with the natural vanishing point F, and the vanishing lines will cut the horizontal parallels into the visual trapezoid and its perspective divisions, the same as without vanishing points. Hemarks. — The reader will observe, that in viewing the surface A E, from the point F, Fig. 34, the plane of the image seen is G E, inclined to the ground line A E, and that a con- 54 THE SCIENCE OF VISION; OR, tinuation of that plane of the picture to the level of the eye H, H E becomes the perspective distance of the horizontal line F, from the base line E, as seen in Fig. 35, in which F is the point of sight to which all the lines vanish. But as it has been the invariable custom to take sections perpendicular to the ground line, as K E, the point of sight I, has been drawn distant from the base line equal to E I, or less than E H, which pro- duces a different trapezoid and divisions to that seen, but is the true vanishing point for that mathematical section. This latter-mentioned figure is perfectly correct as an abstract ver- tical section of the rays, disconnected from the vision, but with these data, as no image is seen by the eye in any other plane than E G, it cannot be called a perspective production. It is an abstract operation, the method of performing which may be of use in questions of solid geometry, but certainly it is quite irrelevant to the purposes of visual science or practical perspective. Although the student may not yet be supposed to be suffi- ciently acquainted with the reasons of the practice of perspective, it may be well to apprise him, that every abstract section alters the process, which may be thoroughly understood and readily performed in any case, by attention to the last two, and the diagrams No. 36 and 37. If the perpendicular section K E be required, E I will be the distance between the base line and the horizontal line ; I will be the point of sight or vanishing point, and K E the vertical depth of the figure. If the perspective section G E, be required, E H will be the distance between the base and horizontal lines, H the point of sight, and G E the vertical depth of the figure. If any other section inclined either way from the perpendi- cular E I, the production of the line from E, till it intersect the line F H, will give the distance for the base and horizontal lines, and the vanishing points sectionally. NATURAL PERSPECTIVE. 55 Variation of Appearances from a Fixed Point of View through the interposition of other objects. It is often a matter of surprise to students in perspective, that objects appear and are represented differently in combina- tion to what they are when represented disconnectedly. By reflecting on the diagrams 36 and 37 the reason will be evi- dent. On viewing a surface lying in the direction A E from the point F, Fig. 36, the image will be in the plane G E, and appear like the trapezoid in Fig. 35 ; but if we introduce four perpendiculars on the four corners of that surface, that appear- ance from the same point of view becomes like the trapezoid A, B, C, D, E, Fig. 36, with the convergent perpendiculars on the four corners, which are not drawn parallel, because they do not appear so from the point of view F. Explanation. — The rays from the surface only make the lateral plan, A F, E F, Fig. 37, and the plane of the image, E G; but when the perpendicular, E B, is interposed, its rays, B F, E F, when equalized, shew that the picture seen is in the plane B D,and that the surface, A E, intersects that plane in the points D H, which disconnectedly appeared through the plane Ci E. We cannot have more than one equalization or plane, which must proceed from a primary object. The elevated position of the eye foreshortens the perpendiculars, which necessarily lessens the distant parts of the object comparatively. Although the surface or base of the figure, and the position of the eye are not altered, the introduction of perpendiculars causes an approach of the plane from E G to B D, and changes the delineation. To teachers, as well as students, I would seriously recom- mend the making of models of superficies; in which the surface, the rays, and all the principles of the diagram may be seen. This practice is more explanatory to beginners than 56 THE SCIENCE OF VISION ; OR, lines, and facilitates in an extraordinary degree the com- prehension of complicated diagrams which cannot be mo- delled. Take a piece of stout card-paper or board : — describe a square as the Fig. 34 ; on the point S set up a stout piece with a hole in it at the height / F; make the trapezoid m E I, Fig. 35, and gum it down on the line E of the square ; make holes in the corners of the square, and bring fine threads through the four corners, and through the four comers of the trapezoid, and pass them through the hole in the standard intended to represent the spectator, and gum them so that the lines are all tight, or in straight lines; to do which, it will be necessary to make the piece of card, like the trapezoid, incline as the line G E. Solid cubes and other elementary figures may be strung in the same way with their apparent figures introduced in card out- lines within the threads, meeting at the proposed point of view. Juvenile and school pupils may be taught the science of vision and perspective by these models at a very early stage of their education. The master has a fine opportunity by this means of showing pupils the difference between oblique and right bases in a conic or pyramidical system of rays, proceeding either from a superficial or a solid form, which makes the necessity of always taking right bases for perspective appearances clearly to be understood. I have found the greatest service from constructing them ; indeed, to this practice only can I attribute my success in bringing my theoretical ideas to practical demonstration. They enable you to look into all the combinations of a visual pro- duction. The aberration of lines, when reduced to a plane surface, are easily accounted for, and the mind is more firmly impressed by rendering the notions visible to the sense. NATURAL PERSPECTIVE. 57 The Method of Putting a Quadrilateral Surface into Perspective from a Point of View within the Figure seen, i. e. Vertical to a Point in the Surface. Let ah c d ( Fig. 38) be the figure to be put into perspec- tive from a point vertically over, or horizontally at right angles to the point V, at the distance e S. Take the line a d as the plane of the surface. Draw the rays d S, a S ; equalize them by the line af. Draw the axis of vision, S M,by bisecting the horizontal triangle a S d. On this line, in the planes d and a, erect perpendicularly the length a b in lateral plan, marked g and h. On S set up S i equal to e V. Draw the rays to i from each extreme of g and h ; equalize them by the line m n. Draw k I in the plane of the point n parallel to f a. Produce indefinite perpendiculars from f k I and a. Draw the base line o, and on indefinite line I, cut off point b equal to m n ; on indefinite line k cut off the point c equal to m r ; and on indefinite f cut off d, distant from base line equal to m g. These three distances must be taken perpendicularly from thejbase line o, and not in the inclination of the lines of the figure. Join the points abed, and that trapezium will be the appearance from the chosen point of view. This diagram explains a point in perspective upon which there does not appear to be a clear idea ; namely, that from this and other points around the centre, the original figure does not preserve its parallel lines, and that it is contrary to the nature of perspective to represent objects so. It has been argued by able writers, and the notion prevails, that S e being the shortest ray to the surface, and perpendicular to its plane, that d a may be assumed as the plane of the picture, and may be considered perpendicular to the sight. This is an 58 THE SCIENCE OF VISION; OR, error : it is a perpendicular to the ray s e, but not an optical perpendicular. The plane of the originating surface, and the plane of the image seen are distinct planes, except the object be viewed from a central point. The ray S e has also been called, in fact is generally called, the axis of the eye. An axis always conveys the idea of a centre ; but in the case before us, this shortest perpendicular ray from V is not in the centre of the rays generated by the form abed, therefore cannot be considered a centre either of the original form, — the rays pro- duced by it, or the image created from it. The visual axis is always in the centre of the appearance, and is always the shortest ray, as S m is to the plane of the image seen a f. In the representation of a surface from points perpendicular to points in itself, it is immaterial whether the surface stand erect or lie horizontally ; the image in the eye in all these cases will be identical with given or fixed data. It only requires a little thought and ingenuity to fix a ground plan in such manner as will produce the required figure by the sim- plest process. In this example, by treating the sides a b, c d, as two perpendiculars on the ground planes a d, and the point V as an altitude c V, represented by S i, at the distance c S, the conditions at once are made out clearly, and the whole becomes a simple operation. But for the aid of the lateral plan, and the laws of equalizing the rays horizontally by the line/ a, and vertically by the line m n, or the two transverse directions of the projecting plane of the picture, probably the convergence of the four edges and the true points of the natural trapezium, or any other abstract section, could not be found. The only method known is the vertical section pro- duced by vanishing points, on the principles laid down by Brook Taylor, and others. The value of the method of finding any section or construction in practical geometry, I leave to science to estimate. This diagram will be a clear proof that the rectangular NATURAL PERSPECTIVE. 59 figure of a space between the gable ends of two houses, the opening of a street, the remote upright wall of rooms, or any surface viewed from a similar point, ought to be represented as a trapezium, instead of a rectangular form, so commonly drawn. The mathematical accuracy of the system laid before the reader may be seen by describing on the base line, o, the rectangular figure proposed to be put in perspective ; for if a line be drawn through the point d, through the point c, and through the point b of the trapezium, from the three points of the circumscribing parallelogram, those lines will meet in the point V. The perspective point V is the point in the plane f «, through which the ray S e passes from the originat- ing parallelogramic surface. On the demonstrations of this and similar cases are estab- lished the following rules: — The Method of putting a Square or Rectangular Surface into Natural Perspective, producing a Trapezoid. Describe the ground plan of the square a, b, c, d, Fig. 39. Choose a point of station S. Draw the rays a S, b S, c S, d S, bisect the angle a S b, and draw the axis of vision S e. Erect S V, perpendicular to axis, any chosen height for the eye or point of view, and/<7 being the points on the axis of the planes of the two sides ab,c d, draw from those points to the point of view, V. Equalize these rays and draw/ h. Cut off on axis f i equal to f h in the plane of //. Parallel to a b, draw m n, between the rays d S, c S, and through draw k I equal to m n. Join k a, I b, and a b I k. will be the perspective trapezoid sought. Explanation : — In the diagram, the point of view V, the rays drawn from f and g, and the equalizing line f h, are repre- sentations of the rays laterally. They must be supposed to be 60 THE SCIENCE OF VISION; OR, elevated over the point of station S, and to describe the vertical extension of the figure as the ground rays a S, b S, c S, d S,do the horizontal extension. Vertical expansions can only be repre- sented on a fiat surface, by throwing them down sideways, the imagination must elevate them. By conception we perceive the vertical plane of the image, fk, to overhang the originating surface in the inclination / li, so that the nearest edge of the figure seen will be the projecting points a & in the plane a b, and the distant edge of the apparent figure will lie between the rays m n, that being the width between them at the top of the inclination h, which, when transferred to the line k /, gives the image as seen by the eye. The section of the rays / b, perpendicular to the ground line f s, commonly taken for the image seen, would make the ver- tical depth of the figure equal tofb instead of fh, and the line k I equal to p q, which is only an abstract mathematical section, having a trapezoidal outline different to the perspective figure. Very slight inspection of the diagram will satisfy the reader of the error of former custom, for b v f is an oblique triangle having an oblique base. I have demonstrated that every image of a line seen by the eye forms the base of an isos- celes triangle, and, it will hereafter be demonstrated, that every image of a solid object forms the base of a pyramidical system of rays, at right angles latitudinally and longitudinally, to the axis of vision or centre ray. As a b is a right base to S horizontally, so fh must be a right base to V, and perpendicular to the axis or line bisecting the angle h V f. Another method of producing the natural figure is, after proceeding as stated, till / i be drawn equal to / h ; draw an indefinite line through i, perpendicular to a b ; produce / h till it intersects v o, drawn parallel to S e, in o ; cut off / e equal to / o ; draw a e,b e ; draw k I parallel to a b, equal town; in the rays a e,b e. Join k a, lb ; and the same figure is pro- duced as before. NATURAL PERSPECTIVE. 61 This diagram will be again referred to when we come to the explanation of the method of assigning the natural places of vanishing points, which, in the old system, are only applicable to the production of sections vertical to the ground plane of the originating object, such sections being foreign to perspective except in one position of the eye. Instead of producing the figure seen within the ground plan by either of the methods stated, after drawing the ground square and the lateral plan, on drawing the line f h, and the line m n, in the plane of h parallel to a b, — parallel to the axis bring down four indefinite perpendiculars from the points ab n m. Draw the base line, A B, and parallel to it, D C, at the distance, f h. Join B C, AD, and the natural figure is produced in perspective. As each method produces the same result, the draughtsman may use either. To find any Abstract Section of the Rays or Section of a Similar Pyramidical Solid. Instead of the perspective section, f h, Fiq. 39, let it be required to find the image in the section, ef t Fig. 40. Draw a line through e parallel to a b, within those rays ; again, draw a line from /, cutting the rays d S, c S parallel to a b; from those points bring down four indefinite perpendiculars ; draw base line A B, and parallel to it C D, at the distance of the length of the section e f. Join A B, C D, and the abstract figure is obtained. In a similar manner any other section may be produced. 62 THE SCIENCE OF VISION; OR, To put a Square or Rectangular Surface into Per- spective, Viewed Oblique to its Sides, producing an apparent Trapezium. Draw the ground plan a, b, c, d, Fig. 41. Choose the point of station S. Draw the rays a S, b S, cS, d S. Bisect the angle d S b, and produce the axis S e. Let perpendiculars fall on the axis from the four corners a, b, c, d. Erect the chosen point of view, V, perpendicularly on S. Draw from the planes of the corners brought on to the axis to V. Equalize this vertical section of the rays, by the line / i, by taking the length f v, and cutting V i equal to it off e V. From the points of intersection f, g, h, i (perpendicular to vertical axis s e), draw to the ground rays a S, b S, c S, d S, thus the intersection i comes from the point on the axis brought from c ; therefore, from the point i join the ground ray c S : in the same manner join h with the ground ray d S,g with b S, and /with a S ; where these lines intersect the ground rays are the points of projection for the four indefinite perpendiculars A, B, C, D, brought down to produce the figure. Draw the base line A, and parallel to it B D and C, at the distances f, g, h, i. Join the intersections A, B, C, D, and the actual figure pro- duced to the eye from the point of view V, is represented. It has been remarked that no other than the vertical section of the rays has been practised in perspective ; in consequence, only one line of projection has been required, one being suffi- cient for sections vertical to the ground line, but for the visual as well as all other sections, more than one line of projection are necessary to produce the figures. The ground plan shews the number of projecting lines, there being two, m n and a b, to NATURAL PERSPECTIVE. 63 produce a trapezoid {Fig. 39), and four, f, g, h, i, to produce a trapezium {Fig. 41); because the projecting plane of the picture (in the vertical direction) overhangs the originating surface, which is clearly seen by the inclination of the line fx to the ground line e S. The equalizing line, / i, with its inter- mediate points, g h, gives the true visual distances, in vertical expansion, of the four oblique and unequal distances of the corners from the eye. The reason for bringing the comers on the axis will be explained in a future chapter of the work. The other lines of the diagram are explained in the chapter on vanishing points. General Rule I. When a rectangular surface is viewed from any point in a line passing through the centre, parallel to the sides, the appearance will be a trapezoid. (Fig. 39.) General Rule II. When a rectangular surface is viewed from any point in a line passing through the centre or not, but oblique to the sides, the appearance will be a trapezium. (Fig. 41.) No superficial form appears geometric, or similar to ifs abstract form, except it be viewed from a point perpendicular to its centre; thus, a square only appears a square when viewed opposite its centre, the slightest variations produce the changes and figures above mentioned, although the organic evidence is not sensibly felt without considerable inclination of the originating figure ; yet we are sensible, or, more properly speaking, we are conscious the process is going on which finally attracts our notice. Notwithstanding, in an ordinary way, slight deviations from the original shape, caused by trifling inclinations, are not perceived by an uneducated eye, yet if a frame work be interposed, and held at right angles to the vision, the slightest alteration in the apparent form is detectable. For the 64 THE SCIENCE OF VISION ; OR, purpose of noticing these effects, I have invented a Spectrometer, which may thus be constructed. Cut a large stout card- board into a semi-circle, cutting out a small semi-circle in the centre. Join the edges, and the frustrum of a cone is made, expanding 60°, or greatest natural field of view. Affix a square or rectangular frame to the mouth or base of the cone, the side of which should be at least eight inches deep. Cross the frame with parallel threads or wires. Apply the narrow end of the cone to the eye, and compare the edges of the appear- ances with the horizontal and vertical parallel threads, or edges of the frame, which represent the picture, and the slightest convergence of lines becomes perceptible. A few proofs of this effect inform the judgment, and where before, the sense of sight failed to apprize the mind, except in violent cases, the cultivated understanding co-operates with the sense of sight, originates strict ideas, and we see by knowledge as well as sense. The Old System ; or, the General Practice of Per- spective. — {Plate 6.) The general principles of perspective, as they have been practised, may be briefly explained by a description of the manner of putting a cube into perspective. Draw the ground plan abed. (Fig. 42.) Fix the point of station S at the chosen distance a S. Draw the ground rays a S, b S, c S, d S. Draw the line of projection, e /, through the nearest point a, perpendicular to k i, i. e. at right angles to the axis S c. Draw the line S e parallel to a d, and S /parallel to the side a b, which is the way of finding the vanishing poin ts, e f. Draw the base line g g, and bring down perpendicular lines from the points k a i, and also from the two vanishing points, ef. Now if it be proposed to represent this cube with the eye on a level with half its height, to denote that position, the horizontal line, NATURAL PERSPECTIVE. 65 h h, is drawn parallel to the baseline g g, and distant from it equal to half the height of the cube. The geometrical height of the edge of the cube is then set on the base line in the perpen- dicular a, then by ruling the vanishing lines from the top and bottom of this line to the two vanishing points on the hori- zontal line h h, they intersect the sides on the perpendiculars k and i, and produce the usual perspective of the cube from the fixed point of view. Now if it be proposed to represent the same cube from the same distance a S, but raising the eye above the level of half its height, the same ground plan, &c. will serve. To whatever height the eye is proposed to be raised, at that distance draw the horizontal line 1 I from the base line m m (Fig. 44). Then, as before, set up the height of the cube on the centre line, and from either end draw to the vanishing points I I on the hori- zontal line, as before, which produces Fig. 44. Again. — Raise the horizontal line, or geometrical level of the eye n nto a height considerably greater than the height of the cube, as in Fig. 46, and by ruling to the raised vanishing points, Fig. 46 is produced. The old system, it will be readily observed, works by 'parallel perpendiculars in every elevation or depression of the height of the eye; an adjustment of the horizontal line to the geometrical height of the eye above the level of the base of the cube; and a section of the visual rays perpendicular to the ground line, in all cases. These are the three leading features of the old system, and the practices of all masters of all countries, and have constituted the general and only characters of the art. The three figures, 43, 45, 47, placed in juxta-position with Figs. 42, 44, 46, shew the different representations of the old and new systems ; the two first being identical, the others differing, because in them the principles of the first are not sustained. The inconsistency of such figures as 46 has struck every one who has practised the art, without being able to F 66 THE SCIENCE OF VISION; OR, account for the cause of error. The first of these figures, 42, is truly visual, and similar to the one by the new system. It will seem strange that the method which produces one cor- rectly, should not do the same with the rest; the reason is this ; — in Fig. 42 the eye is placed opposite the centre of the mass, and the centres of the upright edges ; all of which, with the visual rays, form isosceles triangles, consequently the plane of the image will be parallel with those edges, and perpendicu- lar to the ground plane, as well as perpendicular to the axis of vision. For these joint reasons the representation is at the same time strictly optical as well as strictly mathematical. But if we take the other cases, we shall see they are strictly mathematical, but by no means optical, from the omission of the fundamental principles of the former case. In Fig. 46, the vertical length of the whole figure is equal to 1 2, equal to the line 1 2, or perpendicular section of the lateral plan of the rays, which section, though vertical to the earth, is oblique to the axis of the rays ; consequently, standing in a position that the eye must foreshorten from the point of view. Now the true, or optical figure 47, in its whole vertical extent, is equal to 3 4, equal to line 3 4, or optical section perpendicular to the eye on the lateral plan. All other sections of this diagram but this will be oblique to the optical perdendicular ; conse- quently, only strictly mathematical. There is no utility in the mathematical sections for the purposes of perspective. They are only useful in abstract questions for purposes in solid geometry, in which cases, the lines of the diagrams, instead of representing visual rays, must be considered to represent the edges of solid bodies. The simple method here introduced will be found greatly to facilitate the operations of the civil engineer, mechanical draughtsman, and others. Artists have hitherto represented objects by their geome- trical dimensions perpendicularly, and by their apparent dimen- NATURAL PERSPECTIVE. 67 sions horizontally. The theories contain no other system. The absurdity of combining the two principles need not be commented on. The Methods of Drawing Solids in true Perspective. The Cube.*— (Plate 5, Fig. 38.) When One of the Edges only is Projected Geometrically ; i. e. when One of the Edges is made the Axis of Revolution, and Two of the Sides are seen as Trapezoids. Draw the ground plan abed (Fig. 49.) Fix the point of station S at any chosen distance. Draw the ground rays a S, b S, c S, dS. Erect on the axis S e for the lateral plan e f g h, each equal to the height of the cube ; also erect perpendicular to the axis S V the height chosen for the eye. Draw the lateral plan of the rays e V, f V, g V, and h v ; equalize them through the nearest point h, by drawing the line i k, making i V equal to k V. Draw I m parallel to a b from the point k ; a b is already drawn from the point h ; draw o p from the point n, and q r from the point i. Bring down perpendiculars parallel to axis from / m, a b, o p, q r. This completes the ground and lateral plan. For the elevation or representation of the figure seen — draw a base line s t, and parallel to it lines at the distances inhk on the line i k. Join the points of intersection s t u v, w x y z, and the vanishing lines vs,ut,z w, and yx, and the natural image is obtained. In the old system it has been customary to represent the image seen by the annexed figure (50), in which there is an inconsis- * A cube is represented as a superficial square, trapezoid, or trapezium, when the eye can only see one side ; the first when viewed over its centre, the second when viewed on inclinations parallel to the sides, and the third when seen from points within the surface oblique to the edges, as described in plane surfaces. F 2 68 THE SCIENCE OF VISION ; OR, tency so marked, that it is remarkable how it can have passed cur- rent in school diagrams and books, without previous detection. One side, it will be observed, is made a perfect square, stuv, while the other is represented as a trapezoid, v u y z ; but as two sides are supposed to be seen, the revolution of the solid, which brings the second side into the view, will turn the square oblique to the eye, and produce in effect a trapezoid, as shewn in Fig. 39. All surfaces viewed obliquely will have vanishing lines, but in this figure we have the remarkable instance of but one vanishing point for two obliquely viewed surfaces. If the diagram be turned and viewed as though an upright side were made a base, and the eye be considered as much from the side as in the other position it is above the cube, then by the only true case in the old theories, the orthographic height (line u v), is set up, the horizontal line S e drawn through the centre, the vanishing points o o* drawn parallel to the side in ground plan, and the figure is pro- duced ^identically with the natural figure reversed. Nothing can more clearly demonstrate the error or inconsistency in principle of the old system, than this familiar diagram, and nothing can be wanting to assure the practitioner of the immu- table principles upon which the new theory is established. The Cube.— (Fig 51, Plate 7.) When all the Edges seen are in Oblique Perspective, and a Corner made the Centre of Revolution — the Eye being Supposed to be Level with the Altitude of the Object. Draw the ground plan of the cube and rays to the point of stations, with their axis s e, the edges seen standing on the two planes a b, on which erect the height of the cube ; unite their extremes with the point of view V. Draw the vertical line of the plane of the picture by the equalizing line e f, NATURAL PERSPECTIVE. 69 perpendicular to the axis S c ; from the points e g f, find the widths within the rays, by the lines h i, k I. From these four points in the ground rays bring down indefinite perpendiculars parallel to axis. Draw the base line and parallels at the distances e g f. Join the points of intersection, and the image seen from the given point is produced. The Cube.— (Fig. 52, Plate 8.) When all the Edges seen are in Oblique Perspective^ and a Corner is made the Centre of Revolution, the Eye being above the Altitude of the Cube. — To Exemplify this Case, the Eye is conceived to be in the Plane of Two Co runs Diagonally through the Centre. Draw the ground plan of the cube, and erect the heights of it on the planes a b c, as in the last figure ; draw a V, b V, c V, and from the upper ends of each. Equalize these rays, by drawing the line efghi. Intersect the ground rays by the lines k /, m n, drawn from the points / and h. From the projecting points k I, m n, in ground plan, bring down indefinite perpendiculars intersecting the parallel lines, drawn at the distances e fg h i. Join the points, and the cube will be in perspective, or as it would be seen from the chosen point, V. If the parallel lines efghibe drawn, and two concentric circles drawn of the radii g e, g i, of the lateral plan from the centre o, those circles will intersect the perspective points of the cube in the same points as the indefinite perpendiculars k ?, m n. The projection of this figure, by the old system, is truly ridiculous, as an optical figure with the data given. The vertical elongation of the figure, its compression in width, its maintenance of parallel perpendicular edges, and the acuteness of the diagonal lines are perfect absurdities in perspective. It is evident from this point of view that the three sides seen 70 THE SCIENCE OF VISION ; OR, must be identical trapeziums, which are easily exhibited by constructing a skeleton cube, and suspending it over a candle, by which means the figure of our diagram is projected in shadow on the ceiling. The Cube.— (Fig. 53, Plate 8.) When all the Sides seen Foreshorten and Converge. If this diagram be carefully observed, it will be seen and easily retained as a working method, that in the lateral plan four rays from the top and four rays from the bottom of the lines representing the height of the cube, intersect the line e f in eight different points. Now the point /and the three next come from the tops ; lines from these points intersect the ground rays and project the indefinite lines for the widths of the upper- most points of the projection of the cube, while e and its two contiguous intersections send forth lines which intersect the ground rays, and send down indefinite perpendiculars which intersect the lower points. Thus we have seven lines of pro- jection if we represent an opaque cube, and eight if we repre- sent a transparent cube. I consider it best for the student to practise every figure as though they were transparent, as Fig. 49. It may make the diagrams look a little more complicated, but it renders the system more explicit. Draw the ground plan abed, Fig. 53, Plate 8. Fix station point S, point of view V ; draw the rays to the point S, and find axis of vision. Bring the corners on the axis, and erect on each the height of the cube. Draw from the top and bottom end of each that is seen to the point v; equalize this lateral plan of the rays, by drawing the line e f. From the points on this line, as in the illustration of Fig. 52, bring lines perpendicular to the axis s c, to the ground rays a s,b s,cs,d s, taking care to join the points which correspond NATURAL PERSPECTIVE. 71 in the two plans ; thus g is the top of the nearest perpendicular, and e the bottom of it, consequently join g with a, and e with a s, which give the projecting points of the nearest line of the perspective figure a e. When the same operation is performed with the other points, the uniting of the seven points completes the figure sought. The point of station for the convenience of the plates is placed very near the object, which causes considerable conver- gence, much more than is usually seen, as objects are seldom viewed so close. There is, however, an advantage in this, as it renders the principle more evident to the student, who will do well to view a similar object near to the eye, and, by turning a small cube about, to have practical experience of the changes and peculiar appearances of the various positions. It is scarcely necessary to give examples of octagonal and objects of many perpendicular edges, because the principle is the same in four as in four hundred. It may be necessary, however, to give a clear explanation of the reason for bringing all the perpendiculars on the axis, and to show that they appear the same on those points as they do on the corners of the square, although at the latter points they are more distant than on the axis. It has been explained that all objects range themselves on a line, forming the chord of the arc of the natural field of view of 60°. On this section of the visual rays, from which we derive the appearances of every thing we see, all similar objects on the same plane, trans- verse to the axis, project equal lengths through the natural plane of the picture, although they produce different angles in the eye ; thus, although a square surface viewed from a point opposite the centre forms a pyramid of rays of many angles on both sides a centre line, yet the two outer edges appear equal to the centre line, because a section parallel to the base and equalizing the marginal rays equalizes the parallel ordinates of the base. The natural plane being similar to the geometrical 72 THE SCIENCE OF VISION; OR, section, a pyramid at right angles to its axis just stated projects equal sines or subtenses of the unequal angles formed in the vertex of the rays. The angle in the eye has been considered the measurement of the dimensions of an object, which has led to many false suppositions. It is by angles we judge of dis- tances, and by the subtenses or right bases of them that we judge of magnitudes. This may be clearly understood by drawing a number of parallel lines of equal length on a piece of card-paper, and running a thread through the end of each line ; on bringing these threads to a point over the centre line, they will exactly represent the visual rays that would proceed from those lines to the eye. By interposing another piece of paper parallel between the base and the vertical point, those rays will, through those different angles, cut off equal lines throughout, so that whether a length appear on the axis or on the same plane to the right and left of it, the subtense of the angle is the same, and is truly represented from the axis. The Method of Putting Pyramids into Perspective. Although the pyramid is the simplest solid form in nature, being composed of the least number of sides, it is a figure that has baffled art strictly to delineate. As it has no perpendicular edges, and all its sides are oblique to the spectator, it has not come under the control of the laws for rectangular surfaces. The Method of Putting a Pyramid into Perspective Opposite One Edge Inclined Directly from the Spectator. — (Plate 8.) Draw the ground plan a b c, Fig. 54. Fix the point of station S. Draw the ground ray a S, b S, c S. Bisect the angle b S c, and draw axis S d. Erect the height of the pyramid on the centre of the triangle, found by the length of a side, a b, NATURAL PERSPECTIVE. 73 and the height of a side, d a, intersecting at e. Choose the point of view V. Draw from the planes d a, the centre 0, and from the height of the pyramid e to the point V. Equalize these rays by the line a f. From the point g, intersect the ground rays c S, 6 S, on the points h and i, from which, bring down indefinite perpendiculars to the parallels of the elevation equal to the lateral distances a gf. Erect a f on the base line, in the line of the axis, join the four points agfh, and the pyramid is produced in perspective. The Method of Putting a Pyramid into Perspective Oblique to the Edges. — {Fig- 55, Plate 9.) Draw the ground plan a b c. Choose station S. Find axis by bisecting angle c S b. Erect point of view V, and draw ground rays c S, b S, as before. Bring the three corner points on the axis. From the axis, through the centre of the triangle, produce the altitude of the pyramid, found as previously de- scribed, by the intersection of the length and height of a side. Draw from the four points on the axis, and also from the ver- tical point of the pyramid, to the point V ; equalize these rays by the line e d, d being the nearest point on the axis. From e intersect the ray from the centre of the triangle. From h intersect the ray b S ; from g intersect the ray c S ; from f intersect the ray from the centre ; a is its own intersecting point. From these five projecting points, bring down perpendiculars, intersecting five parallel planes taken from the line e d. Join ah, h g, g a — h e, a e, g e, and f e, which will define the outline of the pyramid seen from the chosen point of view, and the perpendicular or axis of the pyramid. This figure is represented as though the pyramid were transparent, all the edges seen, and a perpendicular erected from the centre of the base to the vertical point, because of the curious circumstance of that perpendicular not appearing ver- 74 THE SCIENCE OF VISION; OR, tical from points of view oblique to the edges. It will be seen in the diagram that the perpendicular is on the inclination from / to e, because the centre of the base and vertical point of the pyramid are to the right of the axis, diverging from the lower point f, because of the elevated point of view. If the point of view were depressed below the centre of the altitude of the object, the perpendicular would be convergent. On viewing a single perpendicular as a pole, without regard to its thick- ness or any surrounding objects, it always appears perpen- dicular, because it is brought into the plane of the axis of vision ; but as the perpendicular in this case is surrounded by other lines, the appearance of it is controlled by the contour of the whole, which fixes it out of the plane of the axis, and gives it an inclination in the eye and in correct drawing. So that we may say, without parallel lines to produce convergence, we see a single line to incline, which this demonstration clearly proves. It is decidedly a new point to art and science, extremely curious in itself, highly corroborative of the natural principle of convergence, and of the constancy of the maxims of rectified visual science. The Line of Projection. As a section of the visual rays, perpendicular to the level of the eye, has been a conventional or rather a general practice in perspective ; the line termed the line of projection has been sufficient to point out the position of the plane of the picture, because all the points of intersection of the rays would be vertically over that line. Dr. Brook Taylor has laid down the rule, and all subsequent writers have done the same, that this line should be cut at right angles to the axis of vision, that is, at right angles to the line c S, Fig. 42, which bisects the angle of the rays of a ground plan. Yet in almost all works, the writers themselves have lost sight of this rule in their diagrams, NATURAL PERSPECTIVE. 75 and falsified their own true principle. This error has led many into false notions of parallel and oblique perspective as they call them. Properly speaking, there is no such thing as parallel perspective. From not cutting this line by rule, the representation, or rather the figure produced, has been called parallel perspective when this line has been cut parallel to the facial ground line a b, Fig. 56, and oblique perspective when the figure produced has been from a line of projection oblique to the facial line, Fig. 57. Example, supposing a box to be the object to be represented, the ground plan a b c d is drawn, the point of station S is assumed at a chosen distance. The line of projection e f is drawn along the plane of the box e f, or parallel to it; from the intersections of this line indefinite perpendiculars are brought down, upon which the upright edges of the box are afterwards to be defined. The line S e, is drawn parallel to the side a d, to find the vanishing point e. As a parallel to a b, from the point S, would never cut the line e f, no vanishing point can be found for that side, which by this method produces parallel projection, and gives to this system the false name of parallel perspective. The next process is to draw a base line through the indefinite perpendiculars, and a horizontal line drawn parallel to it, at any chosen level of the eye. The perpendicular height of the box is cut off on the perpendicular line g, and another equal to it is on the line It, and a parallel to g h, completes the face of the box. From the extremes of the perpendicular side g, diagonal or vanishing lines are drawn to the vanishing point V, found and brought down to the horizontal line as before explained. Thus, one side of the box is drawn geometrically, and the other side perspec- tively, and this is called parallel perspective. In the other case {Fig. 57), with the same ground plan and station, the line of projection is drawn at right angles to the bisecting ray S e, or visual axis of this view, by which the points of projection are much contracted, and vanishing points 76 THE SCIENCE OF VISION; OR, to the sides a b, ad, are found by parallels to them from the point S intersecting the line of projection in V 1 and V 2. Then the base line is drawn through the indefinite lines, the horizontal line at the level of the eye drawn parallel to it, and the two vanishing points brought down ; then the geometrical height of the box g is set up on the base line, and from its extremes vanishing lines are drawn to the two vanishing points, cutting the indefinite perpendiculars in A A and i i, and forming the box by two trapeziums ; and this is called oblique perspective, because neither side is drawn by parallel projection. The gross absurdity of such a system (if it be worthy to be called a system), will be manifest to the most inexperienced reader, for we have here two delineations of the same thing from the same point of view, and the ridiculousness of it will be still more apparent when it is recollected that any other direction may be assumed for this line of projection (in the old system), and as many figures produced as it may be possible to project. If any body could place a box before their eye and see one side a rectangular shape, and another side a trapezoid or trapezium at the same time, this sort of thing might be called perspec- tive. When there was no other system than that, and when dependance was put in it because of its mathematical principles, it was excusable in masters to teach such rules, but since the introduction of the natural optical principles, it will be imposing on the good sense of the rising generation to plead those prin- ciples to obtain confidence in such methods, and the production of figures falsely called natural or optical. It will be seen a great deal depends on this line as the widths are affected by every change of its direction. In the old system it was only required to project what were called the perspective widths, because the principal height was always set up of the geometrical length, and did not require any foreshortening on the vertical section, as will be seen by the Figs. 44, and 46. But as the eye foreshortens perpen- NATURAL PERSPECTIVE. 77 diculars as well as horizontals, when seen from an oblique position, and as in this case the eye is below the middle of the height of the box, the apparent height will be less than the real dimensions, which will necessarily introduce vertical con- vergence of the surfaces seen, as well as the usually represented horizontal convergence. This natural effect being projected to the eye through a plane perpendicular to the axis of the eye, that plane will not be always perpendicular to the earth, but will incline towards us or from us, according to the elevation or depression of the visual axis. These inclinations of the plane of the picture, from the perpendicular, cause the project- ing points of the natural image seen to be vertical to as many lines as there may be different distances, heights, and widths of points in the originating object. This introduces into visual science many lines of projection. In no previous system has more than one line of projection been introduced. The images of the vertical section of the rays being universally considered to be the natural appearances, and other sections being of little general utility, no familiar means exists of finding any section except that communicated by the common theory of perspective. If the reader refer to Fig. 38, by the old system, the figure is taken from the plane g h, which is perpendicular to the line of projection a b; but by the new system, the natural figure is taken from the plane i k, inclined to a b ; that the points k h n i, are vertical to or overhang the lines of projection I m, a b, o p, q r. Now as those points in a diagram, or on a plane surface, take those places, the widths of the convergences consequent on this inclination of the plane of projection, are familiarly pointed out by the sections of the lines of the ground plan, which corre- spond with and represent, in a transverse direction, the lines of the lateral plan. So that the student becomes conscious of the transverse directions of a projecting plane — that is, its hori- zontal and vertical expansions, which have been but imperfectly 78 THE SCIENCE OF VISION; OR, conveyed to him by the usual line of projection, that line having been used only to convey the horizontal expansion of appearances. The perpendicular expansion of appearances having been somehow or other considered unchangeable, and lines perpendicular to the earth supposed not to be affected by the eye, those persons who have attempted the study of per- spective, being taught to depict them geometrically, have not formed a distinct notion of the plane of the picture or the plane of projection, which is the same thing, by the line of projection. A model of a cube, in the way I have introduced, will at once explain this point to the young student, and render the acquirement of the art pleasing and rapid. In Hayter's work on perspective, a frontispiece of a window, with persons looking through it, is given, and the same notion is described in most works, to explain to pupils the plane of the picture. It is said that the pane of glass is a true repre- sentative of it, and that if the head were kept fixed, and all the interposing points and linesof the objects seenbeyondit were care- fully traced upon the glass, that that picture would be what is seen by the spectator from that fixed point of view. This is an illustration so specious, that enough cannot be said to destroy the delusion, to save draughtsmen from being deceived by it for the future. If the eye be opposite to the centre of the pane of glass, a picture drawn upon it, as described, will be in true perspective, because the plate of glass then stands in the optical plane ; but if the eye be opposite to any other point, it becomes a false medium in optics by position ; — it takes the place of a mathematical section of the rays that pass through the transparent glass. I have pointed out how an interposed object takes the precedence in the formation of a picture, and makes more distant objects secondary or comparative to it. Taking a single pane, or the whole of the window, as the inter- posing object, if the point of view be oblique to its centre, the pane or the window puts itself first into perspective, the image of NATURAL PERSPECTIVE. 79 which will be a trapezoid or a trapezium, according to our position. Then, through these figures formed by the window, we see the distant objects reduced to the perspectives of these planes, which are not where the glass is, but on a medium between it and the eye, as I have explained by the horizontal and vertical equalization or transverse directions of the plane of natural appearances. The old rule is imperative that the eye, horizontally, should be equally distant from the frame of the window on either hand, but no regard has been paid to the oblique direction of the top and bottom sides. If the first rule has any sense in it, the latter condition is equally imperative. By twisting the pane of glass about in thousands of positions, while we sit still, we should see the same picture pass through it, because the optical plane will not alter, but the number of pictures we might trace would all be different if the glass were turned from the position it might be in while drawn on or looked at from any other point of view. We must not stir nor the glass after traced on, nor the glass be looked at fairly by turning and holding it naturally, or we shall observe distortions, which, from our fixed point of view, cannot be seen, and are not the natural images. The artificial figures obtained in this way, on transparent false mediums, must be carefully distin- guished from the images of the eye. Pictures of this distorted character require to be fixed in the angle of the medium from which they were taken, and the eye fixed at a given distance, that thus arranged they may generate in the eye a system of rays, the optical base of which shall project upon the vision a natural perspective image. Observe, objects are not seen by the eye where they are, but in the jylanes of their appearances, except it be an object that can be viewed geometrically, like the cases given of a line and plane surface opposite the centre which produces geometrical perspectives. In all other cases the planes of the images bring forward from the geometrical lines of the object perspective appearances, on 80 THE SCIENCE OF VISION ; OR, that interposed medium, from which naturally we distinguish appearances. This is such a new notion of seeing things, that it will not be comprehended by the public, till perspective becomes a part of general knowledge. Masters will be able to explain this fact by tying a piece of string to each end of a stick, and by placing the stick in every inclina- tion before the eye of the pupil, while he holds the angular point of the string to his eye, and pointing out to him that the appearance comes to him from the length between two points in the strings at equal distances from his eye, when he will perceive the difference between the place of the stick and the place of the length, where he sees the appearance of it. The Method of Putting a Building into Perspective. (Plate 10, Fig. 58.) Draw the ground plan of the building, marking on the visible sides 1 2, 1 3, the spaces of the doors, windows, &c. Fix the point of station s, and draw two rays from the extreme points 2 and 3 of the plan to the station point ; bisect the angle of these rays, and draw the line 4 s through the ground plan, as the axis of vision in ground plan. On this line, at the point of station, erect a perpendicular s v as high as the eye is above the plane on which the building stands (supposing the ground to be level). Draw a line 4 15, through the nearest point (1) of the ground plan, at right angles to the axis of vision. On the axis erect perpendiculars equal to all the geo- metrical heights of the various edges of the building ; thus, on the point 4 erect 4 5, equal to the height of the building ; parallel to it, on the planes of corners 2* and 3 # , erect the same heights. On the planes of the nearest and most distant windows, 6 and 7 in ground plan, set up the heights of the windows, and draw the perpendiculars of the door in the lateral plan, 7 7, 7 7, 6 6, 6 6. By this process it will be seen that every NATURAL PERSPECTIVE. 81 height that is required to be found in perspective must be set up of its geometrical length on the axis of vision, which forms the lateral plan I have introduced, and without which it would be as vain to attempt a perspective delineation as without a ground plan. Having set up the geometrical heights of all the parts on their proper planes, draw from either end of the longest, which is the nearest line 4 5 in this design, to the point of view ; equalize these lines by drawing the line 4 8. From each end of the lines set up perpendicularly on the axis, and from each end of the windows and door draw towards the point of view v, till all the lines intersect the line 4 8. Then draw from all the points of the windows and door on the ground plan, 1 s, 2 s, 3 s, towards the point of station, till they intersect the line 9, which is produced from the point 8, parallel to 4 15. Then, for the elevation in perspective, draw the base line 10, and parallel to it the line 11, at the distance 4 8. From the points on the line 4 15, intersected by the lines to the point of station, draw similar points perpendicularly, by a parallel rule (or mark them off on a strip of paper), on the base line 10, and by the same means transfer the points from the converging line 9 to the line 11. Join the points on the line 10 with those on the line 11. Transfer the points inter- sected by the heights in lateral plan on the line 4 8 to the line 10 11, and from them draw lines parallel to the base line till they intersect the converged lines in all the points of the structure. Unite these points, and the drawing will be com- pleted. By this simple system there is no need of either hori- zontal line or vanishing points, nor of any tedious or compli- cated process of finding proportional points, &c, nor of sur- charging the drawing with lines to be cleared away, as all the points can be kept on three or four lines surrounding the per- spective elevation ; and, above all, the design must be the definite image seen by the draughtsman. In this design the point of station is placed nearer to the G 82 THE SCIENCE OF VISION; OR, building than would be selected, as the convergence is too considerable for ordinary drawings, although it is perfectly natural on so near an approach. An extreme case is, however, necessary to convince the public that the convergence of per- pendiculars, though hitherto unperceived by science or art, is as natural as the convergence of horizontal lines. The prac- tical draughtsman will find this method highly advantageous in the saving of time, paper, and instruments, as every operation can be done within the limits of a convenient space. The practical draughtsman will carefully observe that all heights must be erected on the line representing the axis of vision. For distinctness, in complicated designs, the part, called the lateral plan, may be drawn separately, and the points taken off as in the diagram. If this be done, the distance or station and the point of view must be the same as in the ground plan, but this will seldom be found to be necessary, if the following simple practice be adopted. In a treatise of this sort we are obliged to mark in all the lines of a design, this gives the appearance of complication ; but on practising the science, it will be found extremely sim- ple in its operation, and any mistakes readily avoided, if, after drawing the ground plan, and fixing the point of station, the two extreme rays (as 2 s and 3 s) be drawn and equalized by the horizontal line of projection 4 15, drawn through the nearest point. Then, after erecting all the heights on the axis of vision, by equalizing the extreme rays by the line 4 8, which will be vertical to the axis of vision in lateral plan, the line 9 can be drawn on the plane of point 8, and parallel to 4 15. Now by inking in the lines 4 15, and 9 and 4 8, we can rule with a pencil from the ground points 1, 2, 3, to the point of station, and give the extreme of their heights in lateral plan, &c, till we intersect the lines 4 15, and 9, and 4 8. These points being transferred to the lines 10 and 11, and to the perpendicular 9 10, the contour, or general outline, NATURAL PERSPECTIVE. 83 of the building will be denned. The pencil lines can then be rubbed away from the ground plan, and the vertical and horizontal points of the minutiae may be inserted in the same way, seriatim, without our ever being liable to be confused by a multiplicity of lines in our ground plans. The building introduced as an example is of the simplest kind, that the student may not be confused with a mass of complicated lines. It may not be so pleasing to the sight as a more elaborate structure ; but, regardless of censure on that score, in it are contained all the practical ideas of a more showy view. In every case, a ground plan, with the dimensions of the building, to some scale, must be made. This ground plan can only shew the extension of all super-imposed material horizontally, or in length and breadth ; and it must be borne in mind, that if any parts overhang or project beyond the main walls, the quantity of such projections must be marked on the ground plan just the same as if such parts rose from the ground. By this means the projections can be treated as heights standing on those points in the ground plans, and their exact places marked in the perspective elevation ; for instance, the places of the windows are marked in the ground plan in the diagram, because over those points we have to find the various heights of them. Now a structure, however compli- cated in itself, contains no more than heights, widths, and depths of parts ; and if we have to find a height of a pinnacle, a point in a roof, a chimney, a cornice, &c, put the point properly on the ground plan, and proceed by the rule of finding the perspective of a perpendicular, and no difficulty can occur in the practice. On reference to the representation, it will be perceived that there are three vanishing points for the lines, that is, the top and bottom lines of the side with the door in it converge to- wards a point to the right hand, on a line of the perspective level of the eye; the top and bottom lines of the side with the g 2 84 THE SCIENCE OF VISION ; OR, windows in it, towards a point on the left hand, on the same level ; and the lines which represent the upright edges of the house converge towards a point in the axis line 4. The more oblique the position of a line, the nearer the vanishing point will approach the axis horizontally, and the level of the eye vertically. Thus, by producing the lines of the sides, as de- scribed above, the nearest vanishing point will be on the left hand ; the next distance will be to the right, and the greatest distance on the axis perpendicularly, in the inverse order of the increase of the inclinations geometrically. Although in look- ing downwards upon objects, they converge towards a point in the nadir, as on looking upwards they do towards a point in the zenith, precisely like the two horizontal points in the represen- tation of objects as seen in one view without revolving the head. The lines can never converge to more than three points in the same drawing ; because lines, however placed, or however long, in the same plane, can only appear to tend towards one point. The level of the eye does not break the continuance of the parallel or convergent tendency of lines ; any discon- tinuance of the direction of a line bespeaks the commencement of another line or surface in some other angle with the eye. Revolving the head, on its horizontal or vertical axis, turns the appearance of parallel lines into convergent lines. From the direct view there must be two revolvings of the head horizon- tally on either side of the axis, and two perpendicularly to turn parallel lines into convergent lines in two opposite directions ; but then they will be seen in two views, and on two distinct planes ; — lines that converge in two ways in the same view always indicate different surfaces in different positions. It will be particularly necessary to try these effects. From the manifest convergence of lines upwards and downwards, as well as to the right and left, a notion has crept in that perpen- dicular lines should converge upwards above the level of the eye, and downwards below that level. The same notion has NATURAL PERSPECTIVE. 85 long prevailed as to the convergence of lines in opposite hori- zontal planes. Experiment and reflection will satisfy any one on these points, better than argument without them, especially after studying the rules of this work. How to Make a Perspective Drawing of an Increased or Decreased Size from the same Ground Plan. If the same building should be required to be drawn on a smaller scale, parallel to the vertical equalizing line 4 8, draw the line a b of the extent proposed. At right angles to the axis draw c d in the ground rays through the point a, and parallel to c d draw ef in the plane of point b. Between these two lines, the horizontal breadths and con- vergencies of this reduced scale will be found, as in the former method. Those lines which are drawn to the point of view, and intersect the vertical equalizing line 4 8, producing the apparent altitudes of all the parts, if continued till they inter- sect the line a b, will give the reduced altitudes, which agree with the reduced widths c d, ef In the same manner, if it should be required to increase the scale of the drawing, the ground rays must be extended beyond the ground plan ; the vertical equalizing line must be drawn in the same extension as the ground rays may be cut, and intersected for the heights, by projecting the lines of the ground plan to the proposed increased size of the drawing, How to Represent Parallel Ordi nates, or Rows of Parallel Lines, Equal Heights in Figures, &.c. &c. Let 1, 2, 3, 4, 5, G, 7 (Fig. 59) represent seven equal heights of any sort of objects. S the point of station or distance from them, and V the point of view over S. Draw the line through 86 THE SCIENCE OF VISION; OR, the bases, and join the points with the station point. The line S 4 will be the axis of these ground rays. Draw v c,v b, — c b perpendicular to the axis being equal to c 4, or height of each line. Cut v a equal to v b, and draw equalizing line a b, or vertical plane of the images ; draw d e parallel to g f, through the point a. For the elevation, or picture, draw the base line d 2, e 2 {Fig. 60) equal to d e {Fig. 59), and 1 7 {Fig. 60) equal to line g f {Fig. 59), distant apart equal to a b, with the intermediate five points on each, intersected by the ground rays. Join 1 d 2, 7 c 2, and the others in the same way, and the parallel lines are represented as seen from the given point. The tops of the lines being nearer to the eye than their lower extremes, an apparent downward convergence takes place. The difference of these two distances is c v minus c a, v a being equal to v b. On account of this difference, the length c b foreshortens to a b. In consequence of this difference and foreshortening, the isosceles of the rays, to the tops g sf horizontally, is reduced through the point a to d s e ; then as gf is the whole breadth at the top, and d e the breadth be- tween the rays at the bottom {Fig. 60), projected through these, and the intermediate points, must be the true per- spective. A model of this case is easily made, and would make it intelligible to capacities of any age. The height of these lines are set up on the axis 4 c s, because the effect on the eye is the same with all, standing as they do in the same plane at right angles to the axis, extending equally each way, although the distances severally increase on either hand ; for the plane through which we see them is parallel to that originating plane. The geometrical section of a solid parallel with the base would be similar to Fig. 59, although the angles severally decrease each way. It must be remembered, however, that it is not the angles, but the NATURAL PERSPECTIVE. 87 lines which subtend those angles, that make the images in our eye. We must look to the perspective bases of the rays, and not to the angles for the appearances of lines and objects. The variety of angles has been a difficulty in this study, and having been insisted on as a cause of effect, without the main conside- ration of their subtenses or optical bases, explanation has always been unsatisfactory, and the reasoning not clearly understood. As the point of station in Fig. 59 is central horizontally, the lines of projection g f andd e cannot be foreshortened; but as the eye is not central to the heights, nor vertical to the plane of the objects, being level with the upper ends, the reduction of the geometrical triangles b v c to the optical triangle a v b, so that the vertical or transverse direction at the plane of the picture may be (as it is horizontally) at light angle to the axis, a foreshortening takes place in that direction, as pointed out by the line a b, which must be considered to extend throughout the image as shewn in Fig. 60 by the parallel lines 1 7, d 2, e 2. If the eye were central to the height as well as the width of the objects, they would be seen as geometrically represented in Fig. 59, without any foreshortening or conver- gence, because the bases of the rays and angles would be similar to the geometrical data. An idea is very prevalent that the middle height 4, if viewed opposite the centre of its height, would appear of its geometrical length, and each succeeding parallel on either hand would decrease, as shewn in Fig. 62, because of the decrease of the angles, and increasing distances on either side of the centre height ; but such a repre- sentation must be that of two distinct surfaces angular to each other in different planes. The ideas being properly directed to the optical bases of the rays, instead of the angles, will dissi- pate this erroneous notion. I will now draw the attention of my readers to the change 88 THE SCIENCE OF VISION; OR, of effect and circumstances that will take place on turning the head, and taking only the parallels 1, 2, 3, and 4, as the objects we propose to observe, or make a picture of, from the same point of station. The rays of the eye now traverse equal distances on either side the axis 2 s, which does not with these data bisect the ground line g c, although it bisects the geometrical angle g s c. On equalizing the rays g s, c s, the axis bisects the line of projection h c, as well as the angle, and reduces the ground plan to the same principles as that of the seven parallels which required no alteration of its geometrical treatment. When all the perpendiculars stood on the same plane g f, in Fig 60, only one line of projection was necessary, but in this case, as they range on a line which does not form the base of an isosceles geometrically, they have each distinct planes of projection on the axis of vision 2 s, namely, n o p q. These lines being set up perpendicular to the axis of their geo- metrical height on the planes of 1, 2, 3, 4, and v 2, erected also perpendicular equal to height of the eye, equalize the lateral plan of the rays by the line i r, as we did horizontally or in ground plan. Draw v 2 m, passing through all the upper ends, as the eye is level with them all. Draw from n o p q, towards v 2, intersecting the line i r, which will give the decreased length of each line. To make the figure of these lines from this ground and lateral plan, draw the four parallel lines at the bottom of Fig. 61 , at the distances of the intersections at r in Fig. 59, and the line 1 2 3 4 at the top, at the distance i r. Draw the dotted line perpendicular to the parallels for the axis. Set the points s t u w to the right and left of the dotted axis as in Fig. 60, on the base line, and the same with the points 1 2 3 4 on the upper line, taken from the line h c. Draw from 1 towards s intersecting parallel 1 ; from 2 towards t stopping on the second, from 3 stopping on the third, and joining 4 w, the converged or true oblique perspective will be obtained. The whple figure is a visual trapezium. NATURAL PERSPECTIVE. 89 The method of bringing all heights upon the axis or bisecting line of a ground plan, as though all the perpendiculars to the right and left in the same planes stood on that line, is not only new, but, as a practical rule, simplifies the operation, and is the only means by which the representation of perpendiculars can be obtained with a similar truth to that of widths obtained from a ground plan, if intersected at right angles to the axis. The two directions of the plane of the picture, or image seen, have but one axis ; but it requires to be exhibited in diagrams in transverse directions of that plane, both, however, meaning the same ray. As dis- tance is known to produce a lessening of appearance, it has been generally considered, that from s an object or line at c must appear less than one the same size at the greater distance s f, which has led to the supposition of a gradual diminution of objects either way. But this does not occur except on turning the head to the right or left, by which motion, the axis of obser- vation does not fall on the centre of the objects before observed, neither does the new axis meet the plane of those objects in a perpendicular, but in an oblique direction, and with the new view a new plane of the appearance is generated by the eye. On observing Fig. 60, it will be seen that all the bases of the lines 1, 2, 3, 4, 5, 6, 7, range on the line d 2, e 2, because the axis of the view falls on line 4 in the centre, and all the lines are in the same plane. But on turning the head which produces the image Fig. 61, it will be observed that the different distances c s, 3 s,2s,g s(Fig. 59), produces four planes, stuw, for the bottom of the lines 1, 2, 3, 4 {Fig. 61). The true distances of these parallel planes are found only on an axis s 2(Fig. 59), from points on it n o p q, which points are produced from the geometrical planes of 1, 2, 3, 4, (Fig. 59), parallel to the horizontal direction of the plane of the picture s w. The different planes of Fig. 61 shew the obliquity of view or position of the objects, and shew the absurdity of Fig. 62 90 THE SCIENCE OF VISION; OR, for the representation of objects on the same plane, in which case they must stand on one line. I have dwelt on this point, because of its importance in natural perspective, and to explain the misconception of this case by other writers. The principles of these cases are the general rules for all per- pendiculars in every species of objects. If those lines be made the heights of human figures, the apparent heights are readily found by the same means. To Put a Horizontal Line a b and a Line c d Per- pendicular to its Centre into Perspective, from the Oblique Point of Station S. Draw the ground rays a s, c s, b s (Fig. 63). Equalize the marginal rays by the line a f. Bisect the angle f s a by the axis line s g. Parallel to a f find the plane of end b on the axis by the perpendicular bg ; also the plane of centre c by the line c h, and the plane of a by the line a k. Erect h i equal to c don h, in the plane of c, thus completing the ground plan. For the lateral or transverse section, draw k e, h e, g e, i e. Equalize k e, i • 1, z 2,v 2, 0 1, Z 1, V 1. For the elevation or production of the figure se( n ( Fig. 79, 126 THE SCIENCE OF VISION; OR, Plate 20), draw the base line and others parallel to it at the dis- tances of the intersections on line 1 2 r. From these intersec- tions draw lines perpendicular to axis s f, till they intersect each corresponding ground ray; as point 2r, being the inter- secting point of r circle 2, intersect the ground ray of that point p s in the point 3, from which, parallel to axis f s, bring down the perpendicular line 3 k. Similarly intersect the ground rays from the other points on 1 2 r, and bring down the perpendiculars intersecting the parallels to the base in the points m Iw, circle 2, and kmlw, circle 1. Join these points by elliptical lines, and also k k, I I, when the cylinder will be represented in natural perspective. Remarks. — The sections of elliptical systems of rays are always perfect ellipses, except the one illustrated in this work, which produces a circle. Although connected with right lines, as k k, I I, and the image taken from the visual plane of the whole figure, which is not the plane of either of the elliptical rays of the circles, still the projection of those figures are perfect ellipses, and not eccentric. Such is invariably the case with oblique sections of cones and cylinders. METHOD FOR CORRECTING THE DRAWING OF CIRCULAR BUILDINGS IN PERSPECTIVE. In the perspective drawings of circular buildings and pro- jections, it is very seldom that we see them marked with that propriety which ought to characterise such delineations. The method illustrated in Plate 21, Fig. 80, will correct the usual inaccuracies. The building is represented as though it were transparent, that the nature of the delineation may be perfectly evident. Draw the breadths and heights of all the parts of the building geometrically, as in Fig. 80. Choose the point of station s and view v. Draw v a touching NATURAL PERSPECTIVE. 127 the nearest point, and v b tangential to the dome. Equalize these rays, and draw the vertical line of the plane a b. On the centre c describe circles equal to all the parts of the building ; the largest represents the basement, the next the projection, and the smallest the upper story as well as the base of the dome. Draw lines to each of these circles from the station point in ground plan. Find the tangential points (d e f) of each by perpendiculars to centre c. Draw lines perpendicular from d e fin ground plan to d d, e,f f, in geometrical Fig. 80. Draw from all the points to v, intersecting the line a b. For the production of Fig. 81 draw parallel lines at similar distances to those intersections on a b. To the eye at v, the circle at the base a will appear an ellipse; and on the plane of the picture a b, the minor diameter will be a 2, of which 1 is the centre ; and the circle at the top of the basement will appear an ellipse, the minor diameter of which will be 3 5, and the centre 4 on the plane a b. For the major axes of these two ellipses references must be made to the ground plan, where a describes the point of the circle with which the eye comes first in contact, having no width. Immediately under point 1, in line a b, the width between the two ground rays d d is equal to line 1 in ground plan, which is the length of the major axis of the ground ellipse ; and immediately under point 4 of line a b, the line 2 in the ground rays is the length of the major axis at the top of the basement or greatest circle of the building. In the planes or parallel lines of Fig. 81 cut off and join the two major axes 1 4, and describe the two ellipses a 1 2, 3 4 5, which will complete the perspective of the circular basement. Do the same with the smallest circles f at the bottom and top of the upper story, and also with the circles of the projec- tion or middle-sized circles e. Having obtained and drawn in all these ellipses by the minor axes on a b, and the major axes 128 THE SCIENCE OF VISION; OR, in the ground rays, perpendicularly under each point of that line, the proper manner of drawing the semicircular dome only remains to be explained. I have dotted out the other semicircle of the dome, and treated this part of the building as a globe, to prevent any mis- conception; this globe, and consequently the part of the semi- circle seen, will appear elliptical in consequence of the direction of the plane a b, upon which it is seen, not being at right angles to the rays that proceed from it. Now the rays of the circle of the dome intersect the points 6 b, and the centre 7 for the major axis, and g h in the ground plan for the minor axis of the ellipse {Fig. 82), seen on the plane a b of the image of the whole building. If the plane of the picture were in the dotted line h g, of Fig. 80, or at right angles to the rays of the dome only, it would appear a circle with transverse diameters equal to g h in lateral or ground plan. As the upper circle of the upper story, and the circle of the base of the dome, are the same size, g h or minor axis of the ellipse of the dome, cannot appear greater. This singular effect and production of the vision is also explained in the chapter on the perspectives of circular columns, &c. In drawing the projecting line of the ground plan in the old system, it was always through point a, which in a vertical section is correct ; but when the position of the eye does not admit of such section, but inclines the plane of the picture to the ground line, then there is required more than one horizontal line of projection, which lines are perpendicularly under the different points of the inclining plane in the ground plan ; as the greatest apparent breadth d of the basement appears in the plane of point 1 in a b, which the line 1, immediately under it in the ground plan, shews the extent of horizontally ; and the same of the other points in a b and projecting lines in the ground plan. Whenever there are any circular parts in a building, in NATURAL PERSPECTIVE. 129 putting them into perspective, erect a line for the centre of the circular bases on the ground axis, and at the geometrical height draw the diameters parallel to the axis ; then bring the rays of each end and the centre of each on the vertical line of the plane of the picture, and having thus obtained the major and minor axes, the ellipses will give strict propriety to this hitherto difficult part of the art. HOW TO REPRESENT CIRCULAR COLUMNS OR SPHERES AS WE SEE THEM. The perspective representations of columns, &c, has always presented insurmountable difficulties, inasmuch as they have always been irreconcilable to the senses and the judgment. About thirty years ago, Mr. Gandy introduced a circular line of projection, with a view of throwing some light upon this question, which method has only tended to increase the mys- tery. I shall not enter upon all the arguments that have been adduced, but illustrate the case, and trust to the demonstration of it, and the general principles of visual science contained in this volume, for a satisfactory solution of this problem. Let 1, 2, 3 (Fig. 83, Plate 22), be three circular columns viewed from the point s, let A .... F be any surface behind them ; the visual rays tangential to each column will touch that surface in A B, C D, E F, — C D being less than A B or E F ; the plane of projection of the image seen being a .... f, the appearances of the columns will be similarly unequal, the two outer ones equal, and greater than the centre one, although the centre one is nearest to the eye. As we can only truly represent what we see from a right lined plane, and that plane with these data is a .... f, the quantities on that line cannot be wrong, because they intercept proportional quantities on the back surface A. . . . F, either linearly or visually. K 130 THE SCIENCE OF VISION ' OR, If we adopt the circular line of projection (except in delineating on similar circular surfaces), the quantities on that curvature being equalized, they would not intercept the une- qual quantities on the right line A F, and consequently we must do the ridiculous thing of drawing part of a surface which we cannot see. Taking the columns each as an isolated object, they will appear on either side the centre one, gradually somewhat less and less, because of the increase of distances ; but in combina- tion with other objects, their appearances are according to their intercepting quantities on the plane of projection a which is represented by the plane surface of the paper or canvas of the picture. Now if we view three columns or more within the compass of vision without the necessity of revolving the head; from the point s {Fig. 84), by drawing the ground rays tangential to them, and equalizing the whole angle by the line a/on the natural plane of their appearance, they will be of the respective widths, a b, c d, ef, which the circular line of projection would distort, for a true representation on a right lined surface or picture. On the same principles as those of Fig. 83; three round balls, viewed from the point s, would appear differently, namely, the centre one a perfect sphere, and the others as ellipses, because the tangential rays would intersect greater horizontal breadths (for the two extreme balls), on the plane of pro- jection a f. And according to the principles of vision, the same three round balls, viewed obliquely from the point s (Fig. 84), would all three be truly represented as ellipses, of which a &, c d, e f, would be the major axis. I am aware this is a very difficult effect to be reconciled to the observer, because he turns to each and contemplates them as separate and dis- tinct objects, by which means he views them through several planes which he is not aware of, and which separate planes he NATURAL PERSPECTIVE. 131 cannot avail himself of, when he comes to reduce his view to the simple plane of his picture, which, in reality represents the general impression of the whole view. The accuracy of the deli- neation would be ascertained by interposing the drawing (made on a transparent medium) between the eye and the objects, placing it optically, when it would be seen to intercept the objects perfectly. A model, on the plan of my perspective models, at once explains the principles of the effects I have just illustrated. THE AXIS OF VISION AND PLANE OF THE PICTURE EXPLAINED. The axis of vision is a term in perspective and visual science used to denote the direction of the view ; in speaking of the direction of a view, it must be borne in mind, that there is an infinity of directions in a view composing the pyramidical form of rays meeting in the eye by its revolution on its own axis. The optical central ray of every form of rays created by the eye becomes the axis of the view. The axis of vision is always the shortest ray between the eye and the plane of the appearance, it being perpendicular to the optical centre of the image seen ; it is by this central ray that the direction is determined, and it is of the utmost consequence in the study of perspective to understand it rightly ; it cannot be a matter of choice or selection from amongst the numerous rays launched upon the eye from visible objects — they raise the pyramidical stream of rays, and command a centre peculiar to them ; the choice or will can only direct our sight to such object or objects as we may wish to contemplate on or represent. Having done that, the combination of circumstances contains an axis which is created by them, and not by our will or choice. The eye. does not make the axis of the view, but the objects which k 2 132 THE SCIENCE OF VISION ; OR, make pictures or appearances upon it ; the eye is only a vertex of the axes of vision, the base or opposite point of that line always intersecting the centre of the plane of the appearance or natural image seen. Any direction given to the eye does not constitute an axis till that ray be encompassed by others, and defines the centre of them. Only one ray of any form of rays can occupy the centre and be an axis. The field of view, without revolving the head consistent with the organization of the sight, is 30 degrees in every direction around the axis of direction ; — it is not always necessary to embrace 0 degrees. A lesser field of view may and does frequently serve our pur- poses down to the most microscopic space, as in the inspection of an insect, regardless of all other objects or space around it; space does not make any image, any more than the blank paper around the representation of an object ; it is not the field of view we represent, but the appearances of objects in it. The direction of the eye cannot be fixed conventially so as to produce any particular species of representation, without violating the laws of nature, and making the rules of art a senseless trick. If the eye be directed straight forward, and be made the axis of any field of view, the natural image launched upon the eye, by the object or objects, will be from a plane perpendicular in every direction to that axis ; and if the objects be perpendicular to the ground, the figures will appear perpendicular and parallel to the frame of the picture, if it be made square or rectangular. If the axis be elevated or depressed, the same objects will change their appearances in the elevation by converging upwards, and on the depression by converging downwards ; so also by revolving the eye hori- zontally to the right and left, parallel horizontal lines will appear to converge each way, but not in one view. In these revolutions and oblique directions of the axis of vision, none of NATURAL PERSPECTIVE. 133 the lines will be parallel to the rectangular lines of the frame. The level of the eye is the common vanishing plane of all hori- zontal lines, and the transverse plane the common vanishing plane of all perpendicular lines in objects. The laws of appearances are common to both directions. The horizontal lines of buildings, level with the eye, appear so because they are in the horizontal plane of the eye ; all other lines above and below this one appear to fall and rise, or con- verge to some point in this level line, commonly called the horizontal line. If the eye be raised to a higher point over the spot we stand upon, a higher line in the building becomes a level line, and the level line of our lower position converges to the new level of the eye. In the transverse section of our view of objects, the perpendicular line immediately before us appears so, and all lines to the right and left of it appear to converge to this transverse axis or, more properly, plane of vision. By bringing one of the converging perpendiculars into this plane, by revolving the head, the new plane of direction transforms it into a visual perpendicular, and the parallel perpendiculars on either side of it will then converge to a common vanishing point in it, in the precise manner and for the same reasons as those of the horizontal plane of vision. These two transverse planes of the vision are the true vanishing planes, and in them all vanishing points will be found. All the world have assented to the natural laws of horizontal appearances, and perceived the level of the eye to be a common vanishing line ; the similar influence of the transverse plane of the eye introduces to art and science the natural laws and common vanishing line for perpen- diculars. The axis of vision and the connected plane of appearances may be clearly explained and exhibited, under all the variety of directions incidental to the action of the sight, by taking a square or round frame, and fixing two pieces across in the 134 THE SCIENCE OF VISION ; OR, transverse diameters, or at right angles to each other ; then by erecting a rod perpendicularly on the centre, it will form a model for exemplification in the following way : — on holding the end of the rod towards the eye, in whatever direction it is held, it will shew the variations of the position of the axis of vision, and at the same time the transverse pieces will shew the visual, horizontal, and perpendicular directions of the plane of appearances in any radii of the sphere of vision. The late Mr. John Constable, R. A., told me, that when he was studying the art of painting in his native place, unaided by others, that he might not introduce too much foreground, and that he might sketch the view correctly, he had attached to the upper part of his easel a frame with a pane of glass in it ; this frame was attached by two screw nuts by the two upper corners ; to the four corners he attached four strings, which he brought to his mouth in such a manner as to bring the centre of the glass perpendicular to his eye. On this glass, thus held and secured from shifting by fixing the screw nuts, he traced with colour the outline of the view he decided on repre- senting. From this sketch he made his painting, and of course his drawing must have been true. Afterwards studying in the schools of art, he followed the rules of those schools, and fell into the popular errors as he admitted and regretted. He had not perceived the principle of his framed glass • and as the views he took were mostly landscapes of low or distant objects, or objects of few straight lines, his subjects did not present very striking instances of perpendicular effects ; had his plan been adopted in taking views of buildings, streets, &c, the tracing on his glass would have called for enquiry, differing as those outlines would have done from the rules of art. As it was, he did enquire, but the universal practice was against him, and that universal practice had the advantage of being supported by the mathematical principles of Dr. IBrook Tay- NATURAL PERSPECTIVE. 135 lor and other celebrated scholars. What would have been the improvement and perfection of art in the hands of such talented artists, if instead of the misapplication of principles, a sound and perfect optical theory had been laid down for the aid of genius. I remember having read a controversy between Dr. Brook Taylor and Dr. Barrow, respecting the real meaning of the centre of the picture. The former maintained the point of sight was the centre, that is, that the shortest ray to the object was the axis of vision, and that any quantities equal or une- qual of the field of view about it might be introduced into the drawing. The latter maintained that the centre of the view was the centre of the drawing, and that we were not at liberty to introduce into the picture unequal portions about the shortest ray. Dr. Barrow was no more correct than Dr. Brook Taylor, for both looked to the point of sight as it has been called, and neither of these learned men had a true concep- tion of the natural plane of appearances, mistaking the plane of the objects for it. It is clear popular opinion favoured Dr. Brook Taylor's idea, for that notion generally prevails, espe- cially among scholars who do not practice art. If the reader will turn to Fig. 38, it will be easily perceived wherein Dr. Brook Taylor fell into a mistake ; a d is the plane of the object viewed, d s a the ground plan of the rays, and s e the shortest ray, being perpendicular to a d, coming from the point v to i, or point of view. Now this ray, s e, being the shortest ray, he called it the axis of the system of rays, d s a. If we understand the meaning of an axis, and set any value upon geometrical principles and the propriety of abiding by natural laws, it is ridiculous to denominate the ray s e an axis of vision, d s e being greater than a s e. In the horizontal section of the visual rays, m s describes the axis visually and geome- trically. In the perpendicular section of the same rays, the bisecting of the angle m i n describes the same axis of vision. Nothing can be more simple and clear to be understood. Dr. 136 THE SCIENCE OF VISION; OR, Brook Taylor did not see that an object viewed oblique to its centre generated a system of rays geometrically, which the vision reduces to an optical system; and that the image of the surface abed standing erect upon the plane d a was not seen by the eye in that plane, but in the plane f a. If he had distinguished this peculiarity of visual geometry, he would have found that the axis of vision intersecting the centre of the appearance or picture, was the shortest ray perpendicular to that plane and the true point of sight. To prevent any mis- conception of this important point, it may be well here to ex- plain the distinction between the axis of vision and the centre of gravity. If two fine threads be attached to the end of a stick, a b, (Fig. 63) one string equal to b s and the other to a s, and suspended by the point s, by the laws of gravitation, the line c s will hang perpendicular to the ground, because the parts a c, c b are equal, and produce triangles of equal areas, b s c being equal to c s a ; if the eye be applied to the point s, the stick will generate the same geometrical triangles, but the vision will reduce them to two right angled equal triangles fs k, ask, composing an isosceles, of which s k will be the geome- trical as well as the visual axis ; thus the equalization of the areas of the triangles by gravity and in optics correspond in that principle, but not in form. In the same manner may be demonstrated the centre of gravity in a mass, and the axis of vision on viewing it, by attaching four strings to a square board or modelling figure (39), the centre of the board describ- ing the geometrical perpendicular or centre of gravity, and the visual centre of the trapezoid the axis of vision, or true point of sight. The misunderstandings and wilful miscon- structions put by those who know better upon this point of science, since the introduction of my system, are too con- temptible to be commented upon. The plane of the picture, after the practical study of the cases of this work, will not need further explanation. It is, however, NATURAL PERSPECTIVE. 137 necessary for me here to remark, that it is always at right angles in all directions to the axis above described, and the student has only to consider a picture or drawing to be a faithful repre- sentation of this natural plane. Some artists have wished to make a distinction between the plane of the image seen and the plane of the drawing that represents it. As the delineation represents the objects, so the paper or canvas represents the plane on which those objects were seen by the draughtsman, and as naturally every one holds a picture, while inspecting it, as the image is seen ; in the same position the drawing occupies the precise natural plane. As there is only one natural mode of making a picture, there can be but one natural mode of hanging it. It is impossible to make any rules of art to suit all the whims and inconveniences of hanging pictures. When it is possible, they ought to be hung so that the eye can command a centre view ; when that cannot be done, we must put up with the imperfect effect they may convey. We are said to see through a cone of rays, and most writers and teachers instruct their pupils to believe this. We see through a cone, through a pyramid, or any other shape if we please, but it is quite conventional, and not a law of vision. Whether we see through a conic or any other chosen system of rays, objects of nature make the figures, and we only strictly see through a cone of rays when we view a round object per- pendicular to its centre ; the position of the eye, and the nature of the object, then generating a conic system of ray through which we see a circular image. If we view the same circle oblique to its centre, we look through an elliptical system of rays, and see an oval image. If we view a square surface from a point vertical to its centre, we look through a pyramid of rays and see a square. If we see a square oblique to its centre, we look through a pyramidical form of rays, and see trapezoids or trapeziums ; and if we look at a line in any direction, we see 138 THE SCIENCE OF VISION ; OR, through an expansive triangular plane of rays. Around any of these images we may imagine a conic or any other field of view, as we do in circumscribing the drawing, square, round, oval, or any other shape. The real utility and purpose of describing to pupils that we see through a cone, are to explain to them the axis of vision and the plane of the picture seen by the eye, for on looking at an object there must be an axis or centre ray, and transverse to this a plane on or through which the image of the object is seen. As the movement of the head, or the revolution of the eye on its axis between new points, create new directions of the axis of vision, there necessarily follows new directions of the transverse plane of appearances. In this sense a cone being a regular geometrical figure, its axis from the point to the centre of the base being easily conceived, and the positions of the transverse base, however varied, being always at right angles around the axis of the cone, a more simple illustration cannot be given. The axis of the cone and its base, moved about in every direction, is a practical model of the axis of vision and plane of ap- pearances of a circle viewed similarly in every direction. Although the image of the circle never alters the inclinations of the base of the cone and plane to and from the geometrical, perpendi- cular, and horizontal lines are as various as their governing axes. The plane of the picture can no more remain stationary, with a change of the axis, than the base of a solid cone can by changing the position of its axis. NATURAL PERSPECTIVE. 139 REMARKS. Convergence in Small Objects. When people look up a shaft, they see the diminutive aperture above them, which they know to be as large as the space that surrounds them; the bottom of a well looks smaller, though they know it to be as large as the mouth ; the ceiling of a lofty cathedral, though contracted in appearance, they know to be as broad as the pavement ; and thousands of other instances of vertical convergence are familiar to the knowledge of the public ; and yet the representation of this ocular effect is not understood by artists, nor will it at first be comprehended by society in general. There is then distinctly a defect of common knowledge, which can only be corrected by an appeal to the sense of sight. No one will deny that the effect exists, and every one may satisfy themselves that they cannot avoid seeing it ; but because they have not been as familiarized to it by pictures as they have been by them to the same effect hori- zontally, they will not readily believe their own senses ; hence the necessity of doing away with the delusions of art. It has been argued that the effect only exists in extended or violent cases, and that in an ordinary way it cannot be seen. If the faculty of comparison be used in common with the eye- sight, it will be seen to exist in an equal degree in small objects. By reference to figures A, B, C, D (Plate 13), the convergences of a door, a panel in a frame, and a swing glass will be seen. Now if the panel in Fig. C, which appears a trapezoid, were brought to the same position as the frame which appears a square, it would not appear to converge. Compared with a square, the convergence is visible, but with many persons that effect would not be seen without the rectangular shape, because they would consider it looked like what they know it to be — a square. On looking at a thing it is not common to resolve the appearance to its linear form, nor till what was seen is shown 140 THE SCIENCE OF VISION ; OR, in a drawing, are people conscious of what they observe; hence the utility of studying Art to be able to define those impressions which ought to regulate the ideas. The convergence of small objects is not seen, because it is not known and looked for; besides, the shortness of the lines limiting the extent of the effect is not sufficient to obviate the common impression that such lines appear parallel. A ready means of ascertaining the existence and quantity of convergence in small objects, is to take a stick or rule, and by sitting down before a pane of glass, or a picture frame, above or below the level of the eye, to extend the arm (keeping the head fixed, and for distinct observation closing one eye), measure the breadth of the nearer end of the frame, by fixing the thumb at the length seen on the rule ; then raising the arm (kept equally extended), measure the other end of the frame, when the thumb will have to be brought nearer to the end of the rule, shewing the quantity of convergence. On sitting before a window and trying this practical experiment, its convergence will be similar to that shown in Fig. Gr, Plate 14, but more considerably so if it be a lofty window. Objects seen through the window will converge similarly, and the various lines will coincide with the convergence of each of the bars of the window, which seem in ordinary observation to be parallel. I have before said that lines can only appear to converge in three directions in the same view, which are exhibited in Fig. G, Plate 14; the horizontal lines vanishing to the points g and h, and the upright lines, if produced, vanishing to a point in the line e. On turning the diagram upside down, the effect of viewing the same objects below the level of the eye will be seen. The vanishing point in the line e produced, being in this case in the nadir as it was in the zenith in the former view. If more than three vanishing points are to be found in the same representation, they are what may be termed accidental points, or those thatbelong toobjectsplacedin oblique directions, different to those of the diagram, in which case, there may be NATURAL PERSPECTIVE. 141 more than those three, which especially belong to lengths, breadths, and depths, lying in the usual rectangular positions. All lines parallel to those which produce the point h will vanish to that point, and all those parallel to the lines pro- ducing the point g, will vanish to the same point ; but if other buildings appear which are not parallel to those that vanish to the points g and h, they will have vanishing points of their own, according to their obliquity, and these points will be found in the ground plans, by parallels to them from the point of station, by the same method as for those of the diagram. The line g h, or level of the eye, will always be the common line for all the horizontal vanishing points, regular, as well as what are termed accidental, and the central transverse line e for perpendicular vanishing points. Appearances Altered by the Motion of the Head. If we look at two lines forming a cross, a b, c d ( Fig. E, Plate 13). On keeping the head erect, the line c d we call a perpendicular, and the line a b a horizontal ; they are so in reference to the vision, as well as to a geometrical perpen- dicular and horizontal line ; but if we incline the head to the line e f, although they remain geometrically the same, they become oblique or angular lines to the visual perpendicular ef, which effects arise from motion and position. If the two lines be viewed opposite the centre, making the visual perpendicular c d {Fig. F, Plate 13), and c d be revolved directly before us ; while the line a b remains constant, because the triangle of rays from it does not alter, the line c d foreshortens, because the vision reduces the geometrical triangle caused by the new position of the line, to an isosceles, the base of which is c d (Fig. F). Landscapes. In drawing landscapes, where there may be mansions, &c, in the foreground, the rules of perspective must be adopted the same 142 THE SCIENCE OF VISION. as in architectural drawing ; but in views of great extent, and wherein buildings are distant, it is impossible to reduce the view to actual dimensions; consequently the judgment only (guided by a knowledge of perspective) can be exercised; in which case, a horizontal line, indicative of the elevated or depressed point of view, is the chief requisite for the regulation of the vanishing lines of any buildings in the view. In this edition, I have not illustrated cases in every branch of drawing, considering it to be altogether unnecessary. If the principles and practical methods of this work be thoroughly acquired, there will be no difficulty in applying them univer- sally, as the principles are common to every object in nature. Distance of Station. With respect to the distance of the point of station ; in a general way, the most agreeable is, that at twice the distance of the greatest altitude or width of a building. With the view of supporting the common custom of drawing perpendiculars parallel, some masters recommend the distance to be chosen Jive times the greatest dimensions, so that by reducing the natural convergence to an inconsiderable degree, it may be disregarded and the lines made parallel; which no distance in or out of the reach of the eye can do. But dismissing all evasions ; for practical utility, it will be necessary to make the site of buildings a condition in every true representation, as a devia- tion from natural circumstances favors Fancy at the expense of Taste, and leads to disappointment, when a work of art is com- pared with the effects of nature. THE END. LITERARY NOTICES OF THE FIRST EDITION OF THIS WORK. " The identity of Drawing with Perspective, the latter being the theory, the former the practice of the same art, is a problem so little understood — so evaded by men, who are themselves artists by profession, as well as by the amateur — that we congratulate the public on the appearance of a Treatise which cannot fail to demonstrate the problem, even to the least scientific reader. The enumeration of a new method for producing correct perspective drawings, without the use of vanishing points, is a valuable feature of the present work. The illustrations are apt and numerous — the definitions remarkably clear — the problems selected for their utility to the artist ; principles are laid down with clearness and simplicity, and applied to the operations of the draughtsman in a leading and prompting, rather than in a dictatorial manner. The work suggests while it teaches ; and the future artist will owe an obligation to Mb. Pabsev, as much for his rectification of the existing theories, and his demonstration of an improved practice of perspective, as for his Art of Miniature Painting on Ivory." — Atlas, March, 1836. " We perfectly agree with Mr. Parsey in his opinions, both as to the advantages of a knowledge of perspective, and the facility of acquiring that knowledge, by any one inclined to take the pains. Mr. Parsey has obviously thought much and justly on the principles of art. There is no question, but that the apparent forms of objects, as impressed on the retina, are modified by the construction of the organs of vision ; it is these forms that the artist endeavours to transfer to his canvas, when he draws by eye, as it is termed, and his power of doing this with judgment and facility will doubtlessly be increased by a general acquaintance with the rules of linear perspective." — Magazine of Popular Science. " The author of this work, has long been known among artists, as a Miniature Painter of no inconsiderable ability. Mr. Parsey commences his work with a very appropriate intro- duction ; and he then explains the elementary principles of perspective, and the terms used in the art. We have next a number of comprehensive diagrams, showing the application of those elementary principles to the delineation of rectangular, multiangular, obliqueangled, and curvilineal objects. Mr. Parsey's work is a well got up, handsome, and instructive volume, which deserves a conspicuous place in the bookcase of the architect and painter, in consideration of the philosophical introductory remarks; the advancement of a method of projecting objects without vanishing points ; the judicious remarks on horizontal lines ; the absence of unnecessary technicalities; and, in fact, the popular manner in which Mr. Parsey has treated his subject generally." — Architectural Magazine. TESTIMONIALS. " To Mr. Parsey. My Dear Sir, — I have much pleasure in bearing my testimony to the value of your work on the Science of Perspective. The substitution of the lateral view for the vanishing points of the old system, is as new as it is valuable. And the substitution of the right plane for the vertical plane o( the old system, has so many advantages, that you may safely calculate upon its universal adoption by the draughtsmen of a future generation. That the present is a prejudiced race appears from this ; that while they constantly converge parallel horizontal lines, they cannot tolerate the convergence of parallel perpendiculars. You will do them good service by teaching them the use of their eyes," &c. — The Reverend J. B. Reade, C. if G. College, Cambridge, Oct. 8, 1836. "I have no doubt the work merits the high encomium of the Reverend Mr. Reade." — Dr. Birkbeck. " Mr. Parsey, is a thorough master of perspective, the principles of which he displays in a manner extremely clear j with great truth and originality, which I have had the plea- sure of witnessing at his Lectures, on that most important elementary branch of art." — John Constable, Esq., Royal Academician. LITERARY NOTICES. " The Science of Perspective has hitherto been so clouded by difficulties, as to prevent it T)eing acquired generally, as a rudimental basis of drawing, or for the arts generally. Mr. Parsey's system I declare to be clear, intelligible, and to be comprehended by any person of common understanding." — R.R. Reinagle, Esq., Royal Academician. " I am directed by the president and council, to return you thanks for the work on Perspective you have been so kind as to send them, which they have much pleasure in depositing in the Library of the Royal Academy." — Hy. Howard, Esq., R. A., Secretary. Also by the same Author, \2mo. with Plates, price 7s. 6d. — Longman and Co. THE ART OF MINIATURE PAINTING ON IVORY. LITERARY OPINIONS. #*»»#•_ « yy e bave been led into these remarks by the work before us, which possesses the rare value of keeping the happy medium. It is neither abstrusely scientific, nor loosely general, nor popularly mawkish in its remarks. The uninstructed artist, who possesses, with the divite vena, the wish to acquire knowledge to prepare the ore, will find such knowledge here simply, clearly, and scientifically given. The writer, the draughts- man, and the general reader, will rise from the perusal of Mr. Parsev's little work, improved in the knowledge of their respective studies, as well as he whose sole object is painting on ivory, or delineating on any substance the human face divine. The geometry of the art, the anatomy of its subject, and the rules of practice drawn from both, and from observation, compose the work." — Atlas, Jan. 16, 1831. " The student of the delicate and pleasing branch of the fine arts, upon which it treats, may gather a great deal of information from it ; especially with reference to the selection and preparation of ivory, the choice of pencils, the quality of colours, the composition of tints, the progressive stages of a miniature, the various modes of handling, and, above all, the management of the scraper. We perfectly agree with Mr. Parsev, that the value of this instrument has not yet been adequately appreciated ; and that, by the free but judicious use of it, effects may be produced, which it would be in vain to endeavour to obtain by any other means."— Literary Gazette. " This interesting little work is even worth the attention of men of experience in the art of which it treats, and to the tyro is almost invaluable ; inasmuch as it initiates him into all the mysteries of the profession," kc— Gentleman s Magazine. " This is the work of a practical man, who has sought only to make his readers under- stand him. The art, which to some is a profession, is indulged in by many others, to a considerable extent, as an accomplishment ; to both of these classes the work will be of infinite service."— Royal Ladies' Magazine. " Mr. Parsey has written a clever and a useful book. He evidently understands his profession thoroughly, and has adopted a very pleasant method of communicating his information to others. The rules laid down appear to us sensible and easy, and upon the several topics necessary for the student, his views are those of a rational, experienced, and skilful master."— New Monthly Magazine. Also, by the same Author, with Wood Cuts, price 2s. 6d.— Longman and Co, ARITHMETIC ILLUSTRATED ; Showing the Accordance of Numbers with Forms, by which System the Principles of Calculation may be Acquired as an Amusement. " Mr. Parsey is just the sort of teacher for youth ; he would rather encourage than frighten them, and strew the path of learning with flowers. His arithmetical system is admirable, lucid, easy of comprehension, and, above all, practicable. The illustrative wood cuts are peculiarly useful, and convey at once to the eye the meaning wished to be impressed upon the mind."— Kidd's London Journal, Feb. 22, 1840. Steam-press of W. H. Cox, 5, Great Queen Street. Plate 1 PLATE £ Plate 4 Plate 6 PX. ATE 7 PLATE S PLATE 9 Pi ATE 10 PLATE 13 Plate 14 Plat e is IT ATE 16 Plate 18 Plate 19 Plate £o * PLATE 21 ■ ' . ■ HI mm MM