■ V M . . : A ? :» r PARSEY’S PERSPECTIVE RECTIFIED; OR, THE PRINCIPLES AND APPLICATION DEMONSTRATED. »> Price 1 2s ' ■ . ■ V . . - k •W • ■ ; a; : . » . » k . : ; .K. •' ’V • Ik fa v# a* ■ • • *. A . ' • \ ' ^ , «c k . '■ *-'/ ■ jS*; — ' : , . jj v / - • . , 3L(f Sr .Ay,. & .1 ■- ’tv A a ■•'ri. . • ■r' . 3 1 . . - t , GREAT QUEEN STREET, LINCOLN'8-INN-FIELDS. CONTENTS. Page Introduction . . . • • . . . . vii Elementary Principles ........ 1 Perspective Terms explained . . . . . . .15) Application of the Principles to Practice ...... 25 The Sectional or Lateral Plan . . . . . . . 2(i Of Ground Plans ........ 34 To put a Cube in Perspective . . . . . . .35 To put an Octagon in Perspective . . . . . 40 To put a Pyramid in Perspective . . . . . . .49 To fix the Height of Figures in Drawings ..... 52 Curvilineal Perspective . . . . . . . .53 Definitions ......... 54 To put the Circle in Perspective . . . . . . .55 To put the Circle in Perspective from an y Angle ..... 53 Domes, Arches, Windows, &c. . . . . . . .59 Naval Perspective ........ HO Furniture . . . . . . . . . .63 To put a Circular Staircase in Perspective ..... 67 The Ultimate Diagram explained . . . . . . -79 On Horizontal Lines ........ 78 Of Shadows . ......... 80 Remarks ...... 82 ALSO, BY THE SAME AUTHOR, 12mo. with plates, price 7 s. Qd. THE ART OF MINIATURE PAINTING ON IVORY. LONGMAN AND CO. 1ZTE2URT OPINIONS. ******. “ We have 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 draughtsman, and the general reader, will rise from the perusal of Mr. Parsey’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, tne 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. Parsey, 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 worthy 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, &c.” — Gentleman’s Magazine. “ This is the work of a practical man, who has sought only to make his readers understand him, and has set all literary considerations at defiance. 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 Lady’s Magazine. Vide also, the Monthly, New Monthly, and other Reviews, for 1831. DIRECTIONS TO THE HINDER. Platte 1 to face page 2 2 6 3 10 4 24 5 28 6 34 7 46 8 48 Plate 9 to face page 52 JO 54 11 58 12 59 13 60 14 62 15 66 16 70 INTRODUCTION. The Art of Perspective is a branch of knowledge very rarely cultivated, from the prevailing idea that it is useful only to architects and some few artists, and that it is in no way recreative or instructive as an accomplishment. This notion evidently arises from the art being misunderstood. Drawing is esteemed a pleasing appendage to a liberal education, and it is singular that two opposite impressions should exist on one art — Per- spective and Drawing being strictly synonymous. Drawing receives but half its share of importance and merits a much higher value than is popularly assigned to it ; for, besides the amusement it affords, when taught on principle, it is a source of extensive knowledge. If it is pursued with the intention only of producing a facsimile of a copy, it is too servile an operation and too limited a view to merit the name of Drawing. As Drawing and Perspective are synonymous, which ever term maybe used hereafter, by it will be meant the principles of imitating correctly objects in nature. Besides raising Drawing to its proper sphere, it is my inten- tion, in the following sheets, to reduce its principles to simple rules, that it may be more generally sought as a valuable attain- ment by the architect, the artist, the amateur, the connoisseur, and the scholar. a 2 Vlll INTRODUCTION. The number of works on Perspective already in print will scarcely warrant the introduction of another ; and at first view it may appear presumptuous to enter the lists, professing- to elucidate an art which has hitherto evidently baffled skill and learning to simplify ; for, after all that has been written on the subject, the knowledge of the art, as it stands at present, is comparatively limited, few artists pretending to profound skill, it being regarded as a study difficult to embrace, and more essential to particular branches than to the arts in general. This is a popular error, which I hope to remove ; and by my method of treating the subject, I am vain enough to expect the art will be differently estimated, and that the simplicity of the principles will enable the student, by a little attentive study, to master the most complicated drawings. 1 am compelled to draw the attention of the public to a particular feature in this work. It demonstrates that in one case only have perspective representations been correct. The advancement of such an assertion may appear to deserve ridicule ; but whatever may be thought of my temerity, a dispassionate examination, I humbly trust, will establish the fact and give to the world this long-sought-for desideratum of art. The comprehension of vanishing points, which govern all perspective diagonal lines, has always been an insurmountable difficulty. I have introduced a method of drawing objects without the use of them, which, I conceive, with a little practice and thought, will dispel any misconception, assign them their proper place, and henceforward produce a true perspective. I have found, from experience, that when persons desire to acquire an art or science, being ignorant of more than the name of it, they are incapable of judging what is required to INTRODUCTION. IX attain it, and of course cannot select the essential and reject the superabundant matter. Only the experienced master can save the student useless labour, by bringing to one focus the scattered materials, and forming them into a progressively instructive treatise. As generally only those persons who are destined for scientific pursuits are taught geometry, a very large portion of the community, ignorant either of its importance or the facility of acquiring it, imagine it difficult and useless ; hence the study of Perspective deters many, when they perceive it must be acquired on geometrical principles. This limited, but popular view of geometry, must not prevent the perspective student from assiduously going through all the rules in this work ; as I know, from experience, the art, without this auxiliary, is insurmountable. The object of the draughtsman is to delineate forms in two ways ; first, simply by their dimensions, or geometrically ; and secondly, by their appearances, or change of those dimensions in appearance, when viewed by any person from some chosen position, and hence called perspective, from perspecio , to see plainly; and is that part of optics which applies to repre- sentation. Artists having to draw the appearance of forms, connoisseurs, to judge of the propriety of their productions, ought to have the knowledge of the principles of perspective, to make their judgement of any value. This knowledge can only be obtained by this art. The principles of perspective introduce us to the source of general knowledge, and are the bases of our ideas. The mathe- matician has no form out of nature, by which to compute either quantity, orbit, or velocity. Thus the botanist has form to X INTRODUCTION. distinguish the various species of vegetable production ; the mineralogist has the forms of fossils, on which to found the numerous classes ; and the same is invariably the case with every science. It is true there is quality, colour, &c. to add, but form is the primitive property and the basis of all others. It appears to me that there is a better general capacity tor art than is conceived ; but the facilities of promoting it being scattered and mixed with irrelevant matter, the knowledge has to be gleaned so slowly, that the more immediate necessities of the greater part of society compel them to abandon the study. However ardent the inclination, it is a difficult thing tor a youth to ascertain the means which will most readily advance him in his favourite study, especially if his circle of friends be ignorant of the knowledge he desires to gain. With all the obstacles thrown in his way, without advice, he must trust to perseverance only, ; but even with the greatest share of this main requisite of genius, unless he be aided by simple principles, he must undergo much useless labour before he can originate them in his own mind. Those who have gained this experience, only perform a public duty in disseminating the result of their studies. There is no labour when the genius can find help to his efforts, and has not to lose time in search of progressive information ; then the requisite practice to constitute an artist is all pleasure. The remarks I have made on the nature of perspective have not been advanced from any pretensions to metaphysical disquisition, but simply under the idea of removing impressions which people raise to their own prejudice ; to liberate the art of which 1 treat from a mystery that prevents its more general dissemina- tion, and to induce people to make efforts, from which they are deterred by prevailing misconception. I am not anxious INTRODUCTION. XI to attribute more value to the arts than they deserve, but I am certainly desirous that they should not lose their just im- portance. To this I am anxious to draw the attention of the public ; for I feel persuaded, if they see the utility of the arts and the tendency they have to expand our ideas, when taught on principle, they will justly appreciate the productions of genius, promote the efforts of perseverance, and advance their own enjoyment, by participating in the pleasures which are only felt by the votaries of taste. I have been obliged to use repetitions, both of terms and illustrations in the course of the work; but 1 question if many would comprehend the art if strict literary rules were to be attended to ; as, even with personal superintendance and the assistance of models, I have found it difficult to make persons comprehend the effect of objects on their own eyesight, most of them confounding the geometrical form with the perspective, and even doubting the appearances in drawings, though produced by demonstrative rules, which equally govern their own eyesight, till I have been able to induce them to divest themselves of prejudices, and yield to the course required by this art. I have not encumbered the work with useless problems, theorems, &c., and have carefully avoided introducing the display of abstruse scientific terms, which take pupils a consider- able study to retain, and encumber the mind so as to retard rather than advance the acquirement of the art. I am much surprised at authors on this art stating that the theory and real appearance of objects are in some instances not in accordance ; from such statement we can only infer that the theory is incorrect. We read, that the top and bottom right lines of walls assume the appearance of curves, and considerable \11 INTRODUCTION. mathematical reasoning is adopted to show that the theory establishes the fact, but that it is deviated from in practice. In perspective projections of ranges of columns, and long walls, it is advanced, that however correct in theory, artists never attempt to delineate them as seen from a particular point of view, since that would produce a drawing directly contrary to the evidence of the senses. I think it will he found that the principles of perspective establish a theory which coincides with the true evidence of the senses. 1 say true evidence ; because, from experience on linear productions, I know how often our own impressions are misunder- stood. This art will establish a demonstrable test for the truth of representations and optical effects. The existing errors of this art have arisen from an oversight of the professors, in mixing real with apparent dimensions, mistaking the sectional direction of the originating plane of the picture, and misplacing the horizontal line, which assigns wrong places to the vanishing points in most cases. In my endeavours to promote science, 1 trust I shall meet with indulgence for any faults ; as, with the needful application to my profession, I have no leisure to cultivate a literary style. No. 19, Strand, near Trafalgar Square. February 15, 183G. THE ART OF PERSPECTIVE. Perspective is the art of representing by lines any form, or number of forms, as they would appear to the fixed eye from any chosen position. There can be no perspective but in the eye of a spectator, and the art represents the appearances of objects seen from certain points of view. It is divided into two classes, recti- linear and curvilineal : the first refers to straight lines, and the latter to circular lines. Thus perspective is the treatment of lines according to the natural appearances of objects, which are known by their edges or contours. A natural appearance is the uniform impression on all minds from identical positions, 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 of intervening atmosphere between the objects and the eye, and is more properly to be referred to the art of light and shade. B 2 THE ART OF PERSPECTIVE. As the attainment of this art depends on the right under- standing of the nature of lines, before any rules are advanced for their application to the representation of forms, it will be necessary to introduce an explanation of the undeviating laws arising from their connexion, which are familiarly given in geometry, the science of quantity, extension, or magnitude, abstractedly considered. This preliminary study will make the necessary terms for explaining perspective intelligible. DEFINITIONS IN GEOMETRY. Definitions are the fixed names for the variety of forms, f he first three are 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. The first three definitions are — a point, a line, a superficies. 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.) THE ART OF PERSPECTIVE. 3 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, pentagons, sexagons, septagons, octagons, & c. A triangle, with two sides equal and the third unequal, is an isosceles. A sealine 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 with geometry must acquire practically this indispensable intro- duction to perspective. THE CIRCLE. {See Jig. 6, plate 1.) The centre of a circle is a point. B 2 4 THE ART OF PERSPECTIVE. The radius o, a, is a right line from the centre to the circum- ference, 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, c,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 cir- cumference. The established division of a circle is into 360 degrees or divi- sions; half a circle, ora 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 divisions of 30 degrees each, to avoid complication. The pupil may readily supply the inter- medial radii in his own mind. Two radii of equal length, a o, o c, lying in the same direction, 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 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. THE ART OF PERSPECTIVE. 5 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 angularity 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 f o, ao, 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 A Square ... 4 A Pentagon... 5 Sh c n 2 1 Hi JZ > u o ( O 1, plate 4). F 34 THE ART OF PERSPECTIVE. When the eye is not opposite to the centre in a perpendicular direction, the leading line, AB, forms the base of an irregular triangle, A, eye, B (fig. 2, plate 4), and a bisection of the angle does not equally divide the line, AB ; but the perspective line, BC, substituted for it, when seen from the vertex, forms the base of an isosceles, and the line which bisects the angle bisects this line at the base. Thus, then, perspective lines are produced from the same principles as the geometrical lines; and lines are in geometrical and perspective proportion to originating lines, on sections of visual rays making regular figures, and are treated singly, in double, or triple connexion as explainedby plate 5. The limited size of plates compels us in making diagrams to place the point of view so near the objects, that they must appear distorted ; this is rather a benefit to learners, as it makes the change more violent and likely to create enquiry. If the point of view is set much further off, BC (Jig. 2, B) becomes so near of a length with the base AB, that the deviation from the square is scarcely perceptible. .!+ , 1 0 Q . • • H i . * | ■* j J Of ground Plans. A ground plan represents a conceived horizontal plane, on which the points from which perpendiculars arise are set out geometrically from a scale. Example : A square box, standing on a table, is a cube, the square base and the surface of the table are on the same plane or level. By marking the four points on the table, taking away the cube and uniting the points by lines, the table, so marked, holds the ground plan of the cube, and the four points are the places from which the four perpen- dicular edges arise. The square, ABCD (fig. 1, B, plate 5), is the ground plan of a THE ART OF PERSPECTIVE. 35 cube ; e, the point on the ground plan, over which the eye is fixed : from that point of view we see the perpendiculars AD, BC, EH, FG, (Jig. 2, B), which, united, shew the appear- ance of the inside of the cube. These perpendiculars are drawn in the diagram from the points A, B, F, E, or perspective of the ground plan, which fix the proper places to set them on. There must be as many points on the ground plan as there are perpendicular edges on the structures to be drawn ; although some may not be in contact with the ground plane, but on higher parallel planes. That the visual breadths may be taken from the plan to the perspective elevation, they must all be brought down to the ground plane. A ground plan is the site of any building or object in nature, and when connected with the vision, the form is said to be parallel when the sides are parallel with, and angular when a corner approaches the line of contact. TO PUT A CUBE IN PERSPECTIVE, With a corner towards us, and the point of view opposite to the centre of its altitude. PRODUCED BY VANISHING POINTS. Let 1 , 2, 3, 4, plan 1 , plate 6, represent the size of the cube ; A the distance or point of station from which it is viewed, and the lines to each corner of the base ; the visual rays from that point. Draw the line of contact, BC, through the nearest point, 1, cutting the two outer rays of equal length. Perpendicularly to the line of contact, BC, from the points 2, 3, 1, 4, on BC, bring down four parallel lines of an indefinite F 2 36 THE ART OF PERSPECTIVE. length, which are the widths the perpendicular edges appear apart. Draw a base line, D, through them horizontally, and parallel to it the horizontal line, F. Now on the ground plan draw AB, parallel to the side of the cube 1, 2, and also AC parallel to side 1, 4; the intersection at B, on the line of contact, is the vanishing point for side 1, 2, and C the vanishing point for the side 1, 4. Bring these two points, B and C, down to the horizontal line by perpendiculars parallel to the four widths. From 1, on the base line, set on the perpendicular line the height of the cube ; draw lines from the ends of it towards VB and VC, and the intersections onlines 2 and 4 are the perspec- tive lengths for edges 2 and 4, which being united by lines repre- sent the two sides that can be seen. If we consider it transparent, and wish to exhibit the six sides, we have only to draw from each end of line 2 to VC, and from each end of line 4 to VB, when the intersections give the line 3 ; the united lines shew the whole cube. As this diagram introduces the current practical use of vanish- ing points, and we shall have to employ them in some cases, l shall endeavour to render them comprehensible. The point of view being always perpendicularly over the point of station, the vanishing points on the line of contact in ground plan are produced by drawing lines from the point of station parallel with the lines of figures in ground plan ; and where these parallels intersect the line of contact (which is the plane of the picture) are the points required. This result accords with the nature of optics. For if we stand on A. No. 1 ,Jig. 5, plate 4, looking forward to THE ART OF PERSPECTIVE. 37 G, and have buildings right and left of us, CB and DE, parallel to this line of vision, the tops of them seem to us to decline and the bottoms to incline to the point G, level with the eye over A. If we are midway between E and B, they appear to decline and incline mutually (Jig. 5, No. 2) ; but if we move horizontally either way, on the line AI, for example, to a No. 3, the point of sight moves to G, and the buildings on that side will appear to incline and decline more acutely, and on the opposite side less, but still tending towards the point of sight. The point of view being over the point of station, and the point of sight being level with it, when we consider them to be dropt on the plane of the base of the buildings, it is faithfully represented in the ground plan, and carried to the elevation on the horizontal line over A. The space within the buildings is like the inside of a cube or rectangular parallelogram. But when we view buildings from a point A, which on hold- ing the diagram (No. 1, Jig. 5, plate 4), makes IH a horizontal line, the direct line of vision will be AE ; and although we have changed our central line of sight, but retain our position, the lines of the buildings, ED, will still seem to our eyesight to incline and decline to G, and the visual ray from A to G (or direct vision in the former position) intersecting AG in H, on the line of contact, is called a vanishing point, and properly termed so ; for all dimensions are lost to view and vanish in a point which truly cannot be seen. By this last position we treat buildings as we do the external appearance of a cube. 38 THE ART OF PERSPECTIVE. THE CUBE IN PERSPECTIVE, By the lateral plan, without vanishing points. Draw the ground plan (2, plate 6), the visual rays, and the point of station, A, as before, with the exception of the vanish- ing parallel lines, AB, AC, {fig. 1). Draw lines through 2, 4, 3, parallel to BC, and through A : make BD the height of the cube and also each of the parallels, 2, 4, 3 ; draw from a to the ends of 1, 2 , 4, 3, and the bases of these rays on BD are lengths for the four perspective perpendiculars. The lines a 1 , a 2, a 4, a 3, are the depths in perspective at B ; a being the point of view in lateral plan, midway between B and D, is the same as the horizontal line in Jig. 1, plate 6. Draw a base line through the indefinite perpendicular lines ; draw parallel lines to it at the distances found on B. Set BD on 1, and the other lengths (found on B) on 2, 4, 3, and uniting the ends, a cube is produced in perspective, similar to the one with vanishing points. REMARKS. By a critical examination of the lateral visual rays {plan 2), it will be seen that the altitudes and depths obtained on BDare not taken from the distances A 1, A 2, A 3, A 4, of the square, but from points on B equal to the points on AD, and three other points on the same line, which are four parallel planes from each corner. Now, at first sight, it would seem that we ought to take the altitudes from distances on B as long as from A 1, A 2, A 3, A 4, or corners of the cube in ground plan to coincide with the THE ART OF PERSPECTIVE. 39 principle illustrated in plate 5 ; but there is no error, for in the drawing- produced from this plan, the full length is set up on the base line taken from the line of contact BD (Jig. 1), and all the others must be taken from planes parallel to it (vide chapter on horizontal lines). It is necessary for every student in this art, not merely to study these examples and explanations, but while doing so to fancy forms standing on the ground plans, and their eyesight taking the directions from the point of station to all the corners ; the lines being merely emblems of their own optical act. By practising the same figure from a different point of view in all the diagrams, it will seem to me extraordinary if any one fail to learn the art thoroughly. TO PUT THE CUBE IN PERSPECTIVE, With the eye not opposite to the centre of its altitude, with vanishing points. Draw a base line through the perpendiculars brought down from the ground plan ; draw the horizontal line parallel to it, at any height above it not exceeding the height of the cube. (Fig. 3, plate 6.) Set the altitude of the cube on line 1, and drawing to the vanishing points VB, VC, on the raised horizontal line, the inter- sections on the perpendiculars 2, 3, 4, produce the three other edges for the cube. From this view the difference in the apparent form of the cube is caused by raising or lowering the eye over the point of station, which is imitated by raising or lowering the horizontal line ; the vanishing points being always on it, whether very near or far apart from the base 40 THE ART OF PERSPECTIVE. line. This is the method laid down in most works on perspec- tive ; and in others, although the methods may vary, they all pro- pose the same result. Again. — With the eye above the altitude of the cube. Having drawn the base line, draw the horizontal line further from it than the height of the cube ; set up the altitude from the base line on perpendicular 1, draw from the ends to the two vanishing points, and again from the intersections on perpen- dicular 2, which gives the intersection 3 ; uniting these points completes the drawing of a cube seen from that point above its height. Reverse this diagram, and it shows its appearance from a point as much below as the other way does above it. N.B. Let the pupil put A differently to the plan explained, and draw the visual rays to the corners; then find the vanishing points from the new station by parallels to the near sides in the plan crossing the line of contact; follow the rule of bringing down the perpendiculars and the vanishing points, and raise the appearance by different distances of the horizontal line from the base line, and the principle of this simple figure will be the principle of what are termed difficult figures — the difficulty consisting only in there being more perpendiculars. TO PUT THE CUBE IN PERSPECTIVE, JVith the eye not opposite to the centre of its altitude , without vanishing points. Having shown the established method of putting the cube in perspective with vanishing points, and without, when the eye is THE ART OF PERSPECTIVE. 41 opposite to the centre of the nearest perpendicular, Jig. 1 and 2, plate 6, in which both drawings coincide. I now draw the attention of my readers to the difference in the two figures, 3 and 4, which represent the same cube from a point near to the top of the nearest perpendicular on the same point of station as in the former Jigs. 1 and 2. Fig. 3 is produced with vanishing points, and Jig. 4 without them, as follows. Let 1, 2, 3, 4, plan 3, be the cube, A the point of station, and A 1, 2, 4, 3, the visual rays to produce the planes of the perpen- diculars as before. Draw B 3, parallel to A 3, at the distance equal to the height of the cube, and parallel to BE, lines 2, 4, 3, the planes of the perpendiculars. Set a on the line A a, the height of the horizontal line in Jig. 3. Draw a 1, a B ; and from a to each end of the lines 2, 4, 3, which are the parallels to BE. Draw the base-line through the perpendiculars brought down from the line of contact, and parallel to the base, the lines 2, 4, 3, at the distances D 2, D 4, D 3 ; set on the base-line and the perpendicular 1, the length, D 1 ; and from the other points of intersection, the lengths between 2, 4, 3, and its fellow outer ray on D 1 ; unite the four lengths thus fixed on the perpen- dicular planes, and the cube is in accurate perspective without vanishing points. Jig. 4. It is evident the current methods or mine must be faulty, or the diagrams 3 and 4 would be identical as in Jigs. 1 and 2. By the usual method, when the perpendicular planes are brought down, and the base-line drawn, the geometrical length of the nearest perpendicular edge of the cube is set up to determine the others, whether the eye be opposite to the centre or not, having no other dimension to start with; but as we have shown the G 42 THE ART OF PERSPECTIVE. distinction of a geometrical from a perspective length, and have changed the position of the point of view, we must have a perspective length to start from, to influence the other lengths, and to coincide with apparent breadths. The perpendiculars, or apparent widths, having been brought down by the diminish- ing principle of perspective, the altitudes to be set on them cannot retain their geometrical property, but must have a corresponding diminution according to the influence of altered position. By setting up the geometrical length on the first line, some of the lines become too acute, which arises from the error of mixing geometrical with perspective dimensions. Now, by the critical principles of perspective, having found the widths in the ground plan, and through the same medium the proportioned heights and depths in section, the whole must coincide with the principles of optics, when in contact with length, breadth, and depth. When the eye is opposite to the centre of the altitude {Jig. 1, plate 6), the horizontal line, F, is drawn half the height of the cube from the base line, D ; but when the eye is not so placed as in Jig. 3, the geometrical height of the eye, BE {plan 3, in the same plate ) becomes D e, which is only necessary to be sought, when it is required for vanishing points. Misplacing the horizontal line, and starting with geometric lengths on the nearest perpendicular plane, have been the two leading causes of errors in perspective. The system of finding the planes and altitudes of perpen- diculars to produce the diagonal lines of figures, which I have termed the lateral or sectional plan, is an opposite operation to the use of vanishing points, which, with the assistance of only THE ART OF PERSPECTIVE. 43 one leading perpendicular, produces the diagonals and their in- tersections, the relative perpendiculars ; but, as their current usage is fraught with many errors, I shall endeavour to point out the true operation of vanishing points. Looking to plan 1, the student will observe that AC is parallel to the side of the square marked 1, 4, and AB parallel to the side marked 1, 2, which produce the two vanishing points B and C on the line of contact; from these two points, lines are brought down perpendicularly, as well as from the four points obtained from the four corners, all uniting with the point of station A. Wherever the horizontal line may be fixed, the vanishing points must always be on it, as in fig. 1, and it is necessary to have it on the same perpendicular plane, whether the horizontal line be near the base, through the centre, or above the altitude of the object, as in Jigs. 1, 3, and 5. Particularly observe the prolonga- tion or acuteness of the lower portion of Jigs. 3 and 5, which arises from assigning the same height (in these cases), for the perpendicular 1 on the base line, although the points of view are higher than that in Jig. 1 ; the horizontal line is raised to the height of the eye, compared with the first perpendicular. Now, it appears, that the method of fixing the horizontal line, is only correct for representing an object, the centre of which is on the horizontal line; on elevating the point of view, the raising of the horizontal line in the drawing must he drawn in comparative proportion to the reduced perpendicular ; for as the perpendicu- lars are reduced to perspective lengths by the elevation of the eye, the place of the horizontal line must be much nearer the base-line, or on the same ratio as the reduction of the perpen- dicular. Now, to produce the vanishing points for Jig. 4, plate 6, G 2 44 THE ART OF PERSPECTIVE. draw a line a E, from the lateral point of view a [plan 3), parallel with A 3, and its opposite parallel 1, 2, 4, 3 ; the intersec- tion e, produces the length D e, which is the perspective ele- vation of the horizontal line above the base, instead of the height employed in diagram 3, which is the current method ; but as it has been shown, that the angle of vision foreshortens the perpen- dicular by elevating the point of view ; on finding the proper reduction of the horizontal line as described above; fixing the vanishing points on it (brought down from the line of contact as by plan 1), erecting the perspective length for perpendicular 1, and ruling from its extremes to each vanishing point, the inter- sections of the indefinite perpendiculars 2, 3, 4, are points, which, when united, form the cube in perspective with vanish- ing points, identical with Jig. 4, produced by lateral design with- out them. The practical draughtsman can employ which of them he pleases, according to the simplicity or complicated nature of his design. In many works on the Art of Perspective, the attention of the student is directed to a pane of glass, through which they see certain objects; they are taught to conceive, that a picture of the same size as the pane of glass, should contain an exact transfer of every line transmitted to the retina through that medium or transverse space, between the view and their eye. This illus- tration is given as a general rule, and intended to explain what is termed the plane of the picture, which in all cases, it is said, should, like the pane of glass, be perpendicular and parallel to the perpendiculars of the objects seen through it. Prirna facia, this appears an evident and just conclusion ; but let the THE ART OF PERSPECTIVE. 45 glazed space occupy a diagonal or inclined position, when com- pared with the perpendiculars of the objects, then it would be a medium, and bound the projected figure or figures which impress the eye-sight : it is not, then, the position of this pane of glass that rectifies the delineation. It is a good mode to communi- cate to the student, that a picture is only the representation of some space between the eye and the objects, and that the position of this space is the plane of the picture. The position of the cutting plane is regulated solely by the objects which originate the drawing, and the rules I have illustrated by plate 4 for the representation of lines, geometrically and perspectively, define the true section or plane of the picture ; for, as an experiment, let any one view a number of objects in a line, placing themselves at a point like that marked eye in fig 1 , plate 4, and they will embrace the whole extent ; it is evident, therefore, the cutting plane is in the line, or parallel with the line of objects AB. Let them again view the same objects from a point like that shown in fig. 2, plate 4, the nearest object will then be at B, and although the objects still occupy their original line, the apparent breadth will be only BC. This, the public understand better by the term fore- shortening, which occurs to the sight equally in perpendicular, horizontal, or angular lines. The best general rules I have to offer for regulating the ideas of draughtsmen, are the following : — When engaged with a single line, find the triangle it makes with the eye, and the line which forms the base of an isosceles is the plane of representation, or any reduced proportion parallel to it. When the eye is engaged with more than one line, (a right-lined sur- face will contain at least three, and any solid at least six ) find the figure contained within the rays of vision, and whether they form at the vertex, or eye, a pyramidal or conic figure, the sec- 46 THE ART OF PERSPECTIVE. tion that rectifies them and produces a base perpendicular to the axis or centre ray, is the true plane of the picture. This recon- ciles the theory and practice of perspective to the judgment. TO PUT AN OCTAGON COLUMN IN PERSPECTIVE WITH VANISHING POINTS. (See Plate 7). Make a perfect octagon for the ground plan of the base, and having fixed the point of station A, draw the visual rays to each corner. Draw the line of contact B C, and AB, AC parallel to the two visible sides (1 8, 2 3), intersecting at B and C, for the vanishing points in ground plan. Brin is when the centre of an edge is opposite to the eye, and the vertices of two sides receding from ns horizontally. Fig. 7- i s when the faces and edges are diagonal to the sight. Let ABC represent an ecpiilateral triangle, forming one of the four surfaces of a pyramid. Ilisect any two angles, and the intersection, F, will be the point or centre of the base over which is the vertex. Erect a perpendicular and make DE equal to AD, intersecting the perpendicular at E ; join AE, and AED will give the form of the cube from the point of view, S. {Fig. 1 .) EF is the altitude of the pyramid, and this is the method of finding it geometrically. Fig. 2. The second figure is found by drawing the visual rays to the point of station S, bringing down the perpendiculars from the line of contact, drawing a base line, and drawing parallels to it at the distances on CG, which produce the three perspective points, a, b, c. For the altitude, draw D c equal to FE, join cS, and the length between the rays at the points of contact, CH, is the perspective altitude sought; which, being placed on the middle line, a, and uniting the upper end with the three intersec- tions. a, b, c, completes the perspective. Fig. 3. As the eye is supposed to be opposite to the centre of a side, and the rays must be equally distant from the three corners, we have only to find the centre, as pointed out in fig. 1. and join it with the three corners to form this figure. Fig. 4. This figure, produced from the plan { fig- 2), is more THE ART OF PERSPECTIVE. 51 difficult than the former ones ; the edge being downward, the appearances of the sides are not gained on a base, and nothing but the exercise of thought can decipher this diagram. The vertex of the shaded side is considered to incline towards us, and therefore the appearance of a triangle from the point S, laterally , should be determined. This is done by joining BS AS, and BD is the altitude sought ; D c is the whole altitude, and the breadth of the lower edge, which completes the appearance of this side. Fig. 5. As the eye is conceived to be level with the base, a line describes it ; and as the point comes towards us, one edge appears a perpendicular, which gives to two sides the appearance of two right-angled triangles : the whole outline forms the fourth side. Draw BS, CS {Jig. 3), which will produce DE, the breadth. Draw FS, AS, which will give the height; so that we have only to find the perspective breadth for one edge and the altitude to form Jig. 5 on the top row of plate 8. Fig. 6. The ground plan for Jig. 5 serves for this, which is sup- posed to have an edge towards us, and being on the line of contact is represented geometrically, at its full length perpendicularly ; and another edge, crossing it horizontally from this point of view, is found on DE. In this position the shaded side is one surface ; the whole that is not shaded is another, and the hori- zontal line divides the other two sides of the pyramid. From an oversight, the three plans in plate 8 are marked Jigs. 1, 2, 3. By the references to the letters, the student will be able to distinguish allusions to them, from those to the top row of figures marked 1 , 2, 3, 4, 5, 6, 7- 52 THE ART OF PERSPECTIVE. TO FIX THE RELATIVE HEIGHT OF FIGURES IN DRAWINGS. (See Plate 9.) Let the five points in the ground plan [plate 9), marked with a small circle, be the places on which the figures stand; the one on the nearest plane four feet high, one on the second plane five feet, and another five feet six inches, one on the third plane six feet, and the one on the sixth plane six feet. Let the second plane be three feet from the first, the third five feet from the second, and the fourth three feet from the third, and let the perpendicular or transverse planes marked 1, 2, 3, 4, 5, be three feet apart, and viewed from a point of station twelve feet from the nearest figure, and five feet above the point of station, A ; as a A is equal to five feet. The diagram is set out on a scale of one-fourth of an inch to a foot. According to the process repeatedly explained, between the rays BC we have the perspective depths of the four planes, on which the figures are ranged in the ground plan ; and the heights of these figures, according to our dimensions, are set up on their proper perpendiculars, from the five breadths on BD, between each pair of rays, to the respective heights set up on their planes in ground plan. In making designs, the various figures must have their proper places, and when we have disposed them naturally and agreeably to the subject, this method of fixing the places gives each figure its proper proportion. Any number of perpendicular heights, springing from diversi- 1 THE ART OF PERSPECTIVE. 53 fied points, either in buildings, models, &c. can be arranged by the same plan ; and all the diagonal lines, real or apparent, will fall into their right places on joining the extreme ends. CURVILINEAL PERSPECTIVE. The perspective of circles and curved lines has not been reduced to so many methods, nor explained so fully as rectilinear per- spective. The circular line, ever varying from the straight line, seems to evade the grasp of every rule. Between two adjacent points, on a circumference, we cannot conceive the least right- lined distance. A point on a circumference is similar to an angular point, for on either side of both points the lines deviate from the right line from the very moment motion generates the angular or curved line. Hence the forms which are composed of curved lines have always been most difficult to represent with mathematical precision. It is on this point some mathematicians vaunt over the artist, holding it impossible to arrive at just conclusions, without a profound knowledge of mathematics. With the highest admiration for the £t divine science,” and the computations which produce approximations and results, which can only be understood by the mathematician, I must say they cannot be introduced into the visible operations of the artist. The difference between the artist and the mathematician on this head is, that the calculations, and not the constructions of solids and superficies, are esteemed by the mathematician, while accurate construction (or the emblems of calculation) is the 54 THE ART OF PERSPECTIVE. immediate business of the artist, to whom the calculations are only necessary as a scholar. It is the curvilinear branch of the art which particularly calls for geometrical knowledge and reflection, for without their aid, artists must frequently feel their deficiency, when curved forms mingle with right-lined figures. DEFINITIONS. A geometrical circle has all its radii equal. A perspective circle has its radii unequal. A circle appears geometrical when the eye is opposite or perpendicular to the centre, and every visual ray to the circum- ference of equal length. The circle is in perspective when the eye is not perpendicular to the centre, and consequently the visual rays being distributed to the circumference with unequal lengths, the appearance of the circle becomes elliptical or oval. The section of a spherical figure forms a straight line when the eye is level with its plane ; as the eye gradually describes half a hemisphere, the perpendicular diameter extends, the oval increases in apparent depth, till it becomes as long as the hori- zontal diameter ; and when inspected above the centre, we see a circle. (See Jigs. 3, plate 12.) In conception, our visual rays to all parts of the circumference form a perfect cone, the vertical point of which is in the eye. a THE ART OF PERSPECTIVE. 55 TO PUT A CIRCLE IN PERSPECTIVE. (Vide Plate 10.) Describe the circle to be put in perspective ; divide the cir- cumference into a number of equal parts — the diagram is divided into sixteen division; — mark them from 1 to 16 ; unite by horizontal parallel lines 2 and 16, 3 and 15, 4 and 14, 5 and 13, 6 and 12, 7 and 11, 8 and 10. Fix the point of station, A, and draw the visual rays from that point to the sixteen points on the circle. Now, by the lateral plan, set a at the chosen or required angle from the plane of the circle or given altitude over A. In this diagram the angle is 30 degrees from the centre of the circle. Draw the lateral visual rays from a to the nine points on the centre perpendicular line marked 1, 9 — those nine points being the planes of the sixteen points of the circumference brought on one line. Cut a B equal to a 1, by the line 1 B ; from this line transfer the dotted intersections with great care, to the centre perpendicular, 1, 9; draw horizontal lines through these points thus obtained, and marked 1 to 9, with a star, which are the perspective planes of the perspective circle, which becomes an ellipsis or oval, where they intersect the rays from the station A. Join from point to point elliptically, and the circle is in correct perspective from an angle of 30 degrees. By the peculiar properties of the circle, and its contra-dis- tinction from right lines, it will be seen that we cannot obtain the apparent breadth of the ellipsis on one line of contact in ground plan as we do in prismatic figures ; for, as in those cases, if we draw the line of contact through the point 1, or shortest 56 THE ART OF PERSPECTIVE. ray from A, in this case it has no dimensions, any more than the point of a triangle ; it therefore remains a point only of the perpendicular diameter sought : each pair of points will have their governing line of contact, which is their plane, on which we obtain the relative breadths by the intersections of the rays from A in ground plan. If we were to employ but one line of contact drawn through the pbint 1, the greatest expanse of vision would be only DC, while we have it as long as from F to E, which is found by drawing a line through B, intersecting at G and H, which is the greatest width of the ellipsis, and widest expansion of vision ; shown by the lines to A. The rays from the extremes of the horizontal diameter (5 13), of the originating circle, to the point A in ground plan, intersect a shorter length (for the perspective) than its parallel shorter line 4 14, which produces GH ; the greatest breadth of the per- spective circle or ellipsis. The diameter of a circle in perspective is often drawn as the axis of an ellipsis. That GH is the greatest breadth of the perspective circle, and not DC, and that 1 B is the corresponding apparent depth, from the point of view or angle a, can be made evident to the senses by models, a number of which I have constructed to demonstrate the truth of my theory, on circular as well as right-lined forms, to those persons who may wish to consult me, for more expeditiously putting this conclusive theory to practical use. This diagram represents the circle lying in a horizontal plane, and the point of view vertically over the point of station ; and in these united positions all circular objects may be viewed and drawn exactly by this method. But if the circular, semi-circular, or curved form should stand perpendicular, and the point of view be horizontal or sideways to it, the appearance would be the THE ART OF PERSPECTIVE. 57 same, the position only being altered ; for the form, the distance, and the place of the eye being similar, the image on the retina will be identical. This will be evident, by holding the diagram so that the line A 9 shall lie horizontally, and the ellipsis or half of it be perpendicular, and represent a circular arch from the point a level with A. On viewing the diagram as inserted in the work, by uniting the 15th, 3rd, 7th, and 11th perspective points, and drawing diagonals from 7 to 15, and from 3 to 11 on the oval, the perspective of the inscribed square, and its cen- tre, as well as the centre of the ellipsis on the perspective diameter, is clearly exhibited. By setting out the ground plan of the circle with a great many points, and being extremely careful in the construction, the perspective circle may be brought out with a beautiful approximation, which will bear geometrical demonstration, and coincide with the evidence of the senses. Within the points of the oval, correctly constructed, every regular and irregular superficial figure can be produced in the same way as we have described for the inscribed square. In this, as in the other diagrams, the rays drawn to a are obliged to be drawn horizontally ; but the student must conceive them to be the same as those drawn to A, and to be vertical, or those drawn to a to be lowered down the line a A till they fall on A; when the rays are on the same plane as the surface of the circle to which they fall perpendicularly, and describe the breadths of vision. Diagrams cannot exhibit the meaning of the artist without this licence to the imagination. To make a circle in perspective on a decreased proportion, draw from the dots of the ellipsis to the point of station A, — at any chosen reduction, draw a line for the first line in contact, parallel to CD ; then through the rays to the point of view a, I 58 THE ART OF PERSPECTIVE. draw a line parallel to the line 1 B, observing that the end 1 must be on the plane of the reduced line of contact ; draw horizontals through the rays to A at the nine distances found by the reduced intersections of rays to a ; unite them as in the diagram, and the perspective of the circle will be in reduced proportion. TO PUT THE CIRCLE IN PERSPECTIVE FROM ANY ANGLE. (See Plate 11.) Let AC [plate 11), be the diameter of the circle, ABCD. Set up a perpendicular tangent at e. From the centre of the line AC draw a line to the point on the tangent for ten degrees, and also from the two extremes of AC. At C, the breadth between the rays, is the apparent length of the perpendicular diameter from the angle of ten degrees on the tangent over the distance C e. From the station E (DE being equal to C e) draw AE, CE, and the intersections on the line of contact D is the breadth of the horizontal diameter. Hence THE AXIOMS. The perspective of circles is as their perpendicular diameters are to their horizontal diameters and their consequent parallels. Example : — AC is to BD (Jig. 2), as the circle ABCD appears from ten degrees at e. In setting out the perspective of the circle from the ground plan, a singular circumstance will arrest the attention of the student ; namely, although the diameter AC, ten degrees (Jig. 2, Y n 3 * 5 aW-'- c bit) «3 THE ART OF PERSPECTIVE. 59 plate 11), is the greatest length within a circle, the points FG (Jig. 1), produce a greater length on the line of contact, which is the longest line in the perspective circle — longer than the perspective diameter, according to the greater or lesser distance given to the point of station E. Fig. 2. Shows the circle between two parallel perpendiculars, and the perspective of the circle from ten, thirty, and sixty degrees of elevation on the perpendicular over E. THE PERSPECTIVE OF DOMES, ARCHES, GROINED ARCHES, GOTHIC WINDOWS, &c. (S ee Plate 12.) For the dome or semi-sphere, let AB be the diameter of the base, and E the point of view below its plane. Find the per- spective breadths of the diameter and centre D, with the rays to E. For the height of the dome, draw from E till it touches the circle as a tangent near C. The breadth at B, between the three rays ABD, is the depth for AB, and FB the height for the arc BC, in the perspective elevation. Remark . — The more the point of view E is below the level of the base AB, the tangent EC touches the circle nearer to B on the arc, and the height of it becomes less on BF, and the diameter AB widens. For the Gothic window (Jig. 2). From the point of view E, which horizontally forms the angle EBA, draw EB, EC, EA, ED. Now, making the line AB the horizontal line, A c b are the breadths, and c d the altitude for the perspective. i 2 60 THE ART OF PERSPECTIVE. All elliptical forms yield to these rules for finding the width and depth of diameters, the altitude of segments, and the appa- rent height of arcs. Obverted and inverted, or the external and internal appearances of them, depend on finding the diameters in depth and breadth, the extremes of arcs agreeing with the variations produced by the change in the point of view. NAVAL PERSPECTIVE. (See Plate 13.) The principles of right and curved lines are the same in this department of the art, and the artist has only to acquire the mechanical construction of vessels to give propriety to the drawing. It is surprising that nautical drawing has been more rarely professed than other branches of the art. This sea-girt isle, with its grand naval achievements, has had few first-rate ornaments in the art. The ship offers many inducements to the genius. The towering hull, the firm-braced rigging, and the swelling sails, floating over the sublime and dreadful ocean, can awaken the most sympathetic, pleasing, and patriotic senti- ments ; and more especially to a nation which owes its pre-emi- nence to this bulwark of liberty and freedom. Our naval heroes have seldom devoted their leisure to cultivate art, and the artist, generally, has seen so little of the wondrous element, and knows so little of naval tactics, that the want of art in the one, and practical knowledge in the other, has confined this branch to a narrow compass. The principles of perspective would greatly advance this art ; it would enable the artist to represent a hull THE ART OF PERSPECTIVE. 61 (if in possession of its admeasurement) in any position. The masts must incline with the heeling- of the vessel ; and the yards, if squared or braced, conform to our g-eneral rules for right lines, and the leech of every sail to those for curved lines. The undulations of the waters are regulated by the same notions. In plate 13, the two horizontally prolonged figures (1, 2,) supply the leading form for the bulwark of all vessels ; the ends being turned into stem or stern at pleasure, as in Jigs. A and B. The cutters are turned into brigs or ships by putting channels, ports, and other distinguishing constructions to this primary figure. The masts, yards, bowsprit, boom, gafts, and all spars, must be regulated by the rules for perpendicular, horizontal, and angular lengths. The Jig. C shows the masts and yards in a broadside view, the yards appearing very short in consequence ; for let Jig. d be the height of the mast and length of the yards, and D the point of view, the yard d will appear in broadside at that height as drawn in E. If we have the length and breadth of the deck, the step or place of the masts and spars, or we assume them on the general dimensions, if we require to foreshorten the vessel, make a deck plan, and from any chosen point of station, draw to each end of the taffrel or stern A, and a tangent to the bows C, the section of the rays gives the side BD, and stern AB, in perspective. From the place of each mast erect perpendiculars, and find the altitudes of the masts and lengths of the yards by lateral plan, and by this means every thing can be brought to 62 THE ART OF PERSPECTIVE. demonstration. The sails, swelling from the yards, & c. are easily imitated if we have fixed the extremes of the curves properly. As the shrouds a, a, a , spread to channels, which are placed aft of each mast, as shown in broadside, their spread in bow or quarter-view {Jigs. A and B), must be gained from a deck-plan, the step of each mast o, and the fore dead-eye a, on its weather and lee channel forming triangular points. The steeving of bowsprits F, and the peak of gafts G, are found by imagining a third point on a horizontal line through the lower end, forming a triangle ; the gaft being the hypothe- nuse or longest side of an upright triangle, as shown in G, and bowsprit of the broadside in F, plate 13. The particular terms for the parts of vessels, the proper sails to carry in stress of weather, and the appropriate representation of the agitation of the water, depend on nautical knowledge. The agitation of water is briefly explained by the diagrams marked 1, 2, 3, at the bottom of plate 13. No. 1 shows the undulations of water uninfluenced by wind, as in ground swells, &c. No. 2 is the appearance when the wind follows the tide, which throws the head of the wave forward. No. 3. When the wind meets the tide, the head of the wave is forced backward and foams on the stream. The heads of waves are never parallel or run in regular rows, and however agitated or various these watery hills may be, a general plane, or plane from which they rise, should manifest itself in the drawing. As practical nautical knowledge cannot be acquired by all loIlL THE ART OF PERSPECTIVE. 63 artists, it cannot be expected that the principles of perspec- tive should, as by magic, teach it ; but these explanations may enable many artists to avoid sullying their otherwise good drawings by errors, which expose their want of knowledge in shipping. PERSPECTIVE OF FURNITURE, MODELS, &c. (See Plate 14.) The perspective of furniture has always been considered difficult; but as the principles of the art apply to form generally, no dif- ficulty can occur if they are properly applied, by bringing on the ground plan every requisite point, and using a little judgment in fixing points for any circular, so as to combine them with straight lines. In representations of splendid apartments, the furniture standing in so many directions, and consisting of so many varieties and sizes, requires every rule to be practically under- stood by the draughtsman, for the whole to be readily recognized as a faithful drawing. Before I proceed to apply the principles by a few par- ticular cases, I shall suggest to the student the necessary pre- liminary calculations to be made in drawing a furnished apartment. The measure of the room in length, breadth, and height, must be treated as the inside of a cube, with all doors, windows, chimney-pieces, &c. by a ground plan and a lateral plan. The lateral plan, giving the precise size of the remote end of the room from the fixed point of view, prevents a prolongation, 64 THE ART OF PERSPECTIVE. which sometimes gives an idea of much greater space than the apartment contains. The heights of the various pieces of furniture should now be taken and applied to the lateral plan, each on its proper plane ; that by the depths taken off the perpendicular line of contact, one article may rise over the other, and diminish relatively as they do to the eye. By this preparation, the construction of the apartment supplies many points for the comparative height and proportion of the furniture ; and an artist who can reduce every individual thing to pure perspective, having some leading points lie can make every thing conform so strictly to rule, that if great pains were taken to detect an error, it would be too trifling to confer any credit on the critic. In drawing interiors of furnished rooms, as the most part or the whole of three sides may be required to be shown, the fourth side must be conceived to be removed, and the eye placed at a convenient distance out of the apartment, as though it looked into a box with the side taken away, whether we view the remote end at right angles or diagonally. The size of the picture being the representative of the side of the room conceived to be removed, by taking its geometrical dimensions to a lateral plan, the rays to the point of view are sure to secure the proportioned apparent depth of the ceiling : the height of the remote end and the depth of the floor according with the horizontal breadths of every part, and uniting these points, we cannot fail to produce every diagonal line with truth. Sofas. Let the figure A ( plate 14), be the sofa to be put in perspective from an angular point of view of the following dimensions. THE ART OF PERSPECTIVE. 65 The castors four feet six inches apart in width, and one foot six inches in depth. The frame, resting on the legs, five feet by two feet. From outside to outside of either scroll end, six feet, and two feet deep. The raised back six inches high. Set out in ground plan B, the dimensions from leg to leg, i, k, /, m ; the size of the frame, e,f, g, h ; and the space over the scrolls, a, d, c, b. Join these twelve points by rays to the point of station, draw the line of contact DE and find the two vanishing points. Transfer the intersections on the line of con- tact, and draw the twelve indefinite perpendiculars between the base and the horizontal lines. On the perpendicular a, draw by scale, ten inches for the height of the legs, four inches for the frame, and sixteen inches for the height of the scrolls — in all thirty inches. Draw from these points on the line a to the vanishing points DE ; the intersections on the perpendiculars d, c, b, produce the perspective of a parallelopipedon equal to the height, width, and depth of the greatest dimensions of the sofa. The lines drawn from a intersect the perpendiculars i, m, l, k , the points of the castors, and also the perpendiculars e, f, g, h, the points of the frame or seat. From the frame within the points of intersection, draw the turned legs and add the scrolls to the points on the frame. Find the centre of the raised back, that the ovola-quirks may have their proportioned extension, and the sofa appears in perspective. The squab, or stuffed seat, and the bolsters are easily made to conform to this design. The sofa is a good example by which students may be able to draw many dimen- sions of straight and curved forms in combination. They will reflect that there is a total length, breadth, and depth ; or, as it were, a case about the whole, with parts within it, occupying K 66 THE ART OF PERSPECTIVE. smaller areas or parts lying within parts, all of which must be treated distinctly, to form an accurate combination. Each of these parts must be drawn on the ground plan, that in drawing the rays to the point of station, the line of contact may produce all the perpendicular lines to be intersected by lines to the vanishing points, by which all the parts of the model may be drawn in perspective. Or, set up the height of each part in sectional or lateral plan ; lind the apparent perpendicular dimensions, unite them, and the form of the sofa is produced in perspective, without the use of vanishing points. Chairs. To draw a chair, get a clear idea of its construction by its side A, and front dimensions 13, without regard to appearance. The back two feet nine inches high ; the front legs seventeen inches high; the side rail, including the thickness of the leg and back, sixteen inches. The ground plan of the legs eighteen inches in front, and fourteen and a half inches behind ; and from back to front leg nineteen and a half inches. Set out the ground plan for the breadths and depths by the horizontal and sectional rays, as in former diagrams. Bring points 2, 3, 4, on the line 1, to the station ; set on 3 and 4 the height of the back, and on 1 and 2 the height of the legs ; draw to the point of view, and the intersections on the line of contact give the perspective heights of the two front and back legs, to place on the planes and perpendiculars in Jig. D. The fig. C is from a higher view, which the student will readily understand, after the variety of examples given. I have made the fig. D, with a single line, to familiarize the THE ART OF PERSPECTIVE. 67 simple idea of skeleton form, upon which ingenuity moulds the various fashions. Bedsteads, bookcases, tables, models, &c. subjected to these rules, are equally easy to produce in perspective ; and probably more examples would be superfluous. TO PUT A CIRCULAR STAIRCASE IN PERSPECTIVE. (See Plate 15.) First make a ground plan ( plate 15), describe a circle with a radius of the length of each stair ; divide it into as many equal parts as there are stairs in the round ; draw lines from point to point on the circumference, to represent the position of the ends, and mark them from 1 to 12, as in the plate. Join 1 11, 2 10, 3 9, 4 8, 5 7, 6 6, for the planes of the ends in lateral section. Draw the line of contact AB. Fix the point of station C, and with lines from the twelve points on the circle, intersect the line of contact, and bring down the twelve perpendiculars ; draw the base-line D, and mark under it the twelve points in their perspec- tive order, 9, 10, 8, 7, 11, 6, 6, 1, 5, 4, 2, 3, on which the near upright edges of the stairs are to be placed. On the base line D, at a convenient distance, make a lateral plan ; describe a circle equal to the one in ground plan, and on the centre of the diameter ; set up a perpendicular also on the sectional planes, 1, 2, 3, 4, 5, 6. Parallel with the base draw twelve lines, each intersecting K 2 68 THE ART OF PERSPECTIVE. point being the height of each stair, and the whole will be the altitude. From the point of sight E 1, intersect the perpendicular 6, with lines to each point on the centre upright length of each stair. W ith a parallel rule, mark these intersections on the centre perpendicular C, on the elevation plan. Then, from the point of sight E 2, draw lines to the top and bottom of the riser, or upright end of each stair, intersecting the perpendicular 1. With a parallel rule, from these points draw horizontal lines through the perpendiculars on D. For the bottom point of the visible parallel upright ends of stairs 1 and 2, intersect the perpendicular 1 in lateral plan by lines' from E 2 to 2 and 3, on the first and second planes in the section ; and do the same from the tenth and eleventh planes, for the ends 10 and 11. These being carried to the elevation plan, and having drawn all the upright lines (marked by a stronger line in the plate), within their proper points, and on their own perpendiculars, we have only to join them with angular lines to the twelve points on the perpendicular C, and the staircase is in proper per- spective. Xote . — The points of sight E 1 and E 2 are the same, but are placed on either side of the section to prevent the confusion of so many lines crossing the perpendicular 1, as it is necessary to be very particular to have the intersections in the plan for the elevation very exact, that all the angular lines may fall in their proper places. THE ART OF PERSPECTIVE. 69 It requires a little consideration to set out the section geo- metrically, the ends of the stairs having two perpendicular and two horizontal planes for the four points. Take the first stair as an example; the tread or upper surface has one point on 1, and the other on 2, in depth or horizontally, as shown in sectional plan ; and the riser or surface of the end has one point on the base-line, and another on the first plane, parallel with it ; the intersections from which points give us the four perspective points in the drawing. In a circular form like this, the nearest corners of the first six stairs are towards us ; the sixth shows itself equally on each side of the line C, and the near edge of the next six being transferred to the opposite corner by this duplex step, the planes for 7> 8, 9, 10, 11, 11, being parallel with 5, 4, 3, 2, 1, must be set on these points in the section. Every thing but this is simple and evident; and such points as these will become so, by students fancying a real staircase, or whatever form they may have to depict, to be present to their senses, when setting out the ground plan and section. It is of little use to look at diagrams as mere lines ; to understand their meaning, the reality should never be absent from our minds. In the process of making this diagram, when the upright near end of each stair is marked, and the strong stroke is not confused with the diagonal lines, the force and leading power is very evident; when the extremes of these are joined with their points on the centre upright, they appear like the wings of a fly-wheel, and the addition of the angular lines on the ends gives the finished appearance. The peculiarity of these circumstances cannot be recognized so readily on the whole diagram ; and to produce them in 70 THE ART OF PERSPECTIVE. additional plates might be an encouragement to the too common practice of shunning the necessary labour of making a copy of each diagram. THE ULTIMATE DIAGRAM. (See Plate 16.) In this figure (a cylinder with two parallel ends) the elements of all lines are brought under one view, and it forms a perspicuous summary of the foregoing examples. The two elliptical ends represent two parallel circles ; the centre perpendicular AB, jig. A, an axis, and ABCD a paral- lelogram, or prolonged square, revolved about that axis with the parallel lines to DA, CB, and the diagonals CA, BD. The circles are supposed to be divided into 360 equal parts or degrees. In the first place, in a drawing, as in diagram B, the circles contain one latidutinal and one longitudinal diameter ; the rest are angular. Every species of curvature is produced on the circular line by beginning to revolve the circular plane, which appears a line when level with the eye, and increasing the latitudinal diameter of the oval till it is equal to the longitudinal, when the radii become equal, and we have the perfect circle. The radii in this revolved circle generate horizontal right lines in every possible diverging direction. In the next place, the plane ABCD, when on the apparent latitudinal radius, as in Jig. B, forms one straight or perpendicular line only; when it is revolved some distance, as in Jig. C, the A C . . THE ART OF PERSPECTIVE. 71 axis AB, and its parallel DC, appear unequal perpendiculars, but approximate as the plane revolves (as in D), till they coincide over the longitudinal radius CB,^g. A. The parallels to DA in fig. A, are very acute at the commencement of the revolving ; are less so in C ; still less in D, and fall gradually till they become horizontals and parallels over the longitudinal radius. The conceived revolving of this surface with its parallels makes the same changes in their appearances as our movement around fixed bodies produces ; for if we are opposite to the centre of right-lined forms, the horizontals appear so ; but if we revolve till the eye is in the same plane, the object undergoes all the changes of the revolved surface of our diagram. The perpen- diculars are always perpendiculars of this revolved plane ; and the extremes in each variation govern the diagonal lines, so that the importance of giving our best consideration to them must manifest itself to every reflecting person. The width apart and the apparent unequal length of two equal perpendiculars, depend on one cause — the quantity or angle of revolution. So that the apparent heights and apparent widths, commanding the angular depths, are the leading features of accurate representation. Now, if we wish to represent this surface over any radius, the operation is very simple, and would demonstrate the appearance of any rectangular surface — perpendicularly ; and by turning the diagram, and making the axis horizontal — horizontally . A number of surfaces will require to be conceived to exist in the planes of the radii, perpendicularly ; or in the planes of horizontals to the axis, to define their boundaries in perspective. As perpendicular surfaces, however various in size, must, as it were, stand upon or over some radius, in a drawing containing 72 THE ART OF PERSPECTIVE. many surfaces, the horizontal edges would be on some degrees of the parallel circles, which circles are of various axes, accord- ing to the altitudes of the surfaces, as the parallels between DA, CB, are to the parallels DA, CB, in the diagram. The parallels to DA, CB, are various planes; so that surfaces may have their bases on any, and occupy any quantity on or over the radii ; and we may, by imagining the circles and axes to circumscribe all we include in the drawing, readily conceive all the surfaces on their proper radii, whether touching the axes or only parallel to it, what particular parallel describes the base, and what points on the radii originate the perpendiculars. Any diagonal planes, as well as these perpendicular or horizontal planes, are as readily conceived to extend between points of one plane to another in any angular direction. The novelty of these considerations, to persons who previously have had no occasion for them, will require study. A little meditation will enable the student to understand them, assisted by practical illustrations of some of the points on a panellel door, which is a model at hand for every one. The whole door will be the greatest perpendicular surface ; the door revolved over the floor describes the semi-circle ; the panels being surfaces of smaller dimensions, on the same perpen- dicular plane as the door ; the horizontal edges parallel with the top and bottom of the door ; and the perpendicular edges of the panels parallel with the axis. The top and bottom edges of the panels being less than the width of the door, which describes the circle, are a part of the radius only, and the surface for them are drawn within those points. It' the door be opened till the edge or thickness ol the door THE ART OF PERSPECTIVE. 73 can only be seen, Jig. B will present itself ; by revolving the door a little way, the fig. C ; and closing’ the door further, the fig. D ; and on shutting 1 it, the Jig. A. This operation will show all the diagonal variations in the horizontal top and bottom of the door. By marking on the door lines parallel to the top and bottom, their corresponding changes will be observed, and two lines from corner to corner will practically exemplify the appearance of perpendicular triangles in various points of view. The student can place the eye opposite to any point on the perpendicular edge of the door, and observe from multiplied directions the variations of right lines, when connected with the eye, at a fixed distance, and at a chosen altitude. The revolving of the diagonal AC, will readily impress the observer w T ith the idea of a cone of the height of the door, with a base equal to twice its breadth, and pyramids, with bases of regular or irregular polygons, will suggest themselves by con- ceiving edges from any points on the radii to the axis ; and to convey an idea of elliptical forms, I subjoin the definitions of conic sections. Remark . — ACB is a triangle ; which, being revolved about the axis AB, generates a cone and sections, perpendicularly, hori- zontally, or angularly — the ideas of the conic sections. DEFINITIONS. (See Plate 11.) “ 1. Conic sections are the figures made by the mutual intersec- tion of a cone and a plane. “2. According to the different positions of the cutting plane, L 74 THE ART OF PERSPECTIVE. there arise five different figures or sections ; namely, a tri- angle, a circle, an ellipse, an hyperbola, and a parabola ; the three last of which only are peculiarly called conic sections. “ 3. If the cutting plane pass through the vertex of the cone, and any part of the base, the section will evidently be a triangle, as VAB,$g. 3, plate 11. “ 4. If the plane cut the cone parallel to the base, or make no angle with it, the section will be a circle, as ABD, Jig. 4, plate 1 1 . “ 5. The section DAB is an ellipse, when the cone is cut obliquely through both sides; or when the plane is inclined to the base in a less angle than the side of the cone is. [Fig. 5, plate 11.) “ 6. The section is a parabola when the cone is cut by a plane parallel to the side ; or when the cutting plane and the side of the cone make equal angles with the base. [Fig. 6, plate 11.) “7- The section is an hyperbola when the cutting plane makes a greater angle with the base than the side of the cone makes.” [Fig. J, plate 11.) A study of these definitions have a considerable influence on the mind, when we have to describe forms similar to those generated by the cutting planes ; as arches, church windows, gateways, spiral edifices, triangular roofs, elliptical compartments in ceilings, & c. Every proficient in perspective must be accustomed to think freely, subjecting all appearances in nature to the general laws which govern them, and which can be delineated by points within the ultimate diagram, and demonstrated by the principles of this art. THE ART OF PERSPECTIVE. 75 Parallel circles, or sections of circular cylinders, are generated by the revolving of the parallels to the top and bottom ol the door, each having a different latitudinal diameter to its bounding circle, or ellipsis. Turning the diagram shows that the principle is the same, whether the sections are cut horizontally or perpendicularly. Geometrically, the section of a cylinder is thus described. Theorem CVII. Huttons third edition. “ If a cylinder be cut by a plane parallel to its base, the section will be a circle equal to its base. Q.E.D.” Let AF be a cylinder, and GHI any section parallel to the base ABC, then will GHI be a circle, equal to ABC. {Fig. 8, plate 11.) “ For, let the planes KE, KF, pass through the axis of the cylinder MK, and meet the section GHI, in the three points H, I, L, and join the points as in the figure. “ Then, since KL, Cl, are parallels, and the plane KI meeting the two parallel planes ABC, GHI, makes the two sections KC, LI, parallel ; the Jig. KL, IC, is therefore a parallelogram, and consequently has the opposite sides, LI, KC, equal, where KC is a radius of the circular base. In like manner it is shown that LH is equal to the radius KB ; and that any other lines drawn from the point L to the circumference of the section GHI, is a circle, and equal to ABC. Q.E.D.” Domes, semi-spheres, and sections, are derived from the sphere generated by the circular plane revolved, and making the diameter an axis perpendicularly, horizontally, or angularly. The perspective differing from the geometrical constructions according to their points of view. l 2 THE ART OF PERSPECTIVE. 76 Thus, the semi-sphere in fig. B, viewed from the point in our diagram, opposite the centre of the axis, lias its lime or visible circular surface composed of an arc greater than the generating circle, because a greater apparent length than the diameter influences the elliptical base or section of the sphere, as explained in the perspective of the circle, in reference to the latitudinal and longitudinal diameters. Thus we have in this diagram the origin of every line and form, singly and combined — geometrically and perspectively- and the draughtsman, if at a loss for a critical definition, has only to submit his query to this test. Lest this mathematical manner of describing the origin of lines and forms may not be readily comprehended by persons unac- customed to seek the radical principles of practical rules, and whose geometrical skill may be imperfect, L will suggest the following practical operation. — Take a cylinder of wood, or other substance, with two parallel ends similar to the figure in the diagram. If a solid cube is required, set four equal points on the rim or circumference of the ends, cut off the four slabs, and the cube remains. Three equally distant points on each end, cut in the same manner, will leave a triangular prism ; and according to the number of points, prisms named after their bases. By putting the cylinder in the lathe, we can turn this block into a sphere or a cone. But if the forms we wish to produce do not require us to have the ends, or the circular surfaces, as guides to regular forms from points on the radii, which we can mark on the ends, we can cut off what parts we please, and produce any irregular THE ART OF PERSPECTIVE. 77 figure, or figure less than the whole circumscribing figure of the cylinder. This mechanical operation would be a practical illustration of this theoretical diagram; and the mechanist, to be a clever work- man, must have these notions to set out his work, and bring rude matter into form. The first ideas of perspective students should be strictly mechanical, and directed to the principles which give form, on which are founded the rules for all the diversities it will assume when seen from different directions. Points, edges, and surfaces, are the properties of shape ; the place of the first, the length of the second, and the contents of the last, comprise limited quantity. Rules for practical perspective cannot serve practitioners in every case, unless they will make themselves masters of the principles on which they are demonstrably established. Having shown the principle of putting the circle in perspec- tive, let the learner make two with an axis, three inches long, forming a drawing like the diagram ; join a great many points from circle to circle, making perpendiculars, and they will each be the perspective of three inches in as many positions, which cannot fail to establish in the mind a correct idea of the appear- ance of perpendiculars ; and joining any two by two diagonal lines, making them a surface, wdll be a self-evident proof for the appearance of any superficies. By prolonging the diagonal lines which have joined two per- pendiculars, as in Jig. C and D, till they intersect each other, the idea of vanishing points is gathered. In the Jig. B, having no diagonal lines, there is no vanishing point, which is a point of imagined angularity where the two lines would meet if produced, 78 THE ART OF PERSPECTIVE. which are much nearer to the axis in C than in D ; the plane of the surface represented in C being- much nearer to the plane of the eye than the one on D. ON HORIZONTAL LINES. As it has been a matter of question, whether long horizontal lines should or should not be represented to decline from the centre of the picture either way, as the extreme ends are more distant from the eye than the centre, I shall advance the follow- ing reasons for drawing them horizontally through the picture. Suppose the eye to be stationed opposite to the centre man of a tile of soldiers of equal heights, of an extent that does not require the head to be turned, the eye only revolving. The visual rays to the feet and to the top of each figure may have an equal expan- sion, and the space contained within the rays will form a rectan- gular based pyramid ; the vertex being the eye, and the file of men the base. Now, any section parallel to the base will be in proportion , and accurately represent the file of men throughout the line of equal altitudes ; for although at an equal distance from the vertex on each pair of rays (that is, the rays to the top and foot of each man), the angle or expansion is less, the further removed from the centre pair — yet, where the sectional right line cuts, there is a proportional increase of distance from the vertex in each pair of rays ; and we find the same expansion lying all along, and an equal height from every ray to the ground, on any line parallel with the plane of the file of men : but if the plane of the men is diagonal to the view, although the visual rays are equally THE ART OF PERSPECTIVE. 79 expanded at the place of each man, the angles at the vertex gradually diminish, and the section that cuts the two external rays horizontally to an equal length, produces a base gradually diminishing from the nearest to the most distant man on that perspective section, as we see in nature. If, instead of the right-lined section of rays parallel with the base, we describe a circle through them, by that means we shall have the decreasing usually imagined to be proper ; because all those points being equally distant from the vertex, we should find the angles to vary from the centre each way, which is not the case on the true section or plane of the picture. This principle applies to the horizontal lines of buildings, or those we have defined as geometrical lines, the visual rays to each end being equal in length. If we insist on rigid and microscopic nicety, no line is purely horizontal, any more than any two perpendiculars are parallel ; for, as by the laws of gravi- tation, every thing tends towards the centre of the earth, lines must in a trifling degree diverge ; and as we inhabit a spherical body, the tops of equal perpendiculars will describe a circle ; but it would be difficult to make it evident to the senses ; it would be a puzzling calculation to compute the area of a segment con- tained within a horizontal line of one hundred yards long. As we draw perpendicular lines parallel, let us be content to draw horizontals straight; and as we can fix the points of their extremes, by uniting them we shall have the diagonals too accurate for reasonable minds to find fault with ; or so near, that the senses cannot detect the variations, any more than they can do in nature. 80 THE ART OF PERSPECTIVE. OF SHADOWS. The projection of shadows can be easily comprehended after a study of the principles of perspective. We have explained that drawings represent objects from a medium or plane, which makes a section of our visual rays transversely, or at right angles, to our centre visual ray. With regard to shadows, the light is the vertex and takes the place of the eye; the object that casts a shadow, takes the place of the medium ; and the shadow takes the place of the originating object of the perspective representa- tion. fbe rays of light passing onward around the contour of a form are like the prismatic visual rays, and the surfaces which stay their further progress are like solid bodies which arrest the visual rays. The distribution of light from a focus, if obstructed by an object, projects a shadow, which must be conic or pris- matic. If the focus be opposed to the centre of a surface, it pro- jects it geometrically, supposing the receiving surface to be parallel to the surface which originates the shadow ; but if the receiving surface form an oblique plane, or the planes be not parallel, then the shadow is elongated, as if the perspective line, which cuts the visual rays to equal lengths, were elongated to the the originating diagonal line. The rays of light may also be diagonally cast on the object, and the receiving surface may be diagonal to the plane of the object, in which cases the projection of shadows become more difficult to give rules for than Per- spective; but if we know the principles of the latter art, and the positions we have to contest with, the former is not more difficult to practise. In these remarks, I assume that light is projected in right lines. As it has been discussed whether light is projected THE ART OF PERSPECTIVE. 81 in right lines, I feel a considerable diffidence in making any remarks ; but as I have drawn a parallel between perspective and the projection of shadows, attempting to establish them on undeviating principles, I am compelled to announce my in- ferences. Rays of vision, I presume to be received in direct lines ; for if a surface interpose between the eye and a greater surface, the boundary of the interposing surface is contained within the section of direct visual rays, which diverge from the eye, forming the sides of cones or pyramids from the surfaces which project them. The centre of these rays is the right line of vision, and this ray, amidst its surrounding rays, must traverse every line to be introduced into a drawing ; edges and points attract it with magnetic influence, while the spreading rays are vaguely scattered over extended surfaces. Surfaces can only exist in boundaries, and when these boun- daries are visible, they evince the existence of bodies ; but when they are only conceived, they are superficies, or ideas, or what- ever other name will serve to distinguish the operations of the mind from those of the senses. With respect to light, the edge of a shadow is loosely defined, on account of the light transmitting inferior rays around the focus. The termination of the edges of a shadow become less perceptibly marked, the farther the object or the plane which receives the shadow is removed from the light, which we perhaps may account for, as we do in aerial perspective, by the quantity of obscuring matter through which the rays of light or sight have to pass. However, the forms of shadows always correspond with the solids which produce them, subject to the considerations of the light, and the object, and the receiving plane before stated. M 82 THE ART OF PERSPECTIVE. REMARKS. 1 have made no change in representing perpendicular edges of structures, having drawn them in the diagrams of this work by perpendicular lines. To be critically correct, perpendiculars should only be drawn so, when the eye is central ; in other points of view, the cause that shortens the length of the perpendicular in appearance, lessens the breadth between a parallel, at that end which is more distant from the eye. The base expands horizontally a greater angle of vision than (at the same distance from the eye) is contained between the visual rays to the top. As most lines of structures are not of great extent, and are generally viewed from considerable distances, the eye does not detect the converging and diverging of perpendiculars, so that I did not think it necessary to direct students to subject them to the perspective test; the practitioner therefore must exercise his judgment when to adopt the rigid rules. One perpendicular line appears, and is drawn so from every point of view. When we look at two or more, they cease to appear perpendiculars, when the eye is not opposite to the centre of their altitudes. Synthetically, the distance of the eye from the altitudes originates the quantity of divergence ; analytically, by the quantity of divergence in a drawing, the distance of the eye may be found, if the dimensions of the originating form be known. As none of the diagrams exhibit a combination of forms, it is necessary to observe that the line of contact must be drawn at right angles to the centre ray, which bisects the angle of the two outer rays, embracing all the objects introduced into the THE ART OF PERSPECTIVE. 83 drawing ; the ground plan, of course, must contain all the bases, and in practice, a sufficient distance should be given to the point of station, to obviate extreme reductions of originating dimen- sions. Projecting points of the mouldings of cornices, vertices of porticos, &c., central points of groined arches, domes, angular points of roofs, spires, as well as any summit, must be treated as the tops of perpendiculars above the base, or ground plan, from which the apparent breadths are ascertained, and the altitudes determined by lateral plan, as exemplified on plate 4. The quantity of sky and foreground can be added above and below the objects in a drawing, at the discretion of the artist. Ranges of windows, columns, and similar forms, are graduated in size, as they appear to the eye, by finding the position for the top and bottom lines of that nearest ; then for the most distant, and drawing from one to the other, intersecting the apparent graduating perpendiculars, previously drawn from the line of contact containing the widths. The preceding sheets contain the theory and application of perspective, as far as description can communicate them. The student will perceive that the elements are founded in nature, and supported by geometry ; both are created by intel- lectual perception, which must be acquired by pupils to render the principles available in simple or intricate cases. The know- ledge necessary to understand perspective thoroughly, must result from practical exercise, and depends on the diligence and M 2 84 THE ART OF PERSPECTIVE. intelligence of the student. The rules, though simple and few, may not be evident at first sight. The effect of objects on the mind requires the nicest consideration to enable us to detect true from false ideas. By exercising the intellectual faculties, guided by the rules in this work, the artist, architect, or con- noisseur, will be able to add a consciousness of the causes of eff ects to the mere act of seeing, with which few persons would be content if they had the least conception of the pleasure derivable from a knowledge of perspective. To comprehend the principles of perspective cannot be said to require great capacity ; but they require considerable ingenuity to apply them to practice; this, a treatise cannot communi- cate. The art cannot be reduced to that mechanical simplicity as to be made obvious to children, although based on few and simple rules ; it must ever be a valuable science, and a study requiring deep thought. THE END. Printed by W. H. Cux, 5, Great Queen Street. UftjsM 'li%o * - . ,J|<“ • m » . t *4 » . * r. ■* w ir •• >v ' , L, ' ' ■ | .1 * » * « ■- , ■ ' 'y ’• . • "'-h . ' i r».‘? Tjwrwtf c v ■ J -7r • • - I r • •* ■ f .. : i t , ' *„ M ■ • • * Al *• * ». M • - t \*W ■•, * 1 V / £ • n . Fjfi life