LECTURES 
 
 ON 
 
 THE PRINCIPLES AND PRACTICE 
 
 OF 
 
 PERSPECTIVE, 
 
 AS 
 
 DELIVERED AT THE ROYAL INSTITUTION, 
 
 ACCOMPANIED WITH 
 
 A MECHANICAL APPARATUS, 
 AND ILLUSTRATED BY ENGRAVINGS. 
 
 By JOHN GEORGE WOOD, F. A. S. 
 
 Whoever would paint or draw must first learn Perspective. 
 
 LIONARDO DA VINCI. 
 
 THE SECOND EDITION, 
 
 CORRECTED AND ENLARGED. 
 
 LONDON: 
 
 PRINTED FOR T. CADELL AND W. DA VIES, STRAND. 
 
 BY J. M'CREERY, FLEET-STREET. 
 
 1809. 
 
THE J. PAUL GETTY QENTER 
 
PREFACE. 
 
 Encouraged by the flattering approbation these Lec- 
 tures received when deUvered in pubUc, and by the 
 hope that the accompanying apparatus might render the 
 study of Perspective considerably less difficult, the Au- 
 thor has ventured to offer a second edition of this work ; 
 the professed object of which is to render the simple 
 rules of the Art clear and intelligible by a more fa- 
 miliar mode of explanation, and by frequent reference 
 to the apparatus in lieu of geometrical demonstration, 
 which, although not so satisfactory to the mathemati- 
 cian, will be more readily comprehended by those who 
 are not previously prepared by a course of study in 
 geometry, and will enable them to pursue the subject 
 through all its intricacies with greater facility here- 
 after. 
 
 In order to avoid the inconvenience of carrying the 
 vanishing points out of the plate, the distance of the 
 picture in several of the diagrams is taken too short, 
 which occasions a degree of distortion in the Perspec- 
 tive of some objects ; as for instance of the oblique 
 wheel, Plate 3, Fig. ^, &c. 
 
iv 
 
 PREFACE. 
 
 Complicated examples have been carefully avoided, 
 as tending rather to confuse than assist the student in 
 the general application of a rule, and those simple ones 
 adopted, which are the immediate result of the pre- 
 ceding principles. For this reason the projections of 
 the bases and pedestals of columns, with their mould- 
 ings, are omitted, as the simple rules contained in 
 these Lectures will be fully sufficient for the Perspec- 
 tive representation of the principal Hues of which they 
 are composed, and the rest must depend upon cor- 
 rectness of eye. 
 
 In the former Edition the horizontal line was intend- 
 ed to have been the only vanishing line treated of, but 
 it being found necessary to touch slightly upon the na- 
 ture of vanishing lines in general, preparatory to the 
 perspective of shadows, the Author has thought it ad- 
 visable to enter still farther into that part of the sci- 
 ence in the present publication. He takes this oppor- 
 tunity of acknowledging the advantage he has derived 
 from the perusal of many treatises on Perspective of 
 great merit, some of whose figures he has adopted, and 
 also of apologizing for the frequent repetitions of the 
 same expressions, which for the sake of perspicuity he 
 has preferred doing. 
 
CONTENTS. 
 
 LECTURE I. 
 
 Page. 
 
 The Art of Perspective necessary to those who would Paint or Draw . 1 
 
 Definitions 3 
 
 Preparation of the Picture 15 
 
 Ground-plauy Picture, and Point of Distance placed upon one Plane . 16 
 
 LECTURE II. 
 
 Of Lines Perpendicular to the Picture 1 9 
 
 Of Lines Oblique to the Picture 22 
 
 Of Lines Parallel to the Picture , 25 
 
 Of Vanishing Lines 28 
 
 General Rules 30 
 
 LECTURE III. 
 
 The Square represented Perspectively, one side being Parallel to the 
 
 Picture 33 
 
 Method of cutting off given Portions from a Line in Perspective .... 35 
 
 The Perspective Representation of the Square, one side being given in 
 
 the picture 37 
 
 The Square when Perperidicular to the Ground and Picture 39 
 
vi CONTENTS. 
 
 Page. 
 
 The Cube 40 
 
 Buildings Parallel to the Picture , 41 
 
 LECTURE IV. 
 
 Square oblique to the Picture 44 
 
 Buildings ditto 45 
 
 The Circle applied to circular Towers, Wheels, S(c 49 
 
 The Perspective of Doors, 8(c, when open 54 
 
 LECTURE V. 
 
 The Line of Elevation , 56 
 
 Arches 60 
 
 Bridge 63 
 
 Steps 66 
 
 LECTURE VL 
 
 Vanishing Line 70 
 
 Inclined Planes 71 
 
 Perspective of Shadoivs 77 
 
 LECTURE VII. 
 
 The Meanders of a River 85 
 
 Refections in Water 87 
 
 Station or Point of View 88 
 
 A Building placed in the Picture according to a given Scale 90 
 
 The Triangle 91 
 
 Hexagon 92 
 
 Directions for Sketching from Nature 93 
 
 Conclusion 95 
 
THE APPARATUS. 
 
 The present Apparatus differs from the former in many particulars, 
 but retains all its advantages, together with that of greater porta- 
 bility and less chance of injury. To prepare it for use, the glass must 
 be raised perpendicular to the board, and kept in that position by 
 opening the triangular support till it points to the letter T ; the place 
 of the eye E must be raised in a similar manner, and also the two planes 
 upon the other part of the boards. If when the eye is applied to its 
 place E, the tracings upon the glass do not coincide with the respective 
 lines 1, 7—2, 8, &c. upon the raised planes, the fault most probably 
 will be, either in the hinge of the two boards forming the ground plane, 
 or in the inequality of the table upon which it stands, and must be 
 altered till they agree. From the construction of this Apparatus the 
 line R s O K P must be termed the bottom, or base line, of the picture, 
 as it agrees with the bottom line of the glass, within its frame, when 
 viewed from the Eye-hole E. The small tubes at each end of the line, 
 marked H L upon the glass, are intended for the reception of the wires, 
 in the small case, on the right of the Apparatus, in order to prolong the 
 horizontal line. From the unavoidable shortness of the distance be- 
 tween the place of the eye and the glass, it will be necessary to ac- 
 commodate the sight to that distance, and the perforation marked E 
 is made large in order to admit of that accommodation. 
 
LECTURES ON PERSPECTIVE. 
 
 Perspective is the art of describing the representations of 
 objects upon paper, canvass, or any plane surface, or as they 
 would appear when viewed through a pane of glass, the ap- 
 pearance and reality being materially different; for example, 
 the two sides of a regular street, appear nearer to each other, 
 and the buildings lower, at the end most remote from the eye, 
 than they do at the end nearest the eye ; although in reality 
 the street is known to be of equal width, and the buildings 
 equally high at both ends. If objects seen through any trans- 
 parent medium, as glass, or the pane of a window, are traced upon 
 that glass, or pane, the tracing will of course be an exact re- 
 presentation of those objects, as they appear to the eye from a 
 fixed point, and it belongs to the art of perspective, to furnish 
 unerring rules for representing objects with equal accuracy 
 upon a flat surface, such as paper, canvass, kc. 
 
 The utility of a knowledge of perspective to those who 
 would excel in the arts of design is now so universally ac- 
 
 B knowledged, 
 
5 
 
 LECTURES ON PERSPECTIVE. 
 
 knowledged, that it were almost superfluous to insist upon it. 
 But, as we frequently observe the most glaring defects in this 
 particular, even in the present highly cultivated state of art, 
 it is impossible not to regret that such defects should have 
 crept into works so highly to be commended in every other 
 respect. An error in perspective renders the representation 
 unlike the original ; and, although the cause may not be dis- 
 cerned by the common observer, the effect is visible to every 
 one ; and an object so represented presents an appearance un- 
 satisfactory, and in many cases peculiary unpleasant, for in- 
 stance, a figure intended to be sitting, appears sliding out of 
 the chair, tables meant to be represented flat seem inclined, 
 and the objects upon the table consequently slipping off. It 
 were endless to enumerate the variety of instances Mhere a de- 
 ficiency in the knowledge of perspective is apparent, we will 
 therefore be content to turn to the works of the Chinese, which 
 furnish the most striking examples of the extreme absurdities 
 to which an ignorance of this art is liable ; in all their pictures 
 we may trace an attempt at perspective, but their knowledge 
 does not seem to extend beyond that which is apparent to every 
 one, namely, that objects appear to diminish in proportion as 
 their distance from the eye increases. But even this most evi- 
 dent principle is sadly misapplied in their pictures, for human 
 figures at a considerable distance are not unfrequently even 
 larger than those in the foreground. Their buildings seem to 
 encrease with their distance from the eye, and water to run up 
 hill, kc. kc. 
 
 The assistance derived from perspective in that most gratify- 
 ing branch of art, sketching landscape scenery from nature, is 
 incalculable. It enables us to look upon the objects of which the 
 
 picture 
 
LECTURES ON PERSPECTIVE. 
 
 3 
 
 picture is formed with other eyes, and immediately determines 
 the relative position, and also the direction of every line. It 
 prevents the commission of those mistakes which the most cor- 
 rect eye would infallibly be guilty of, and determines the dis- 
 tance of the nearest object with which the picture may begin. 
 In sketches made by those unacquainted with this science, the 
 eye often appears to have been in several places at one and the 
 same moment : the impossibility of which will be evident by the 
 smallest attention to the nature of the picture ; for two build- 
 ings equally high, will exhibit, the one its roof, the other not, kc. 
 It has been occasionally alledged that a regular attention to the 
 rules of this art, while drawing from nature, impedes the pro- 
 gress of the artist, but will not the man who clearly sees his 
 road before him, arrive at the end of his journey sooner than 
 he whose doubts oblige him frequently to hesitate lest he should 
 wander from his path ? 
 
 The position of the picture is supposed always to be similar 
 to a pane of glass in a window, (i. e.) perpendicular to the 
 ground, and if a piece of glass be placed in that position op- 
 posite to the eye, and the scene beyond traced upon it, the eye 
 being fixed to one point, it becomes a picture of that scene. 
 
 DEFINITIONS. 
 
 Although it is the professed object of this treatise to prove 
 the truth of the rules without having recourse to mathematical 
 demonstration, yet, it is necessary that certain geometrical fi- 
 gures should be understood ; and, first, 
 
 1. PARALLEL 
 
4 
 
 LECTURES ON PERSPECTIVE. 
 
 1. PARALLEL LINES. 
 
 Parallel lines are equally distant from each other in every 
 part, and if continued to any length, would never meet nor 
 approach nearer together ; thus. 
 
 2,. A RIGHT ANGLE. 
 
 A right angle may be sufficiently explained by the junction 
 of any two lines which form the two sides of a square ; thus, 
 
 3. PERPENDICULAR TO THE PICTURE. 
 
 The term perpendicular to any plane, (as for example to the 
 picture) so frequently occurs, and is so necessary to the general 
 description of certain lines, that it merits particular attention. 
 The term means simply, that if a line falls directly upon any 
 plane so as not to lean or incline to that plane on either side, 
 such line is said to be perpendicular to that plane. As a fami- 
 liar example, suppose a candlestick, with a flat square base, 
 placed upon the table, it would then be said to be perpendi- 
 cular, because it did not incline towards the table on either 
 
 side. 
 
LECTURES ON PERSPECTIVE. 5 
 
 side. Let a wedge be placed under one side of the base, and 
 the candlestick will lean on the opposite side towards the table, 
 and would be said to be out of the perpendicular ; it would be 
 so with regard to the table or the ground, but would still re- 
 tain its perpendicular position with respect to its base, and 
 even if it were to be laid upon the table, the shaft would still 
 be perpendicular to the base. — We are so much accustomed to 
 associate the ideas of a perpendicular with that of an up- 
 right, (that is, perpendicular or upright with regard to the 
 ground) that it is not without some effort that we can admit 
 the more comprehensive application of the term which is 
 the object of the present definition. A stick pointed directly 
 towards a wall, neither inclining upwards nor downwards, to 
 the one side or to the other, is perpendicular to that wall, let 
 the wall be termed a plane, and a stick so directed would be 
 termed perpendicular to that plane. In other words, the term 
 may be defined thus, — a line is said to be perpendicular to a 
 plane, or line, when its direction forms a right angle to the 
 plane or line ; thus. 
 
 The line a b is perpendicular to the line c d. 
 
 A 
 
 4. PLANE 
 
LECTURES ON PERSPECTIVE. 
 
 4. PLANE OF THE PICTURE. 
 
 By the plane of the picture is meant, not only the picture 
 itself, but an extension of it on every side ; as for example, if 
 abed, fig. 2, plate I, were the size of the picture, all the rest 
 of the paper on every side of it will be in the plane of that picture, 
 or if the scene beyond were traced or drawn upon one pane of 
 glass^ in a window, all the other panes in that sash of the window 
 will be considered in the plane of that picture ; or if a view 
 were painted upon one pannel on the side of a room, all the 
 x)ther pannels on the same side would be in the plane of that 
 picture. In speaking of a line being perpendicular or oblique 
 to the plane of the picture, it is not always meant that it would 
 if continued meet the circumscribed limits of the picture, but, 
 that it would meet a continuation of the plane of the picture. 
 Thus upon the apparatus, the line g n cannot meet the picture 
 itself^ but would meet thQ plane of the picture if extended to r, 
 therefore the line f a is said to be perpendicular, and g n ob- 
 lique to the plane of the picture. The use of the plane of the 
 picture is to receive those original lines which could not strike 
 the picture itself, and thus the horizontal and ground lines 
 may be continued to any required length in the plane of the 
 picture. 
 
 5. GROUND PLANE. 
 
 In perspective, the ground is supposed to be divested of in- 
 equalities, and perfectly flat, that is, a perfect plane ; thus, in 
 the apparatus the bottom x represents the ground plane. 
 
 6. THE 
 
LECTURES ON PERSPECTIVE. 
 
 7 
 
 6. THE POINT OF SIGHT. 
 
 The point of sight is the real situation of the eye when 
 
 viewing any object in nature with intent to draw it; thus the 
 
 point of sight is the aperture at the end e of the apparatus, 
 
 where the eye is applied to see the representation upon the 
 glass or picture. 
 
 The old writers made use of this term in a very different 
 sense, and applied it to the point which Dr. Brook Taylor 
 changed to that of, Centre of the Picture. 
 
 7. HORIZONTAL LINE. 
 
 The horizontal line is a line drawn alone the picture, ex- 
 actly the height of the eye, and parallel to the bottom of the 
 picture : thus in the apparatus, the horizontal line h l is ex- 
 actly the height of the point of sight or eye e, and drawn from 
 one side of the picture to the other ; if the eye be raised the ho- 
 rizontal line rises with it : and vice versa. The old authors were 
 not acquainted with any other vanishing line, but the compre- 
 hensive principles of that excellent mathematician Dr. Brook 
 Taylor, stripped it of its long enjoyed honours, and shewed that 
 it had not the slightest title to pre-eminence over any other va- 
 nishing line, and lest his readers should still remain in the 
 same error, he formed the schemes in his treatise, for the most 
 part by means of other vanishing lines. 
 
 8. THE CENTRE OF THE PICTURE. 
 
 The centre of the picture is the point directly before the eye 
 when looking straight forwards, neither upwards nor down- 
 wards ; 
 
LECTURES ON PERSPECTIVE. 
 
 wards ; and if the wire be put through the place of the eye e in 
 the apparatus, and carried straight forwards, perpendicular to 
 the glass or picture, the point c, where it meets it, is the centre 
 of the picture^ and consequently falls upon the horizontal line. 
 
 Dr. B. Taylor substituted this term for that of the point of sights 
 used by preceding authors. By the centre of the picture he 
 evidently meant the centre of vision ; thus, if the eye be stead- 
 fastly directed to any one point, as for instance the point x, that 
 point will be distinctly visible, and for a certain space around 
 it objects may be clearly discerned, but as their distance from 
 the point increases, they must appear weaker and weaker, till 
 at length they become confused, and nothing can be seen be- 
 yond a certain space. Let that space be represented by the 
 circle abed, and the gradual diminution of the strength of 
 vision by the radii from the centre ; thus a b c d is the circle 
 of vision, and x its centre. 
 
 
 
 7— 
 
 A 
 
 
 
 
 f 
 
 D 
 
 X then is the point termed by Dr. B. Taylor the centre of the 
 picture. But as from the point so called rarely falling in the 
 
 middle 
 
LECTURES ON PERSPECTIVE. 
 
 9 
 
 middle of the paper, or canvass, much confusion may arise ia 
 the mind of the student ; it will be necessary to observe, that 
 the long square or parallelogram a b c d is found to be a more 
 convenient form than the circle, and thus the centre of the pic- 
 ture X does not fall in the middle but nearer to the bottom 
 D c, than to the top a b, of the picture, but still continues the 
 centre of vision. Again, it is not unusual to find this point 
 placed nearer to one end of the picture than to the other, and 
 in such case we may conclude that a portion of the scene in 
 nature was not consistent with the plan of the artist, and 
 therefore rejected, and the picture terminated, as marked by 
 the dotted line e f, the rejected matter, had it been introduced^ 
 would have filled up the space e b c f, but the picture now 
 remains a e f d, and x, the centre of the picture, much nearer 
 to E F than to a d, but still remaining the centre of vision, 
 
 9. DISTANCE OF THE PICTURE. 
 
 The distance of the picture is the distance of the eye from 
 the picture. For example, in the apparatus it is the distance 
 of the eye e from the glass representing the picture upon which 
 the objects beyond it are drawn. In order to make this still 
 better understood, if a small frame, with a glass in it, be held 
 up before the eye in the position of the picture, and the objects 
 seen through it, traced or drawn upon it, it is evident if this 
 frame be held very near the eye, objects very near in nature 
 may be traced or drawn upon the glass, and the drawing would 
 be made with a very short or small distance : but if the frame 
 be held much farther from the eye, many objects before traced 
 upon the glass, cannot b^ introduced, not being included with- 
 in the frame : and this drawing would be made with a greater 
 
 G distance ; 
 
10 
 
 LECTURES ON PERSPECTIVE. 
 
 distance; and as by moving the frame nearer to, or farther 
 from, the eye, before the tracing upon the glass be compleat- 
 ed, would occasion an alteration in the appearance of the ob- 
 jects already traced ; it is evident that the distance of the picture 
 must never change during the representation of any one scene. 
 In the first mentioned or short distance, a human figure stand- 
 ing very near the eye of the person drawing, might be seen 
 within the frame, and introduced in the picture, and the pro- 
 portion his representation would bear to other objects must 
 appear preposterous. But by the last mentioned or longer 
 distance, this figure could not be introduced, and the picture 
 would begin with some object considerably farther removed 
 from the eye. 
 
 Thus the distance of the picture appears to determine how far 
 we should remove from an object, in order to represent it 
 satisfactorily. It ought always to equal the greatest length of 
 the picture, and if the frame and glass, before-mentioned, be 
 12 inches long by 9 inches high, it ought to be held at the 
 distance of 12 inches from the eye, at least. Suppose a frame 
 so placed, and a large building, such as St. Pauls', or West- 
 minster Abbey, to be the subject about to be represented ; it is 
 evident, if the artist be near the building, but a very small 
 portion of it can be seen, or traced, within the frame ; and it 
 will be necessary to retire to a greater distance, still keeping the 
 frame \2 inches from the eye, and when the whole of the 
 building occupies a convenient space within the frame, the 
 distance at which it ought to be drawn is a proper one, and the 
 perspective will be easy and agreeable, whereas apparent dis- 
 tortion, occasioned by the violence of the perspective, must be 
 the consequence of standing so near the building as to be 
 
 obliged 
 
LECTURES ON PERSPECTIVE. 
 
 11 
 
 obliged to place the frame close to the eye, in order to conir 
 prehend the whole edifice within it. 
 
 10. VANISHING LINE. 
 
 It is well known that the end farthest from the eye, of a 
 very long room, gallery, or avenue of trees, appears much 
 smaller than the end nearest the eye : and if the two sides of 
 the room, or avenue, are supposed to be continued to 
 such an extreme length as to appear to meet, the line in 
 which they appear to meet would be called the vanishing 
 line of the two sides of the room, or avenue : and if the 
 ceiling and floor of a room were continued to an extreme 
 length, they would appear to meet in the vanishing line of 
 the ceiling and floor. In either case the vanishing line is 
 directly opposite the eye, but that of the ceiling and floor 
 (or of planes parallel to the horizon) will always be the height 
 of the eye, and parallel to the ground ; and is the horizontal 
 line (Def 7.) Again, if the eye be directed straight forwards, 
 neither upwards, nor downwards, and a thin plane, as of 
 pasteboard or card, be held up exactly the height of the eye, 
 and parallel to the ground, it will there appear to the eye 
 as a line, the edge only being seen, and in that situation it is 
 upon the vanishing line of the ceiling and floor, (which is the 
 horizontal line) but if it be raised higher the under surface 
 will appear, and if it be lowered the upper will appear. 
 Again, if a pasteboard be laid upon the apparatus so as to 
 form a kind of ceiling, it will be perceived to the eye at e, 
 that the lines forming the sides of the ceiling, appear (if 
 continued) to meet in the horizontal line upon the glass or 
 picture ; the lines also forming the sides of the floor from 1 to 
 
 c 5 3, and 
 
15 
 
 LECTURES ON PERSPECTIVE. 
 
 3, and 6 to 4, appear to meet in the same line ; therefore the 
 horizontal line is the vanishing line of the ceiling and floor, or 
 of all planes parallel to the horizon, and divides those objects 
 of which we see the top, from those of which we see the 
 bottom. A hoop held exactly as high as the eye, and parallel 
 to the ground, will appear as a straight line. The hoop then 
 would be lost in a line, or fall into its vanishing line, but let it 
 be held either higher or lower, retaining its parallelism, and the 
 space within the circumference will become visible. Thin 
 planes approaching each other from the sides of a room, and 
 keeping their parallelism to those sides, would, in their 
 junction opposite to the eye, present the appearance of a 
 single line, that is, the planes would no longer appear as 
 planes but as a line, which is their vanishing line. 
 
 11. VANISHING Point. 
 
 The vanishing point is that point upon the picture 
 where the representation of lines parallel to each other in 
 nature would meet in it ; as for example, in the apparatus it 
 is the point where the lines upon the glass or picture, repre- 
 senting from 7 to 9, and from 15 to 10; and from 1 to 3, 
 and 6 to 4, would meet in the picture, and these lines con- 
 tinued on the glass (as is done by dots) would meet in the 
 centre of the picture ; which is, in this case, a vanishing point. 
 If a straight wire be held below or above the eye, on the right 
 or on the left, we perceive that it has length, but let it be 
 gradually brought opposite, and pointing towards the eye, 
 and all appearance of length is lost, and only a point becomes 
 visible, which point is the vanishing point of such line, and if 
 we suppose this wire to be the axis of a cylinder, and the ribs 
 
 of 
 
LECTURES ON PERSPECTIVE. 13 
 
 of it to be parallel to the above mentioned wire, it is evident 
 that the farther end of the cylinder will appear smaller than 
 the nearer, and that the ribs will seem to converge towards the 
 axis, till if the cylinder were extended to a sufficient length, 
 they would appear absolutely to meet or come to a point, 
 which would be their vanishing point. If two men were to 
 walk in a direction parallel to each other, it is clear not 
 only that they themselves would appear to diminish as they 
 receded, but also the space between them would seem less 
 and less, till both themselves and the intermediate space 
 would be lost together, that is, would fall into their vanishing 
 point. 
 
 1% ORIGINAL OBJECT. 
 
 By original object or line is meant the object or line to be 
 represented. 
 
 13. INTERSECTING POINT. 
 
 If a line lying on the ground be continued till it 
 meet the bottom of the picture, it is there called the inter- 
 secting point of that line ; thus upon the apparatus, if the 
 line G I be continued it will meet the bottom of the pic- 
 ture in K, which is its intersecting point. Again, if the 
 line lie in another direction, as g n ; the bottom of the 
 picture not being long enough, may be continued (as is 
 done by dots) and where it meets it at r is its intersecting 
 point. Upon paper. Fig. Plate I, if the line s r be con- 
 tinued, it will meet the bottom of the picture in u its inter- 
 secting 
 
14 
 
 LECTURES ON PERSPECTIVE. 
 
 mting point, and the line v t would find its intersecting point 
 upon the bottom of the picture continued at w. 
 
 The representation of lines which are parallel to each 
 other in reality, and also parallel to the position or plane of 
 the picture, will not have a vanishing point upon it, but will 
 be drawn or represented parallel to each other ; as upon the 
 apparatus the tracing of the lines from 1 to 6, and from 7 to 1^, 
 are drawn parallel to each other upon the glass, and they are 
 parallel also to the picture ; for if they were continued to any 
 distance, and the plane of the picture also, it is evident they 
 would never meet, but always remain equally separated from 
 each other. 
 
 If a person placed at one end of a room, directs the eye 
 straight forwards, or perpendicular to the other end of the 
 room, and holds the frame and glass before-mentioned in 
 the position of the picture; then traces the lines of the 
 cornice and floor of the opposite end of the room upon the 
 glass, they will appear to be parallel to each other. 
 
 The representation of lines which are parallel to each 
 other, but not parallel to the position or plane of the pic- 
 ture, will have the same vanishing point upon the picture; 
 for the person remaining at the end of the room as in the 
 foregoing case, knows, that the lines of the cornice, and 
 floor of each side of the room, are in reality parallel to each 
 other: but in the tracing upon the glass, the lines represent- 
 ing the cornice and floor on each side will appear to ap- 
 proach each other, and if continued would meet in a point. 
 
 The 
 
LECTURES ON PERSPECTIVE. 
 
 15 
 
 The lines of the cornice and floor on each side of the room 
 not being parallel to the plane of the picture, hut perpendi- 
 cular to it. In the apparatus, the lines upon the glass or pic- 
 ture, representing from 6 to 4, (which may be called the 
 bottom of the room,) and from I2i to 10, (which may be 
 supposed the cornice^,) appear to meet, or have their va- 
 nishing point in c upon the horizontal line. The same may 
 be seen of lines representing from 1 to 3 and from 7 to 9 ; 
 they have the same vanishing point because parallel in 
 reahty to 6 to 4 and 1^ to 10. 
 
 Thus upon the apparatus the representation of lines pa- 
 rallel to each other, and to the picture, as from 1 to 6, 
 7 to l^j 8 to I I, kc. are represented parallel upon the picture, 
 and cannot have a vanishing point upon it. 
 
 But the representation of lines parallel to each other, but 
 not to the picture, as from 6 to 4, 1 to 3, 7 to 9, &c. will 
 have a vanishing point upon the picture, for if they are con- 
 tinued, they will meet upon the horizontal line in c, the cen- 
 tre of the picture. 
 
 To prepare the picture for drawing views from nature by 
 the rules of Perspective, the horizontal line should first be 
 drawn along it, and as its place depends upon the height of 
 the eye, and the nature of the scenery, it must of course b<e 
 regulated by these circumstances; about one third of the 
 height of the picture is found the most useful for general, 
 practice. If the person about to draw is upon an eminence, 
 with an extent of country beneath him, the horizontal line 
 must be placed high in the picture, because the spectator is 
 
 elevated ; 
 
16 
 
 LECTURES ON PERSPECTIVE. 
 
 elevated ; and if he is on the contrary upon a plain, or low 
 ground, the horizontal line will consequently be low. 
 
 The centre of the picture must be marked upon the 
 horizontal line, in the middle, or inclining to either side, 
 as may suit the plan of the artist: but in the closet the 
 preparation may be carried still further, and the point of 
 distance marked on the same table or board upon which the 
 drawing lays, Plate I, Fig. 1, h. l, is the horizontal line c, 
 the centre of the picture, and if the plane c e be raised till 
 it be perpendicular to h l the horizontal line, then would e 
 be the natural position of the eye, but as lines cannot be 
 drawn upon the air, it becomes necessary to transfer that 
 point over the picture to e, which may be done by laying 
 down the folding plane c e. 
 
 In order to put the ground plan of a building, or of any 
 other object, whose dimensions are given, in Perspective: 
 the paper, or picture upon which it is intended to be repre- 
 sented according to rule, must be placed upon a table suf- 
 ficiently large for the purpose ; and the paper containing the 
 ground plan adjoining the bottom of the picture : the picture 
 must then be prepared, as already explained, by drawing 
 the horizontal line, marking the centre of the picture on it, 
 and also the distance of the picture, or point of distance 
 over it : thus the picture upon which the ground plan is to be 
 put in Perspective, is placed between the ground plan and the 
 point of distance. The distance of the picture should always 
 exceed its longest diameter, because the contrary is productive 
 of distortion, as may be observed in Fig. 3, Plate I, for let 
 A B D F be the ground plan of a square, the perspective re- 
 presentation 
 
LECTURES ON PERSPECTIVE. 
 
 17 
 
 presentation of which is required ; when put in perspective 
 by the longest, being a proper distance of the picture, it will 
 appear thus as a b d f , but by a shorter and improper distance 
 it will appear thus a b g h ; the first resembles a square seen 
 in Perspective, but the latter is a distorted representation, 
 and scarcely conveys a proper idea of that figure, arising 
 from the circumstance of its being seen too near or under an 
 improper angle. 
 
 LECTURE 
 
LECTURE II. 
 
 Consisting of Demonstrations of those Rules by which the Vanish- 
 ing Points of Lines are found. 
 
 The rule for finding the vanishing point of any line, is, that 
 a line must be drawn from the place of the eye, or point of distance, 
 parallel to the original line, or line about to be represented, till it 
 meets the picture, and where it meets it is the vanishing point of 
 that line; and also the vanishing point of all lines parallel to it. 
 For example, let it be required to find the vanishing point of 
 the line g i on the ground plane of the apparatus. By attend- 
 ing to the foregoing rule, we learn, that it is to be found by 
 drawing a line from the place of the eye, or point of distance e, 
 parallel to the original line, or line to be represented g i, till it 
 meets the picture, and where it meets it is the vanishing point 
 required. Let the wire be put through the point of distance, 
 or place of the eye e, and carried straight forwards parallel to 
 G I, (or its dotted continuation on the ground plane) and it 
 must strike the glass or picture in c, the centre of the picture,, 
 which is consequently the vanishing point required, according 
 to the foregoing rule ; but as f a and d b are parallel in reality 
 
 to 
 
50 
 
 LECTURES ON PERSPECTIVE. 
 
 to G I, the line which was drawn from the eye e parallel to g i 
 must be parallel to f a and d b ; therefore the point in the pic- 
 ture found to be the vanishing point of c i, must be the vanish- 
 ing point of F A and D b, and of all lines parallel to them, as the 
 lines connecting the tops of the pillars from 7 to 9 and I'^to 10, 
 and the bottoms of the same pillars from 1 to 3 and 6 to 4. 
 
 The Perspective representation on the picture of any original 
 line continued to an extreme length, is a line drawn on the 
 picture from the intersecting point (see Def 13,) of the original 
 line to its vanishing point. For example, to give the Perspec- 
 tive representation of the original line g i upon the picture, 
 (supposing I g continued to an extreme length,) a line must be 
 drawn from its intersecting point k, to its vanishing point; 
 which was found by the above rule to be the centre of the pic- 
 ture c ; thus a line drawn from k to c is the indefinite ❖ repre- 
 sentation of g I, and if the Perspective representation of the ori- 
 ginai line f a be required, a line must be drawn on the picture 
 from 0 its intersecting point, to c, its vanishing point, which 
 line is the indefinite representation of the original line f a, and 
 a line drawn from the intersecting point p to c, is the indefinite 
 representation of d b upon the picture. Apply the eye to its 
 place at e, and it will be seen that the original lines f a, g i, 
 D B, are represented or traced on the glass or picture, by the 
 
 lines 
 
 * By the term indefinite representation of an original line^ is meant the representation 
 of such a line if continued to an infinite distance, till it absolutely seemed to arrive at its 
 vamshmg point, thus if any two or more lines are drawn upon the picture, till they meet 
 m the vanishing point, the intervening space between those lines, although in reality 
 equally wide at either end, appears to diminish till it is totally lost, and vanishes into a 
 nomt ; such lines are the indefinite representation of original lines. 
 
LECTURES ON PERSPECTIVE. 
 
 ^1 
 
 lines o c^ K c, p c, which all meet in one point, c, the centre of 
 the picture, which is their vanishing point. This is an uner- 
 ring rule for finding the vanishing point of a line, and drawing 
 its representation. 
 
 Thus the following general rules are established : 
 
 1. The vanishing point of any original line, will be the* 
 vanishing point of all lines parallel to it. 
 
 5. That the centre of the picture is always the vanishing 
 point of all lines perpendicular ❖ to the plane of the picture ; 
 therefore, in drawing from nature, if one end of a right angled 
 building be parallel to the position or plane of the picture, the 
 sides will of course be perpendicular to it, and the lines forming 
 the top and bottom of the sides, being also perpendicular to 
 the picture must be drawn towards the centre of the pic- 
 ture, as their vanishing point : and if one end of a square, or 
 right angled room, be directly opposite the eye, or parallel to 
 the plane of the pig tlire, the sides of that room will be perpen- 
 dicular to it, and the lines forming the cornice, and base af the 
 sides, being also perpendicular to the picture, must be drawn 
 towards the centre as their vanishing point. 
 
 To apply the foregoing to practice, let it be required to find 
 
 the 
 
 * Since it has been proved that the centre of the picture is the vanishing point of 
 the original line g i on the ground plane of the apparatus, and since the line g [ (see 
 Def. 3.) is 'perpendicular to the picture, it follows that all original lines parallel to g i 
 must be perpendicular to the picture, and therefore have the same vanishing point, 
 that is, the centre of the picture, thus the lines 1, 3,-6, 4, 8ic. app. being parallel to 
 G I, perpendicular to the picture, vanish in the same point. 
 
22 LECTURES ON PERSPECTIVE. 
 
 the vanishing point of the original line g i (PI. I, Fig. Z) The 
 picture abed being prepared by drawing the horizontal line, 
 making the centre of the picture c, and the point of distance or 
 place of the eye e. According to the rule for finding the va- 
 nishing point of any original line, a line must be drawn from the 
 place of the eye, or point of distance, parallel to the original line, 
 till it meets the picture, which is the vanishing point required. 
 For example, from e the place of the eye, or point of distance,^a 
 line must be drawn parallel to g i, till it meets the horizontal 
 line in the picture, which it does in the centre, then is c the 
 centre of the picture, found to be the vanishing point of g i. 
 If the vanishing point of f a be required, a line drawn from e 
 the point of distance, paralled to f a will meet the picture in c 
 also; therefore is c the centre of the picture, the vanishing 
 point of F A and g i, and since d b is parallel to g i and f a, the 
 line drawn from e parallel to g i, must be parallel to d b, and 
 consequently c the centre of the picture, is the vanishing point 
 of D B also ; and r s, t v, being parallel to d b, g i, kc. the same 
 line from e, which was parallel to g i, must be so to r s and t v, 
 therefore the same point c must be their vanishing point also. 
 To draw the indefinite representation of g i upon the picture, a 
 line must be drawn from its intersecting point k, to its vanish- 
 ing point c, and k c is the indefinite representation of the line 
 g I, continued to an extreme length. The same may be done 
 by F A, and o c becomes its indefinite representation: p c the in- 
 definite representation of d b ; u c of s r ; w c of v t ; and thus 
 of any other lines parallel to gi. Thus far concerning lines 
 perpendicular to the plane of the picture. 
 
 It will now be required to find the vanishing point of lines 
 which lie in an oblique direction to the position or plane of the 
 
 . picture. 
 
LECTURES ON PERSPECTIVE. 
 
 ^3 
 
 picture. As for example, m k upon the ground plane or board 
 X of the apparatus, which is oblique to the position of the glass 
 or picture. The rule for finding the vanishing point of lines 
 perpendicular to the picture, is also the rule for finding the va- 
 nishing point of lines in any other direction. 
 
 If the vanishing point of the oblique line m k, apparatus is 
 required ; a line must be drawn, agreeable to the rule, from the 
 place of the eye or point of distance e, parallel to the original 
 line M K, 'till this line from the eye e meets the picture ; and 
 the point where it does meet it, will be the vanishing point re- 
 quired. Put the wire through the place of the eye e in the 
 apparatus as before, and carry it in a direction parallel to the 
 original line m k, until it meets the picture ; and as in the pre- 
 ceding case, it will give the vanishing point of the line m k ; 
 then will the line drawn upon the glass or picture, from the 
 intersecting point k, to the vanishing point, appear to the eye 
 at e to conceal the original line m k, or in other words to be the 
 tracing, or indefinite representation of m k. But the original 
 lines D A, G N, are parallel in reality to m k, and therefore are 
 said to have the same vanishing point ; this may be proved by 
 placing the wire from s, the intersecting point of d a, to the va- 
 iiishing point of that line, (just found to be the vanishing point 
 of M K,) and if it conceals the original line d a from the eye at 
 E, it certainly is the vanishing point of d a, i. e. it is the point 
 upon the glass or picture, to which the representation of d a 
 must be drawn. The oblique line g n, has its intersecting 
 point at R ; and if one end of the wire be placed at r and the 
 other at the same vanishing point, it will be found to conceal 
 G N from the eye at e ; and thus of any number of lines parallel 
 in reality to m k. 
 
 If 
 
24 
 
 LECTURES ON PERSPECTIVE. 
 
 If the original line lies in a direction of considerable obli- 
 quity to the plane of the picture, a parallel to it from the eye 
 will be carried beyond the margin of the picture, and therefore 
 the horizontal line must be extended, in the plane of the pic- 
 ture, in order to receive it as c f, Plate I, Fig. 4. Upon the 
 apparatus a wire must be fixed in the tube at the end of the 
 horizontal line as its continuation, and the place of any vanish- 
 ing point, when found, may be marked by a small piece of pa- 
 per slipped on the wire. 
 
 Upon paper (Plate I, Fig. 4,) let d a be the line whose va- 
 nishing point is required ; from e the place of the eye, or point 
 of distance, draw a line e f parallel to the original line d a ; 
 this line e f meets the plane of the picture (for it is beyond the 
 margin of the picture) at f upon the horizontal line, continued 
 on purpose to receive it : f is therefore the vanishing point, as 
 was just proved by the apparatus, and a line drawn from s the 
 intersecting point of d a to f its vanishing point, will give the 
 indefinite representation of the line d a. Thus s f is the inde- 
 finite representation of d a ; but m k is parallel to d a, therefore 
 the line e f drawn from e, parallel to d a, must be parallel to 
 M K, and consequently the point f must be the vanishing point 
 of the line m k also, and the line k f drawn from its intersecting 
 point K, to its vanishing point f, is the indefinite representation 
 of M K. G N being also parallel to d a, or m k, e f must be pa- 
 rallel to it, and f its vanishing point, and the line r f from the 
 intersecting point to the vanishing point, must be the indefinite 
 representation of g n. 
 
 Hence we learn the reason why in the representation of build- 
 ings, the lines forming the cornice and basement of any plane 
 
 side 
 
LECTURES ON PERSPECTIVE. 
 
 55 
 
 side of a building, must be drawn towards the same vanishing 
 point upon the horizontal line ; namely, because a line drawn 
 from the eye, parallel to one, will be parallel to all, and conse- 
 quently having found the vanishing point of one line, it be- 
 comes the vanishing point of all others parallel to it. — The 
 upper and lower lines of the windows, kc. in the same side, 
 and in short all lines parallel to them, must be drawn to the 
 same vanishing point. But when the side of a building is pa- 
 rallel to the position, or plane of the picture, the lines will not 
 have any vanishing point. That such lines cannot have a va- 
 nishing point may be easily proved, for let it be required to 
 find the vanishing point of the original line a b (which is pa- 
 rallel to the picture) on the apparatus. According to the rule 
 for finding a vanishing point, a line must be drawn from the 
 place of the eye e parallel to the original line a b till it meets 
 the picture. Put the wire to the place of the eye e in a direc- 
 tion parallel to a b, (for it cannot be put through e, as in other 
 examples, so as to be parallel to a b,) but since a b is parallel 
 to the plane of the picture, and consequently can never meet 
 it, or have an intersecting point ; neither can the wire at the 
 place of the eye meet the picture, to find a vanishing point ; 
 consequently lines parallel to the plane of the picture can nei- 
 ther have vanishing, nor intersecting points upon the picture, 
 but must be drawn parallel. Let a b d f, Plate I, Fig. 1, be the 
 picture, g i a line parallel to the plane of the picture; if a line 
 N o be drawn through e the place of the eye, parallel to g \, it 
 can never meet the picture, and consequently g i cannot have a 
 vanishing point on the picture. 
 
 The indefinite representation of a line in nature, supposed to 
 be extended to an extreme length, is produced by a line drawn 
 
 E from 
 
26 
 
 LECTURES ON PERSPECTIVE. 
 
 from the intersecting to the vanishing point of that line. As for 
 example, the indefinite representation of the line i g apparatus, 
 supposed to be extended beyond c to an extreme length, is pro- 
 duced by a line drawn upon the glass or picture from k its in- 
 tersecting point, to c its vanishing point, and k c is the indefinite 
 representation of g i ; by the same rule p c is the indefinite re- 
 presentation of D B, and o c of F A, kc. kc. Since the indefinite 
 representation of a whole original line infinitely extended, is 
 produced by drawing a line upon the picture, from the inter- 
 secting to the vanishing point ; it follows that the representa- 
 tion of any part of that original line must be a portion of the 
 representation of the whole. For example, the line drawn from 
 K (apparatus) the intersecting point of g i to c its vanishing 
 point, gives the indefinite representation of g i extended ; but 
 the representation of that part only included between g and i, 
 must be found somewhere between k and c ; that is, between 
 the intersecting and vanishing point of g i. This part of the 
 line is marked upon the glass or picture by two red dots, which 
 to the eye at e will appear to conceal the points g and i, and 
 consequently to include the representation of that portion of 
 the line between them. The point between a and f will be 
 found included in red dots upon the line drawn from o, its in- 
 tersecting point, to c its vanishing point. The same may be 
 said of D B. The representation of the part included between 
 A and D in the oblique line a d will be found in the line drawn 
 from s its intersecting, to its vanishing point upon the continu- 
 ation of the horizontal line ; the representation of g n or m k, 
 kc. kc. in the same manner. Universally the representation of a 
 part of a line, will always be found in the representation of the 
 whole, i. e. will be found between the intersecting and vanish- 
 ing points of that line. Upon paper, Plate I, Fig. 2, the line 
 
 drawn 
 
LECTURES ON PERSPECTIVE. 
 
 57 
 
 drawn from k the intersecting, to c the vanishing point of g i, is 
 the indefinite representation of g i ; but since k c is the inde- 
 finite representation of i g continued to an extreme length, the 
 representation of the part included between i and g must be 
 found between k and c ; by the same rule the representation of 
 the part included between a and f, must be found in the line 
 o c, and so of all other lines. 
 
 Upon the apparatus, suppose a thread were drawn from the 
 point F through the glass or picture, to e the place of the eye 
 or point of distance, and another thread from the point a 
 through the glass or picture, to e the place of the eye. It is 
 evident that these two threads coming in straight lines from f 
 and A, to E, must pass through the glass or picture exactly where 
 the points f and a appear upon the glass to the eye at e, and the 
 part included between the perforation of these two threads will 
 represent that part of the line included between a and f, the 
 same of g i, d b, or the oblique lines a d, n g, kc. kc. Now the 
 thread drawn from f through the glass or picture, to e the place 
 of the eye or point of distance in the apparatus, represents a 
 visual ray, and consequently must be a straight line ; and there- 
 fore upon paper, Plate I, Fig. 5, if a line be drawn from a, the 
 point whose representation is required through the picture, to 
 E the place of the eye or point of distance, it will cut o c in 1 , 
 which is the representation of the point a upon the picture, and 
 if the point f be required, a line drawn through the picture 
 from F to E will cut o c in 5, which will be the representation 
 of the point f on the picture, and consequently that part of the 
 line o c included between 1 and 5, is the representation of a f 
 upon the picture; in the same manner the representation of 
 B D will be found upon ? c, and of r s upon u c. In Plate I, 
 
 E ^ Fig. 
 
28 
 
 LECTURES ON PERSPECTIVE. 
 
 Fig. 4, the representation of m k will be found upon k f, by- 
 drawing lines from m and k through the picture to the place of 
 the eye, and k 1 will be the representation of k m. The repre- 
 sentation of D A will be found upon s f, and g n upon r f, and 
 so of all other lines where aground plan is made use of If 
 the perspective representation of a line parallel to the picture 
 is required, as a Plate I, Fig. 2, as this line has neither an in- 
 tersecting nor vanishing point ; it is necessary to draw a line 
 from each end a and b to the bottom of the picture, in order to 
 obtain intersecting points, and as we know the centre of the 
 picture to be always the vanishing point of lines perpendicular 
 to the picture, it is most convenient to draw them perpendi- 
 cular, as A o, B p : o is now the intersecting point of a o, and p 
 of B p ; draw o c and p c for the indefinite representation of a o 
 and BP. If a line be drawn from a through the picture to e 
 the eye, it will cut o c in 1 which is the representation of a 
 upon the picture, and a line from b through the picture to e 
 gives the representation of b upon p c at 4, join 1—4, and the 
 representation of a b is completed in the picture. 
 
 To hnd the vanishing line of any original plane, " a plane must 
 be passed from the eye parallel to the original plane^ and con- 
 tinued till it cuts the picture^ and where it cuts it is the va- 
 nishing line of that original plane, and of all planes parallel to 
 it." The vanishing line of an original plane is found by a me- 
 thod very similar to that employed in finding the vanishing 
 point of an original line ; the only difference being, that in the 
 one a line is to be drawn from the eye to the picture parallel to 
 the original line whose vanishing point is required ; and in the 
 other, a plane is to be passed from the eye till it cuts the pic- 
 ture parallel to the original plane whose vanishing line is re- 
 quired ; 
 
LECTURES ON PERSPECTIVE. - 
 
 quired; where the line from the eye cuts the picture is the 
 vanishing point, and where the plane from the eye cuts the pic- 
 ture is the vanishing line. As an example, let a large card, 
 which may serve as a plane, be passed from the place of the 
 eye in the apparatus, in a position parallel to the ground plane, 
 till it cuts the glass or picture, and it will be found to cut it in 
 the horizontal line; then is the horizontal line the vanishing 
 line of the ground plane, and since the ceiling is parallel in 
 reality to the ground, the horizontal line will be the vanishing 
 line of the ceiling also ; but this must evidently be the case, 
 because, if the card or plane be passed in a direction parallel to 
 the ground, it must be parallel to all other planes parallel to 
 that, and therefore gives the vanishing line of all those planes, 
 as a line from the eye, parallel to any original line, gives the 
 vanishing point of all other original lines parallel to that. So 
 that as all original lines parallel to each other have one and the 
 same vanishing point upon the picture, all original planes pa- 
 rallel to each other have one and the same vanishing line in the 
 picture. If this required any further illustration, it m,ight, per- 
 haps, be rendered stil] more evident, by supposing the spec- 
 tator to be placed on the first floor of a house, and that the front 
 of the house in the opposite side of the street was taken down 
 so as to expose the various floors of that house, it is evident 
 that the floor nearest the level of that upon which the spectator 
 stands will appear the narrowest; as the eye is directed upwards 
 each floor will appear wider and wider, but the under surface only 
 will be seen, those below the eye again will appear wider, Sec, but 
 the upper surface will be seen, shewing, that in order to repre- 
 sent this appearance, all above the eye must be drawn down- 
 wards, and all below upwards ; the lines meeting in a point 
 somewhere upon the horizontal line, that is, in the vanishing 
 
 line 
 
30 
 
 LECTURES ON PERSPECTIVE. 
 
 line of those planes. — The general rules resulting from this 
 theory will be. 
 
 1 . To find the vanishing point of an original line ; a line 
 must be drawn from the place of the eye or point of distance, 
 towards the picture, in a direction parallel to the original line, 
 until it meets the picture, and where it meets it is the vanish- 
 ing point of that original line. 
 
 % All original lines parallel to each other must have the 
 same vanishing point upon the picture. 
 
 3. That the vanishing line of any original plane is that of all 
 original planes parallel to it. 
 
 4. The vanishing points of original lines will always be 
 found in the vanishing lines of the planes in which they lay, 
 for if the whole plane vanishes into any vanishing line, conse- 
 quently every line in that plane must vanish in the same line. 
 
 5. The centre of the picture will always be the vanishing 
 point of original lines perpendicular to the position or plane of 
 the picture. 
 
 6. The vanishing point of original lines oblique to the posi- 
 tion or plane of the picture, will be on one side or other of the 
 centre of the picture, and will be farther from, or nearer to the 
 centre, in proportion as their position is more or less oblique ; 
 as for example, k t upon the apparatus is more oblique to the 
 picture than k m, and consequently a parallel to k t drawn from 
 £, the place of the eye, will find the vanishing point farther off 
 
 upon 
 
LECTURES ON PERSPECTIVE. 
 
 31 
 
 upon the horizontal line, than the vanishing point of k m, which 
 may be proved by putting the wire through the place of the 
 eye e, and carrying it parallel to k t until it meets a continua- 
 tion of the horizontal line, and it will be found much farther 
 from the centre of the picture than the vanishing point of k m, 
 and if it lies still more oblique as k v its vanishing point will be 
 yet farther removed from the centre, till it becomes quite pa- 
 rallel to the picture when it has no vanishing point at all. 
 This may be proved upon paper by finding the vanishing points 
 of oblique lines by rule 1st. 
 
 7. Original lines parallel to the position or plane of the pic- 
 ture cannot have a vanishing point upon the picture, but must 
 be drawn parallel. 
 
 Thus rules have been established for drawing lines parallel, 
 perpendicular, and oblique to the picture according to the prin- 
 ciples of Perspective; and if these be well understood, most of 
 its difficulties may be considered as conquered ; this Lecture 
 therefore requires particular attention, as very much of the 
 science of Perspective is dependent upon it. 
 
 LECTURE 
 
LECTURE III. 
 
 The preceding Lecture contained that part of the Theory of Per- 
 spective relating the Vanishing Points of Lines and Vanishing 
 Lines of Planes. The Practice depending upon that theory must 
 now be considered, and as the Square is a figure of the utmost 
 importance, (almost every thing being done with a reference to 
 it,) particular attention should be paid to the method of putting 
 it into Perspective. 
 
 Let it first be required to put the square a B d f (appara- 
 tus) into Perspective ; in this case one side a b is parallel to 
 the picture, and consequently a f and b d perpendicular to it, 
 find the vanishing point of a f (by Rule 1, Lect. II,) and it 
 will prove to be c the centre of the picture, (Rule 5,) which 
 will also be the vanishing point of its parallel b d, (Rule 
 find the intersecting points of f a, d b, at o and p, now if from 
 0 and p lines are drawn to c the centre of the picture, just 
 found to be the vanishing point of f a, d b, these lines o c, 
 p c will represent a f, d b, infinitely extended ; and if threads, 
 representing visual rays, are supposed to be drawn in straight 
 lines from a and f to e the place of the eye or point of distance, 
 
 F and 
 
34 
 
 LECTURES ON PERSPECTIVE. 
 
 and the same from b and d to e, it is evident they would pass 
 through the glass or picture exactly where the representations 
 of A F, D B would prove to the eye at e, and these re- 
 presentations prove to be upon the lines o c, p c drawn 
 from their intersecting to their vanishing points ; join the 
 points representing a b and f d, and the square is com- 
 pleated. 
 
 Upon paper (Fig. PI. I,) let a b d f be the square upon 
 the ground plan, a b c d the picture, h l the horizontal line, 
 c the centre of the picture, and e the place of the eye or 
 point of distance. To find the vanishing point of a f or b d 
 a line must be drawn from e the place of the eye, parallel to 
 the original line a f or b d, till it meets the picture, (see Rule 1,) 
 which it does in c the centre. The lines a f and b d being 
 perpendicular to the picture, c is found to be their vanishing 
 point, (see Rule 5,) continue a f and d b to the bottom of the 
 picture, and their intersecting points will be found at o and 
 p : draw o c, p c, and you have the indefinite representation 
 of A f, B D, infinitely extended; if from a and f lines be 
 drawn through the picture to e the place of the eye, as by 
 the dotted lines representing visual rays, they will cut the 
 line o c in 1 and 5, which are the representations of the points 
 a and F upon the picture, and if from b and d lines be drawn 
 through the picture to e, the representations of b and d are 
 obtained upon the picture at 3 and 4 ; join 1 4 and ^ 3, and 
 the square is compleated within the figures 1 2 3 4. If the 
 ground plan consisted of a greater number of regular parts, 
 still the operation would be the same ; as for example, the 
 line N M being continued, would find its intersecting point 
 at X, and being parallel to a f has the same vanishing point 
 
 c, (by 
 
LECTURES ON PERSPECTIVE. 
 
 35 
 
 c, (by Rule 2,) draw xc and you have the indefinite re- 
 presentation of M N, if from m and n lines be drawn to the 
 place of the eye or point of distance e, they will give the 
 points M and n upon x c at 5 and 6 ; draw lines parallel to 
 the bottom of the picture at 5 and 6, till they meet the line 
 o c, and the figure is compleated» 
 
 It may next be required to put the square in Perspective, 
 having one side given in the picture; but before this is at- 
 tempted, it is necessary to explain the method of cutting off 
 any given portion from a line in Perspective. As for exam- 
 ple, from the line a c in Perspective, (Fig. 5, Plate I,) let it 
 be required to cut off a portion equal to the given line a b, 
 A c is the line from which a portion is to be cut off, therefore 
 place one foot of the compasses in the vanishing point of a c 
 (which is c the centre of the picture) and the other foot at e 
 the place of the eye or point of distance ; transfer the point 
 of distance e to the horizontal line at e, by making c e equal 
 to c e ; draw from b (the extreme end of a b) to e the point 
 of distance transferred to the horizontal line, and where it 
 cuts A c in F is the length required, and a f is in Perspective 
 the representation of a portion equal to a b, but being fore- 
 shortened does not appear so long as a b. In the instance just 
 given, the line a c from which the portion was to be cut off, 
 was the representation of a line in reality perpendicular to the 
 plane of the picture ; for its vanishing point was the centre. 
 (See Rule 5.) 
 
 The vanishing point of a line, already drawn in the picture, 
 will always be formed by continuing that line till it strikes the 
 vanishing line of the plane in which it lays, but as the 
 
 F 2 horizontal 
 
36 
 
 LECTURES ON PERSPECTIVE. 
 
 horizontal line is the only vanishing line made use of, hitherto 
 the vanishing points of lines drawn in the picture will be 
 found by continuing those lines till they strike the horizontal 
 line. 
 
 Let it now be required to cut off a portion equal to a b 
 (Fig. 5, Plate 1,) from the oblique line a d. Because d is the 
 vanishing point of a one foot of the compasses must be 
 placed in d and the other in e the point of distance ; transfer 
 the point of distance to the horizontal line at f, draw from b 
 to f, and where b f intersects ad at g, is the point required ; 
 and A g is in Perspective the representation of a line equal 
 to A B ; if A B is called twenty feet, a f or a g are each the 
 representation of twenty feet in Perspective. 
 
 A sufficient proof of the truth of this method may be 
 obtained thus : Let it be required to cut off from a c a 
 portion equal to a b, (Fig. 5, Plate I,) complete the geome- 
 trical square a b m n upon a b ; now the line a n is equal to 
 A B being a side of the square ; and being perpendicular to 
 the picture, its representation vanishes in the centre, and 
 A c is the indefinite representation of an; draw from n 
 through the picture to e the point of distance, and where it 
 cuts A c in F is the point required, and a f is the Perspective 
 representation of a n equal to a b, and it was found equal to 
 A B by the method without the geometrical plan. As this 
 rule is very useful, another proof may perhaps be allowed : 
 draw the diagonal n b of the square a b m n ; now if it be re- 
 quired to find the representation of the point n on the pic- 
 ture^ it will first be necessary to find the vanishing point of 
 the oblique line n b by drawing its parallel from e (Rule L) 
 
 and 
 
LECTURES ON PERSPECTIVE. 
 
 37 
 
 and e is the vanishing point of n b ; a hne drawn from b its 
 intersecting, to e its vanishing point, gives the indefinite re- 
 presentation of N B, and to find the point n upon b e in the 
 picture, a Hne or visual ray must be drawn from n through 
 the picture to e, cutting B e in f which is the representation 
 of N, and A F is the representation of a n equal to a b, which 
 was to be proved. 
 
 The rule for cutting off a given portion from a Hne in Per- 
 spective may be thus expressed: at the vanishing point of 
 any line from which a given portion is to be cut off, place 
 one foot of the compasses, and with the other transfer the 
 point of distance to the horizontal line : upon the ground line 
 set off the portion intended to be cut off, and draw from that 
 point through the line in Perspective to the point of distance 
 transferred to the horizontal line, and it will cut off the 
 portion required'. ❖ 
 
 It will now be required to put the square in Perspective 
 without the assistance of a ground plan, (i. e.) by having one 
 side given in the picture, and let that side be parallel to the 
 picture; for example, in the picture abed, (Fig. 6, Plate I,) 
 a b is the line given, [I e.) a b is the side of a square parallel 
 m nature to the plane of the picture, and it has been shewn, 
 that if an end of a right-angled or square object is parallel to 
 the plane of the picture, the sides must be perpendicular to 
 
 it, 
 
 * In cases where the Hne, from which a portion is to be cut off, does not begin at 
 the ground line, but at some distance from it within the picture, it is,generally more 
 convenient to draw a parallel to the ground line from the nearest end of the line in 
 Perspective, upon which line the given portion may be set off and a line drawn from 
 thence to the point of distance transferred as befo re. 
 
38 
 
 LECTURES ON PERSPECTIVE. 
 
 it, and consequently have their vanishing point in the cen- 
 tre; (see Rule 5,) therefore the lines drawn from a and b 
 forming the sides of the square, must be drawn to c the 
 centre, as a c, b c. Now a g and b c are indefinite repre- 
 sentations of the sides of the square, and a portion is to be 
 cut off from a c equal to a b ; to do which one foot of the 
 eompasses must be placed in the vanishing point c of a c, 
 and the other foot at e the point of distance ; transfer or carry 
 the point of distance to the horizontal line at e, and where the 
 line drawn from b to e cuts a c in f is the point required, 
 and A F is equal to a b, (i. e.) a f is the Perspective repre- 
 sentation of one side of the square, of which a b is the side 
 given; by transferring the point of distance e to the hori- 
 zontal line at f on the other side of the centre, a portion 
 may be cut off from b c at d equal to b a for the other side 
 of the square, but since the line opposite to a b in the original 
 square is parallel to it, and a b is parallel to the plane of the 
 picture, a Hne drawn from f parallel to a b till it meets b c, 
 will answer the purpose without the trouble of transferring the 
 point of distance to both sides of the centre of the picture, 
 and F D is in Perspective equal to a b, and the square a b d f 
 is compleated. 
 
 This method may be explained thus. From the two ex- 
 treme points of the given line draw to the centre of the pic- 
 ture which is the vanishing point of the sides of the square, 
 set off the distance of the picture upon the horizontal line, 
 and draw from one end of the given line through either of 
 the forementioned, to the point of distance transferred to the 
 horizontal line, and where that line cuts the line drawn from 
 the other end of the given line to the vanishing point, is the 
 
 point 
 
LECTURES ON PERSPECTIVE. 
 
 39 
 
 point required ; draw a parallel to the given line from that 
 point and the square is compleated. 
 
 The square lying on the ground with one side parallel to 
 the picture having been put in Perspective, it will now be 
 required to put the square in Perspective, standing perpen- 
 dicularly upon the ground and at right angles to the plane of 
 the picture, (or perpendicularly to it^) having one side given 
 as A B ; (Fig. 7, Plate I,) the line of the bottom of the plane 
 must therefore vanish in the centre, by Rule 5 ; and as the 
 top and bottom are parallel to each other, they must have 
 the same vanishing point, as a c, b g, (see Rule 2,:) a b is the 
 given side of the square, and it is necessary to cut off from 
 B c a portion equal to a b for the bottom of the square; in 
 order to do this draw from b a parallel to the bottom of the 
 picture as b g, and set off upon it b d equal to a b ; from c 
 the vanishing point of b e transfer the point of distance to the 
 horizontal line at e, and draw ne which will cut b c in i, and 
 b I is equal in Perspective to b d, (i. e.) to a b, and conse- 
 quently represents the bottom of the square ; raise a perpen- 
 dicular at I till it meets a c in k, and a b i k is the square re- 
 quired. If the plane be twice as long as high, cut off from b 
 a length equal to twice a b as b draw f e and it cuts b c in 
 N, erect the perpendicular n m, and a b n m is a plane twice 
 as long as high; if it is required to be three times the length, 
 make b g equal to three times a b, and draw c e which cuts 
 b c in o, raise o p, and a b o p is a plane three times as long as 
 high ; and thus for any length. Let it now be supposed that 
 the square plane (of which a b is the side given) stands in a 
 position oblique to the plane of the picture, and it will con- 
 sequently have its vanishing point on one side of the centre 
 
 of 
 
40 
 
 LECTURES ON PERSPECTIVE. 
 
 of the picture, by Rule 6. Let 1 be the vanishing point of 
 the obUque line b i upon which the square stands ; draw a 1 ; 
 and A 1^ B 1 are indefinite representations of the top and 
 bottom lines of the square plane. A portion must next be 
 cut off from b 1, which is done as in the preceding example, 
 by drawing a parallel to the bottom of the picture from b, 
 and setting off b d equal to a b ; then with one foot of the 
 compasses in 1, the vanishing point of b 1, and the other 
 foot in E, transfer the point of distance to the horizontal line 
 at 5, draw d ^, cutting b 1 in 3, and b 3 is equal to b 
 (i. e.) to A B, and consequently represents the bottom of the 
 oblique square. Erect a perpendicular at 3, till it meets a 1 
 in 4, and a b 3 4 is the squcire required. If twice the length 
 in proportion to the height is wanted, make b f equal to 
 twice A B, and draw r 2 cutting b 1 in 5, and a b 5 6 is a 
 plane twice as long as high. The square a b 3 4 being more 
 turned towards the eye, appears much wider than a b i k al- 
 though they are the representations of the same square in 
 reality, and a b is common to both. 
 
 Having put the square into Perspective with one side pa- 
 rallel to the plane of the picture, both by the ground plan 
 and by one side given in the picture ; it remains to erect a 
 building upon this foundation: and as an immediate step to it, 
 it may be advisable to put the cube into Perspective. ❖ Let 
 A b (Plate 2, Fig. 1,) be the given line, from a and b draw 
 to c the centre as a c, b c, cut olf from a c a portion equal to 
 A B at F, and compleat the square a b d f: at a and b raise 
 perpendiculars equal in length to a b, as a i, b g ; join i g and 
 
 A B G I 
 
 * A cube is a solid figure consisting of six equal sides. 
 
LECTURES ON PERSPECTIVE. 
 
 41 
 
 A B G I is the end of the cube parallel to the plane of the pic- 
 ture: from G and i draw to c the centre; raise perpendicu- 
 lars at F and d till they meet i c, g c in k and m, join k m, 
 and the cube is compleated. The same operation may be 
 performed by No. 2, which is below the horizontal line ; and 
 also by No. 3, which is above it, the same letters of reference 
 applying to each. 
 
 Fig. 2, Plate % contains buildings in Perspective afte 
 end being parallel to the plane of the picture, and hating 
 the same letters of reference with the cubes Fig. 1 ; except- 
 ing those which are hidden by the solidity of the building. 
 A B Fig. 2, is the line given, let the height of the building be 
 equal to a b, draw a i, b g; join i g and a i b g is the end of 
 the building, No. 1 ; the same may be done by No. 2, and 
 as the building is to be twice as long as it is high, a length 
 equal to twice b g must be set off upon the base line, as b o, 
 draw from o to the point of distance e upon the horizontal 
 line, and it cuts b c in d, and b d is the representation of a 
 portion equal to twice b g ; compleat the figure, and b g k d 
 is the side of the building perpendicular to the picture, and 
 c is its vanishing point, (Rule 5,) the chimnies having one 
 side parallel to b g k d must have c for the vanishing point 
 of that side ; the upper and lower lines of the windows being 
 parallel in nature to g k or b d must have the same vanish- 
 ing point, (Rule Z) Having drawn the chimney nearest the 
 eye at n, and knowing the other to be of the same height 
 and size, draw from the upper corners to the vanishing point 
 c, and these lines will give the proportion to the other, 
 as is seen by the dotted lines. The windows in the end 
 parallel to the picture, having their upper and lower lines 
 
 G parallel 
 
LECTURES ON PERSPECTIVE. 
 
 parallel also to the picture, will consequently be drawn pa- 
 rallel and not vanish in any point ; the same operation must 
 be performed in putting No. 3 in Perspective, except that 
 it is better to transfer the point of distance to f and draw 
 from p to f, and a c will be cut at f, and ^ f in Perspective 
 will equal twice a i. In the centre building the end only 
 is seen; but a considerable portion of one side of each of 
 the others appears. If the centre building No. I be re- 
 moved, the two sides No. 2, and 3 may be continued to a 
 regular street by making the length equal to 20 or 30 times 
 instead of only twice. The same building above the hori- 
 zontal line as at No, 4, will, from its situation, have its lines 
 directed downwards toward the vanishing point. 
 
 LECTURE 
 
LECTURE IV. 
 
 In the last Lecture the Square was put into Perspective^ having 
 one side parallel to the Picture, both by the ground plan, and 
 by one side given in the Picture ; buildings were also put into 
 Perspective with one side parallel to the Picture. The method 
 of putting the Square into Perspective when neither of its sides 
 are parallel to the Plane of the Picture, but every side oblique, 
 will now be explained. 
 
 Let k n g m be the square in the ground plan, (Fig. 3, 
 Plate II,) the sides of this square are all oblique to x y the 
 ground line or bottom of the picture ; e is the point of dis- 
 tance, c the centre of the picture, and h l the horizontal line. 
 The picture being thus prepared, find the vanishing point of 
 the side g m or of its parallel n k by Rule 1 , and i will be the 
 vanishing point required; by the same Rule s will prove the 
 vanishing point of g n or of its parallel m k ; continue g m 
 and GN to their respective intersecting points q and r, draw 
 from Q and k to s the vanishing point of g m and n k, and 
 from R and k to i the vanishing point of g n and m k, and 
 
 G ^ the 
 
44 
 
 LECTURES ON PER'sPECTIVE. 
 
 the points in which they intersect each other in the picture 
 at k n g m give the representation required. This may be 
 proved by drawing lines from the points g m n k in the 
 ground plan through the picture to e the point of distance, 
 and they will pass through the same points k n g m in the 
 picture. The method of finding the vanishing points of lines 
 was so fully explained in the second Lecture, that it will be 
 unnecessary to repeat this example upon the apparatus, but 
 those who wish to do it may find the vanishing and inter- 
 secting points of the square k m g n on the apparatus, and 
 covering the ground plan, compleat the figure upon the glass 
 or picture by the rules of Perspective ; remove the covering 
 from the plan, and if the vanishing and intersecting points are 
 true, the representation upon the glass will appear to the eye 
 at E to be the exact tracing of the original square upon the 
 ground plan. 
 
 Let it now be required to draw the square in Perspective 
 when oblique to the picture, having one side given upon the 
 picture, and let k m be the given side, Plate II, Fig. 3, (it 
 is supposed that the line k m is the only line Jirst drawn in 
 the picture, as in No. 1, and that the square is to be com- 
 pleated upon that line k m Fig. 3, as one of its sides) continue 
 K m to the horizontal line, and where it meets it at i is its va- 
 nishing point, but in order to find the vanishing point of the 
 other side of the square, a line must first be draAvn from i 
 the vanishing point of Km, to e the point of distance, and 
 since a square is formed of right angles, a right angle must 
 be made at the point of distance e with the line i e ; continue 
 the line forming the right angle with i e, from e till it meets 
 
 the 
 
LECTURES ON PERSPECTIVE. 
 
 45 
 
 the horizontal line, which it must do at s, thus is s the vanish- 
 ing point of the other side of the square; draw k s: but a 
 portion must be cut off from k s equal to the given side k m, 
 and in order to find the real length of Km, (for k m is the 
 Perspective or fore-shortened appearance of a certain length,) 
 one foot of the compasses must be placed in i the vanishing 
 point of K m, and the point of distance e transferred to the 
 horizontal line at e, (making i e equal to i e,) draw from e 
 through m, and it will meet the bottom of the picture at o, 
 then is K o the real length of which k m is the representation 
 upon the picture: from k set off a distance equal to k o on 
 the other side of k as k ? ; set one foot of the compasses in s 
 the vanishing point of k s, and transfer the point of distance e 
 to the horizontal line at f, making s f equal to s e, draw from 
 p to f and the point in which it intersects k s at ?t gives the 
 representation in Perspective of a portion equal to k p, (i. e.) 
 to K m, which was required : and because, of the four sides of 
 a square two and two must be parallel to each other in reality, 
 the representation of those sides will have the same vanishing 
 points, (Rule 2^) draw n i and m s, and where they intersect 
 at g compleats the square k m g n. The truth of this requires 
 no other proof than that the same diagram answers for both 
 demonstrations, whether the ground plan is used or a line given 
 in the picture. 
 
 A building may now be put into Perspective viewed upon 
 the angle, or having neither side parallel to the picture, but 
 every side oblique; and k a (Plate II, Fig. 4,) shall be a per- 
 pendicular to the ground representing the corner of the build- 
 ing nearest the eye, and k n the inclination of the base line 
 of the same building upwards, as near as the person about to 
 
 draw 
 
46 
 
 LECTURES ON PERSPECTIVE. 
 
 draw it from nature can judge continue k n to the hori- 
 zontal line, and where it meets it at s is the vanishing point 
 of K n, and consequently the vanishing point of the top line 
 of that side of the building from a, because the top and 
 bottom of the same side are in reality parallel to each other. 
 Draw A s : upon n, erect a perpendicular till it meets as in b, 
 and K a B n is one side of the building viewed upon the angle ; 
 the representation of the other side of the building is found 
 by the foregoing rule, thus ; draw from s the vanishing point of 
 K n to E the point of distance, and at e make a right angle 
 with s E, and continue the line till it meets the horizontal 
 line at i, and i is the vanishing point of the other side of 
 the building, as in the foregoing example of the square ; draw 
 K I and A I, and if each side of the building is as long as it 
 is high, set off k p and k o upon a parallel to the bottom of 
 the picture at k ; equal to k a. Find e and f (the transferred 
 distances) as before, and draw from p to f and from o to e, and 
 the points n and m will be found upon k s and k \, erect the 
 perpendicular mo; (n b being already drawn,) and the sides 
 of the building are put in Perspective. The top of the roof, 
 chimnies, windows, kc. will of course go to the vanishing 
 points of their respective sides ; suppose another building 
 upon 0 R, with q t for its height ; by continuing q r to the 
 horizontal line, its vanishing point will be found at v, and 
 by proceeding as in the last case, the other vanishing point will 
 be at w ; compleat the figure as before. 
 
 This rule may be thus given. Having drawn the perpen- 
 dicular 
 
 * It is of no consequence whether the upper or lower line is taken as the line 
 given, but the line farthest from the horizontal line, is to be preferred, because its 
 apparent inclination will be more evident. 
 
LECTURES ON PERSPECTIVE; 
 
 41 
 
 dicular representing the angle nearest the eye of the building 
 viewed obliquely, and determined as near as possible the in- 
 clination of the top, or bottom line of either side, (for, as 
 before observed, it is of no consequence with which the 
 operation is begun,) continue the line till it meets the 
 horizontal line which is the vanishing point of that line, and 
 of all lines parallel to it ; draw from that vanishing point to 
 the place of the eye or point of distance, and there make a 
 right angle ; continue the line to the horizontal line, and 
 where it meets it, is the vanishing point of the other side, 
 and also of all lines parallel to the top or bottom of the other 
 side of the building. . 
 
 In the example just given, the angle at the eye was to be a 
 right angle, because the object was a right angled object, and 
 that which most commonly occurs in buildings : but in every 
 case, whatever may be the form of the original object, a 
 similar angle must be made at the eye, in order to obtain its 
 vanishing points. 
 
 Let it now be required' to find the point of distance, with which 
 any right angled building viewed upon the angle was drawn, 
 having the two vanishing points and centre of the picture given. 
 Suppose the building a a b n k m (Plate II, Fig. 4,) to have 
 been drawn from nature ; by continuing the lines k n or Km 
 to the horizontal line, s and i will prove the vanishing points, 
 c is the centre of the picture, and since the point of distance 
 is always in a line perpendicular to the centre of the picture, 
 draw c E at pleasure, upon c e assume a point as f ; by laying a 
 ruler from either of the vanishing points s or i to the point 
 F, say s, it will be seen whether a right angle at that point, 
 
 with 
 
48 
 
 LECTURES ON PERSPECTIVE. 
 
 with such line, will meet the horizontal line in the other 
 vanishing point i; and if it does not, the point f is not the 
 point of distance required, but too short; for the second 
 vanishing point would fall considerably nearer the centre of 
 the picture than i. Assume the point g and it will be found 
 too great, for the second vanishing point would fall beyond 
 the point i; the true point of distance then lies between f and g, 
 and will be found at e, where the right angle made with s e 
 strikes the horizontal line exactly in i. 
 
 This will be found of great use where there are many 
 regular objects in the same sketch, for having thus obtained 
 the point of distance by means of the nearest object which is 
 presumed to have been drawn with attention, the other may 
 be corrected by the same point of distance, and their respective 
 vanishing points, kc. determined. 
 
 It is recommended to every one who wishes to become 
 thoroughly acquainted with these rules, to draw all the 
 figures in their order according to the directions given in the 
 general rules. 
 
 Thus have right angled buildings been put into Perspective, 
 both when viewed with one side parallel to the plane of the 
 picture, and when viewed upon the angle, and as the right angle 
 is most generally used in the construction of buildings, these 
 rules, well understood, will be found of great utility. 
 
 THE 
 
THE CIRCLE. 
 
 In representing the Circle according to the rules of art, the 
 square is found so necessary that the method of putting it 
 into Perspective should be perfectly understood, and also that 
 of cutting off any given portion from a line in Perspective, 
 before the circle, or any figure depending upon it, can be 
 attempted with success. 
 
 Let it be required to put the circle into Perspective by the 
 ground plan R M k, (Plate III, Fig. 1,) draw the diameters 
 R s, km; describe a square about the circle touching the ends 
 of the diameters in r m s and k ; put the square a f b d into 
 Perspective and also the diameter r s, (by drawing it to its 
 vanishing point c the centre of the picture,) and r c is cut 
 by B e at which is the representation of the centre p of 
 the circle ; for if a portion was required to be cut off from 
 R c equal to r b, (i. e.) equal to r p, it would be done by 
 drawing a line from b through r c to e the point of distance 
 transferred to the horizontal line, and b e cuts r c in /?, there- 
 fore p is the representation of the point p (i. e.) of the centre 
 of the circle. Through the point p draw a parallel to the 
 
 H bottom 
 
50 
 
 LECTURES ON PERSPECTIVE. 
 
 bottom of the picture, and the representation of the diame- 
 ter K M is obtained at k m; therefore k m is the representation 
 of one diameter and r s of the other ; and if an oval be de- 
 scribed through the points r m s k, it will represent the circle 
 r M s K in Perspective. This carefully done will be sufficient 
 for common purposes, but when a greater degree of accu- 
 racy is required, diagonals may be drawn in the ground plan, 
 as F A p, and through their intersections with the circum- 
 ference of the circle at 1 ^ 3 and 4, draw the lines no, g i, 
 T V, and u w ; put t v and u w into Perspective, and the dia- 
 gonal A D, by drawing it to d as Ad, and where the diagonals 
 A d and b f, cut w c and v c, draw the parallels n o and g i, 
 and the points I 2, S and 4 are obtained upon the picture ; 
 draw an oval through s^kl r4 m3, and it is the represen- 
 tation of the circle r1 k^sS m4. 
 
 The circle may also be put into • Perspective, having one 
 diameter given in the picture, as a b No. ^, Fig. 1 ; find the 
 centre o of the diameter a b^ which is the centre of the cir- 
 cle and also of the square in which it is described. The 
 square of which a b is one diameter and o the centre^ must 
 first be put into Perspective ; and since the given diameter is 
 parallel to the picture, the sides of the square must be per- 
 pendicular to it, and therefore lines must be drawn from the 
 vanishing point of the sides of the square (which is c the centre 
 of the picture) through a, o, and b : transfer the point of 
 distance to the horizontal line at e, and from e draw through 
 o the centre of the circle and it will cut the line b c in m, 
 and it will also cut g a continued in i. At m and i draw pa- 
 rallels to A b, as g m, I K, and g m k i is a square in Perspec- 
 tive of which A b is the diameter parallel to the picture, and 
 
 consequently 
 
LECTURES ON PERSPECTIVE. 
 
 51 
 
 consequently f d is the other or foreshortened diameter ; 
 draw an oval through the points f a d b, and it is the repre- 
 sentation of a circle in Perspective whose given diameter was 
 A B parallel to the picture.* This rule is useful for repre- 
 senting columns, round towers, or any other circular objects in 
 Perspective in any part of the picture. As for example, if a 
 circular piece of water form part of a scene in nature, its dia- 
 meter parallel to the picture may easily be determined by 
 its apparent proportion to the other objects already drawn, 
 and the form of the oval be decided by the foregoing rule. 
 Again, suppose a d b f, (Plate III, Fig 1,) No. 3, the base of 
 a circular tower whose height is b n, and it is required to find 
 the degree of curvature of the top and of the bottom; b n 
 and A p are the sides of the tower, and p n the longest dia- 
 meter of the circle at the top : first put the circle on the 
 ground into Perspective, whose given diameter is a b, (in 
 the same manner as No. %) then proceed with the top ex- 
 actly as in the former case, by finding the centre of the 
 given diameter p n at o, and o is the centre of the circle ; 
 draw from the vanishing point c through the points p, o, 
 and N, and from e through the centre of the circle o, and 
 it will cut PC in s, and c n if continued in v ; draw the pa- 
 rallels s T, V u, and the shortest diameter r q is obtained ; 
 draw an oval through the points p o n r, and the representa- 
 tion of the top of the tower is compleated. 
 
 If a circle were to be described upon the diameter x y so 
 much nearer the horizontal line, it would have the appear- 
 ance of a flatter oval, and^ if upon the horizontal line, would 
 
 H Z appear 
 
 * The diameter may be taken parallel to the picture in most cases. 
 
LECTURES ON PERSPECTIVE. 
 
 appear only a line as z k, which may be easily seen by 
 proceeding at those points according to rule. 
 
 Thus far relates to circles laying upon the ground or in 
 planes parallel to the horizon, but as carriage wheels, water 
 wheels, kc. often occur, it will be necessary to shew how 
 they are to be put into Perspective. Let it first be required 
 to put a wheel into Perspective standing upright, or perpen- 
 dicular to the ground, and in a position perpendicular also 
 to the flam of the picture: its given height or longest dia- 
 meter is A B, (Fig. 5, Plate III.) Proceed as in the former 
 example by finding the centre o of the given diameter a b, 
 and as the wheel stands perpendicular to the plane of the 
 picture, the top and the bottom of the square in which the 
 circle (or wheel) is to be described, must be di*awn to c the 
 centre of the picture as the vanishing point ; (see Rule 2,) 
 draw from the vanishing point c through a o b, and since b a 
 is the whole diameter of the wheel, b o is the half of it : one 
 half of the diameter of the wheel is required upon o c and 
 the other half upon op; in order to find the half upon o c, 
 a portion must be cut off from b c, equal to b o, (i. e.) half 
 the diameter; draw a parallel to the bottom of the picture 
 from b, and set off b d equal to b o : draw from d to e (the 
 point of distance transferred to the horizontal line) and b c 
 is cut at F, then is b f the representation of a portion equal 
 to B o: raise the perpendicular f g at f, and o c is cut at i, then 
 is o I the representation of a portion equal to b o, or half the 
 diameter, and b a g f is one half of the square in which the 
 circle is to be described, and in order to find the other half 
 on the other side of a b, draw from either of the corners of 
 the square f, or c, through o its centre, till it meets the line 
 
 c A continued 
 
LECTURES ON PERSPECTIVE. 
 
 53 
 
 c A continued in k, or c b in m; raise the perpendicular m k, 
 and the square f g k m is put into Perspective whose given or 
 longest diameter is a b, and shortest found to be i p ; draw 
 an oval through the points a p b i and the wheel is compleated 
 in Perspective. If another wheel of the same height sitood 
 nearer the centre of the picture or almost opposite the eye, 
 as w U;, the oval representing it would appear narrower, as 
 may be seen in the figure. Let r s be the diameter of a 
 wheel standing in an oblique direction and represented in 
 the same picture, its vanishing point being at 3 ; the operation 
 is the same as in the preceding case, only using the vanishing 
 point 3 instead of c the centre of the picture; the point of 
 distance transferred will be at 4 upon the horizontal line, and 
 the shortest diameter found to be v t ; draw an oval through 
 the points r v s t, and the figure of the wheel is represented 
 as required.* 
 
 A water wheel adjoining a mill will have the same position 
 with regard to the picture, with the side of the mill to which 
 it is fixed ; and having drawn its longest diameter, its shortest 
 may be determined by the rule, and the wheel compleated in 
 Perspective, but as water wheels are frequently very broad, it 
 may sometimes be necessary to describe a circle perspectively 
 upon the inner as well as the outer circle. 
 
 In the first example of wheels standing upon the ground, 
 when the half of the square b a g f was found ; it was said, 
 that in order to find the other half, lines should be drawn 
 
 from 
 
 * The disadvantage of too short a distance is here evident, the nearer half t R s 
 of the circle appearing disproportioned to the farther half v r s ; this is unavoidable 
 from want of sufficient space in the plates. 
 
54 
 
 LECTURES ON PERSPECTIVE. 
 
 from the corners g, and f, through o the centre of the cir- 
 cle or wheel, and where those lines met c b, or c a continued, 
 the other corners of the square were founds and a perpendi- 
 cular raised from m to k would compleat the square m f c k. 
 This may be easily proved by considering, that if diagonal 
 lines are drawn from the corners of a square, they will inter- 
 sect exactly in the centre ; therefore, if from the two cor- 
 ners F and G of the square in Perspective^ diagonal lines be 
 drawn through the centre o, they will of course find the 
 other corners by their junction with the two lines g f b 
 continued. This method is very useful ; for, if a door be in 
 the middle of one side of a building thrown into Perspective, 
 it is easy to determine its place, by drawing diagonals from 
 the corners, and in their passage they will intersect in the 
 centre, which centre will appear nearer to one end than the 
 other, as may be seen in the example, where a b d f (Fig. 4, 
 Plate III,) is the side of a building in Perspective, the dia- 
 gonals cross each other at o, which is the centre in Perspec- 
 tive, of the side a b d f ; the centre of the door would there- 
 fore be immediately under the point o and the middle win- 
 dow, if there be an odd number, as 5, 7, 9, &:c. directly 
 over that point as in the figure, but o appears much nearer 
 to the end d b, than to the end f a, for the side of the build- 
 ing being seen in Perspective, the half nearest the eye will 
 appear to occupy more space upon the picture, than the half 
 farthest from it. By this method the centre house of a street 
 may be determined, for if a b d f be considered as one side of 
 a street consisting of 5, 7, 9, kc. houses, the point o would 
 give the middle of the door of the centre house, &;c. kc. 
 
 Doors or casements, when open, may be represented with 
 
 great 
 
LECTURES ON PERSPECTIVE. 
 
 55 
 
 great accuracy by means of the circle, for a door describes a 
 Gompleat semicircle in revolving upon its hinge till checked 
 by the wall, for let. a b d f (Plate VIII, Fig. 6,) be the door, 
 in its revolution upon its hinge a f it would describe a semi- 
 circle upon the ground which in perspective, (the distance of 
 the picture being c e, and its transferred distance at e,) would 
 be big; suppose the door opened as far as m, and a m re- 
 presents the bottom of the door, continue the line a m till it 
 meets the horizontal line at o, and o is its vanishing point; 
 draw from o through f at pleasure, raise a perpendicular from 
 M till it cuts o F continued, which it does at n, and m n f a 
 is the representation of the door thus far opened. Let the door 
 be supposed to open to the point k, continue k a to its va- 
 nishing point p^ draw from p through f at pleasure, raise the 
 perpendicular k r, and the door k r f a is compleated, for the 
 upper and lower lines of the door being parallel to each other 
 must have the same vanishing point. The same operation 
 will answer equally well for windows, whether above or belo^y 
 the horizontal line. 
 
 If the door or window should be situated obliquely with 
 respect to the picture, so that the vanishing point does not fall 
 in the centre, a circle must be described upon the oblique 
 diameter by means of the square, but in this case a second va- 
 nishing point must be found (as in the preceding part of this 
 lecture,) for the other diameter. 
 
 LECTURE 
 
LECTURE V. 
 
 The method of putting the Square and Circle into Perspective ; 
 Buildings both parallel and oblique to the Picture, round 
 Towers, Columns, &c. has been explained: it now remains to 
 shew how to give a due proportion to objects in any part of the 
 Picture, he. 
 
 Upon the glass in the apparatus, the lines from 1 to S and 
 from 6 to A, would, if continued, meet in a point upon the 
 horizontal line, and as both vanish in the same point, they are 
 the representation of original lines parallel to each other, and 
 since the lines representing from 1 to 6, ^ to 5, and from 3 to 4 
 are the representations of lines of equal length, it is evident, 
 that if any line be drawn parallel to 1 , 6 between the two lines 
 1 c and 6 c, it will be the Perspective representation of a line 
 equal in length to 1, 6, and when near the horizontal line will 
 appear very short, because it represents a line very far re- 
 moved from the eye. Plate % Fig. 5, the points 1, ii, iii, iv, 
 V, 6, in the ground plan, are represented by 1, 3, 4, 5, 6, 
 on the picture, and from 3 to 4 is evidently the representation 
 of III, IV, in the ground plan, but iii, iv, is in reality as long 
 
 I as 
 
58 
 
 LECTURES ON PERSPECTIVE. 
 
 as 1, 6, and 8^ 9, is by the same reason equal in Perspective 
 to 1, 6, therefore if from 1, to 6, be called six feet, from 8, to 
 9, is also six feet, but appears much shorter, because it is farther 
 removed from the eye: if it were required to place an object six 
 feet in length at a given point in the picture, as at a, it would 
 be done by laying the ruler from a in a direction parallel to 
 the bottom of the picture till it meet 1 c, in 7, there draw the 
 parallel 7, 7, till it meet 6, c, measure 7, 7, and place it at a, 
 and a B is a length in that part of the picture equal to six 
 feet. If a length equal to six feet be wanted at d, draw 
 from D a parallel to the bottom of the picture till it meets 
 6 c at 5, draw 5, % measure 5, % with compasses, and place 
 it at D and d f represents six feet at d ; by the same rule g m 
 represents 6 feet at g. This method will do for objects lying 
 upon the ground, or in planes parallel to the horizon, but if 
 it be required to give to the human figure, or any other object 
 standing upon the ground, its due proportion in any part of 
 the picture, it will be necessary to make use of a line called 
 the line of elevation: this is an exact resemblance of the 
 forementioned line, except that it is raised perpendicular to 
 the ground, instead of laying upon it. As for example, let 1, 
 6 be called six feet, or the height of a man ; raise a perpendi- 
 cular at 1 equal to 1, 6, as i, k, and by drawing from k to the 
 same vanishing point as 1, c, we know that all perpendiculars 
 between the lines \, c, and k, c, will be the Perspective re- 
 presentations of lines equally high with 1, k, because i c and 
 R c represent lines parallel to each other : this may be seen in 
 the apparatus upon the glass as before, where the lines repre- 
 senting from 1 to 3, and from 7 to 9 meet in one point in the 
 picture if continued, and the line representing from 3 to 9, is 
 the Perspective representation of a line equally high with 1,7; 
 
 therefore 
 
LECTURES ON PERSPECTIVE. 
 
 59 
 
 therefore in order to put a figure six feet high in Perspective 
 at A, (Fig. 5.) a line must be drawn from a parallel to the 
 bottom of the picture till it cuts 1 c in 7 ; raise the perpendi- 
 cular 7 N, measure this line with compasses and place it at a, 
 then is the perpendicular a b, the Perspective representation 
 of six feet at a, or the height of a man. If it be required at d, 
 a parallel to the bottom of the picture from d will cut 1 c in % 
 raise the perpendicular ^, o, and place it upon d, then is d, d, 
 the Perspective representation of six feet at d ; if the same thing 
 be required at p, draw the parallel from p and it will cut 1 c 
 in a, raise a x and place its height upon p, and p i is the 
 Perspective representation of six feet. If any other height be 
 required, the line of elevation must be carried higher ; as for 
 example, if eight feet be wanted in any part of the picture, it 
 must be raised to r by adding two feet to 1 k, and 1 r will be 
 the representation of eight feet, and all perpendiculars 
 between 1 c and r c, are the Perspective representation of 
 lines equal to eight feet. It is of no consequence what part 
 of the horizontal line is chosen for the vanishing point of 
 the lines from the top and bottom of the line of elevation, 
 as may be seen by supposing q to be the point, and if the 
 same operation be performed, (i. e.) drawing the parallels 
 to 1 Q instead of 1 c ; the lines will be found exactly the 
 same length as when done by the other vanishing point ; 
 hence it will be perceived that the line of elevation may be 
 placed out of the margin of the picture, in order to avoid a 
 confusion of lines, but care must be taken that it stands upon 
 a continuation of the bottom of the picture, and that the va- 
 nishing point of the lines from the top and bottom of it be upon 
 31 continuation of the horizontal line. 
 
 If 
 
60 
 
 LECTURES ON PERSPECTIVE. 
 
 If the proportional height of a figure standing in a balcony 
 be required^ a perpendicular must be let fall from the feet of 
 the figure to the ground, and the proportion obtained as if 
 standing upon the ground, which proportion may then be 
 placed in the balcony at any height, provided it be immedi- 
 ately above the point before mentioned; as for instance, if it 
 be required to place a figure upon the point w, (Plate II, Fig. 
 5,) a perpendicular must be let fall from w to the ground at x, 
 and the parallel will cut i c in ^, and ^ o will the height re- 
 quired, which must be measured and placed upon w as w t, 
 for whether an object stand upon the ground plane, or upon a 
 considerable elevation, its apparent height will be the same, if 
 the distance of the picture be not too short. Two figures, one 
 on the top of the Monument of London, and the other at the 
 Base, would undoubtedly appear of very unequal proportions to 
 a spectator, in Monument Yard, for the one on the top would be 
 much farther from him than the other, and appear consider- 
 ably foreshortened ; but let the spectator retire to the opposite 
 side of London Bridge, and there will be no sensible difference 
 in the apparent heights of the two figures, for their distances 
 from his eye will be very nearly equal. The figure in the 
 balconette, (see frontispiece,) appears of the same height, that it 
 would do if standing upon the pavement immediately under 
 the balconette, and its proportion is determined from that point 
 upon the pavement. 
 
 The most certain method of putting arches into Perspec- 
 tive, is by having the exact dimensions of one of them, and 
 placing it upon the picture ; as for example : let a b (Fig. 3, 
 Plate III,) be the width from pillar to pillar, suppose it to be 
 called ten feet, and the height to the capital as b d twice its 
 
 width 
 
LECTURES ON PERSPECTIVE. 61 
 
 width, or twenty feet, the height of the point of the arch 
 from the capital may be ten more feet, so that the whole 
 from B to G is thirty feet. At d draw d f parallel to a b, 
 describe the arch d i f according to actual measurement, and 
 draw G K through i parallel to a b ; draw the diagonals f g 
 D K, and through the points 1 and ^, where they cut the 
 arch, draw the line r s, then put the row of pillars in per- 
 spective according to its position with regard to the plane 
 of the picture; if perpendicular to the picture c the center 
 will be the vanishing point, but if oblique, the vanishing 
 point will be found in some other part of the horizontal line; 
 in the present case let the centre be the vanishing point, and 
 draw B c, g c, then set off b m equal to a b, and m t equal to 
 whatever may be the width of the pillar b d ; draw from m 
 to e (the point of distance transferred to the horizontal line) 
 and it will cut b c in n, and b n will be the Perspective re- 
 presentation of a space equal to a b, or to the distance be- 
 tween the pillars ; draw n q, then from t draw to e, and b c 
 is cut in u, therefore n u represents the width of the pillar ; 
 raise a perpendicular at u. To put the line r s into Per- 
 spective, draw s c, and to put f d into Perspective draw d c. 
 Draw the diagonals q d and g p, and their intersection with 
 each other gives the centre over which the point of the arch 
 must be placed at v ; draw the arch from v through the points 
 I and where the diagonals g p, q d cut s c, as v 1 d, v ^ p, 
 and it is of the same form in Perspective with the original 
 plan fid: the space between the two next pillars may be 
 obtained by setting off a distance from t equal to a b, as 
 t w, and a line drawn from w to e would cut b c in x, and 
 u X will be the distance between the second and third pillars : 
 but as this method would be very inconvenient if there were 
 
 many 
 
62 
 
 LECTURES ON PERSPECTIVE. 
 
 many pillars, owing to the space required for setting off the 
 distances, it is better to draw from m to the vanishing point 
 c of B N ; then since b c and m c vanish in the same point, they 
 must represent original lines parallel to each other, and u o 
 will be the representation of a length equal in perspective to 
 B m; draw from o to e, and it cuts b c in the same, point x as 
 it would have done if drawn from w to e, and therefore 
 answers equally well in its operation, and is much more 
 convenient ; raise the perpendicular at x, and by the dia- 
 gonals as before, put the next arch into Perspective. To 
 get the width of the next pillar at x, draw from y to e, 
 for o y is the representation of a line equal in Perspective 
 to M T, for the same reason that u o was the representation 
 of one equally long in Perspective with b m; and therefore 
 drawing from y to e answers the same purpose as continuing 
 the measurement from w to z, for both cut b c in the same 
 point : the distance between the third and fourth pillars, kc. 
 may be obtained by repeating the same operation. It may be 
 here observed, that if the first arch in Perspective, as b d v p n, 
 were drawn from nature, that by drawing from c (the vanish- 
 ing point of the line of the top of the arches) through v as far 
 as G, and continuing the perpendiculars b d to g, and n p 
 to Q, that the diagonals g p, d q, being drawn, would cut 
 the arch in the points 1 and ^, through which points a line 
 should be drawn to the vanishing point c, and if the arch is 
 correctly drawn, this line will pass through the two points of 
 intersection and the vanishing point, but not so if incorrectly; 
 the other arches might be put into Perspective, as in the pre- 
 ceding example. If there be a corresponding row of arches 
 parallel to the first, the lines they stand upon will conse- 
 quently be drawn towards the same vanishing point ; and 
 
 lines 
 
LECTURES ON PERSPECTIVE. 
 
 63 
 
 lines from the first pillars drawn parallel to the bottom of the 
 picture, till they meet the line upon which the other row 
 stands, will give the place of the corresponding pillars, except 
 when they are viewed obliquely. 
 
 In the last example the pillars are expressed by one line only; 
 but in order to give them their true dimensions, let a b (Plate 
 IX, Fig. 3,) be the width of the square pillar, d e the capital ; 
 cut off from b c a portion equal to a b or b f, as b g, raise the 
 perpendicular g i, draw e c, cutting g i in i, and the pillar is 
 compleated; let f k be the space between the pillars, draw 
 from K to e, and b c is cut in m, raise the perpendicular m n 
 till it meets e c, continue the perpendiculars g i, m n, till 
 they meet the line o c in p and q, draw the diagonals q i, p n, 
 and their intersection gives the centre, immediately over which 
 is the point of the arch at u, draw s c, and then the arch through 
 their points of intersection at 1, ^, as in the preceding ex- 
 ample. From A draw to c cutting m t in t, then is m t 
 perspectively equal to a b, raise the perpendicular t v, and 
 M N V t is equal to b e d» a; from v describe the inner line 
 of the arch, and the first arch is compleated; or if great ac- 
 curacy is required, the inner arch may be described perspec- 
 tively upon t V, w E, as is marked by the dotted lines. Draw 
 M x; from f draw to c cutting m x in y, and from k to c 
 cutting it in x, then from y to e gives m z for the face of the 
 next pillar, and x e gives z a for the second space, kc. kc. 
 Square pillars have here been chosen because the square 
 must be first described in order to represent circular co- 
 lumns. 
 
 The same mode of proceeding will answer equally well 
 
 for 
 
64 
 
 LECTURES ON PERSPECTIVE. 
 
 for a bridge; as for example, let the bridge consist of five 
 arches, the first and last of which may be called eight yards 
 wide, the second and fourth ten, and the centre arch fifteen ; 
 the width of the piers between each arch four yards. If the first 
 arch of the bridge begins from the bottom of the picture a d, 
 (Plate 3, Fig. 5,) set off its dimensions from a towards d, making 
 the first arch from a to f equal to eight equal parts or yards ; 
 the next division four equal parts for the first pier, then ten 
 of the same dimensions for the second arch, the next pier to 
 occupy four, and so on.-;- Let g be the vanishing point of 
 the bridge, and a g will be its inclination towards the horizon- 
 tal line ; set one foot of the compasses in g, its vanishing 
 point, and transfer the place of the eye or point of distance 
 to the horizontal line, draw from f to e, and it cuts a b in i, 
 then A I is the width of the first arch, a line from k to e cuts 
 A B in M, and i m is the width of the first pier ; from n to e 
 cuts A B in o, and gives the width of the second arch ; the 
 next pier and the other arches may be obtained in the same 
 manner ; but to determine their height in Perspective, the 
 line of elevation must be used ; as for example, suppose the 
 height of the first arch equal to its width (i. e.) to ten yards, 
 make the line of elevation a q of any height at pleasure, 
 and upon it set off ten of the equal parts from the bottom, 
 as A R, and a line drawn from r to the vanishing point, will 
 give the height of the first and last arches ; the second arch 
 is thirteen yards high, therefore if from s a line be drawn 
 to G, it will give its Perspective height, and also that of 
 the fourth arch. The centre arch is fifteen yards high, 
 
 therefore 
 
 * If the bridge begins farther within the picture, a parallel to the bottom of the 
 picture may be drawn from the nearest end of the bridge, as A, and the dimensions 
 set off upon it proportioned according to the situation of the parallel in the picture. 
 
LECTURES ON PERSPECTIVE. 
 
 65 
 
 therefore fifteen equal parts or yards must be set off 
 upon the line of elevation, and t g drawn ; from the middle 
 point between r and v, raise a perpendicular to 't g, and 
 the height of the middle arch is obtained. In order to give 
 to the first and last arches the same degree of curvature, the 
 plan of the -arch z a must be made,^:^ and the line x u put 
 into Perspective, which line intersects the diagonals of the 
 last arch in the points through which the arch is to be drawn. 
 If great precision be required, a plan may easily be made 
 for the second arch ; as for example, erase the plan of the 
 first arch, and as a is the point of junction between the two 
 lines A B and A d, raise a perpendicular at a, equal to the 
 height of the second arch, thirteen yards : there make the plan 
 of the arch thirteen yards high and thirteen wide, and of the 
 exact form of the second arch, draw the diagonals and also 
 the line passing through the intersections of the arch by the 
 diagonals; put that line in Perspective, and it will cut the 
 diagonals of the second and fourth in the points through 
 which the arch is to be drawn, compleat the arch as before. 
 
 * This may be done in pencil, and afterwards erased. 
 
 K 
 
 STEPS 
 
STEPS IN PERSPECTIVE. 
 
 f IRST parallel to the plane of the picture, let a b (PI. 4, 
 Fig. 1.) be the length of the step a d its height, draw d f 
 parallel to a b, join b f and a d f b is the face of the bottom 
 step. From d and f, draw to c the center of the picture, 
 because the lines forming the sides of the tread of the steps are 
 perpendicular to the plane of the picture (Rule 3.) In order 
 to cut off from d c a portion equal to ad (i. e.) the height of 
 the step, measure a d and place it upon d f at d, draw from d, 
 to the point of distance transferred to the horizontal line, 
 and D c will be cut in I, and d i is the Perspective repre- 
 sentation of a portion equal to d d or a d. From i draw a 
 parallel to the bottom of the picture, and it will cut f c in 
 G, and D f G I will represent the surface or tread of the lowest 
 step, upon which the foot will be placed in ascending or 
 descending. In order to give to each step its proportional 
 height, raise the perpendicular a r and make d 2, equal to 
 A D or the height of the step, draw q c, and it cuts the per- 
 pendicular I N in N, and thereby gives the height of the 
 second step ; draw n m parallel to the bottom of the picture, 
 and raise g m, and i g m n is the face of the second step, 
 
 make 
 
LECTURES ON PERSPECTIVE. 
 
 67 
 
 make n n equal to n i, and draw from n to the point of dis- 
 tance transferred, and it gives the point k, for the width of the 
 second step : draw the parallel k o, and n m o k is the tread of 
 the second step. Proceed in the same manner for any number 
 of steps required. 
 
 When the steps are obliquely situated, as a b, for ex- 
 ample, (PI. 4, Fig. the second vanishing point must be ob- 
 tained by means of the first, as in the square viewed upon the 
 angle, and a d being the height of the first step, d f must be 
 drawn to the vanishing point of a b, because parallel to it in 
 reality. Join b f, and a b f i> is- the face of the bottom step; 
 but the tread of the step being at right angles to a d b f, 
 must consequently go to the other vanishing point ; draw d f 
 F f, next draw a parallel to the bottom of the picture from d, 
 and set off d d equal to a d, and a line from d to v, the point 
 of distance transferred to the horizontal line, cuts d f in i ; 
 and D I is the Pei^spective representation of a portion equal 
 to D d, or A D ; draw from i to the vanishing point of d f, 
 and F f is cut in C, then d f g i becomes the representation 
 of the tread of the lowest step; or draw the parallel a q, and 
 upon it set off the intended width of the steps as a 1, 1 2, 2 3, 
 kc. kc. draw from 1, 5, 3, &:c. to v and a f will be cut in x y 
 z, kc. where perpendiculars may be raised for the ^, 3, 4, 
 steps, kc. and the widths required will be obtained. Raise 
 the perpendicular a r, and make d q equal to a d, and draw 
 Q f, which by cutting the perpendicular i m in m determines 
 the height of the second step, and by proceeding as before any 
 number of steps may be represented. 
 
 circular steps the diameter of the lowest must be first 
 
 K 2 taken 
 
LECTURES ON PERSPECTIVE. 
 
 taken as a b (PI. 4, Fig. 3,) and a circle described upon it, 
 A D B will be the visible part of the bottom of the step ; raise 
 the perpendiculars a f and b g equal to the height of the step, 
 and F G will be the diameter of the upper surface of the 
 lowest step : describe a circle upon the diameter f g ; and 
 FIG, B D A will give the representation of the first step ; let 
 k M be the lowest diameter of the second step : describe a 
 circle upon it, and k o m is the visible part; raise k n, and 
 M p, for the heighth of the second step, and n p is the dia- 
 meter of its upper surface, upon which describe the per- 
 spective circle n q p R, and two steps are compleated ; by the 
 same method any number of circular steps may be put into 
 Perspective. 
 
 LECTURE 
 
LECTURE VI. 
 
 Treats of Vanishing Lines in general. The Perspective of 
 
 Shadows^ <b-c. 
 
 The horizontal line has hitherto been the only vanishing 
 line made use of, it now becomes necessary to explain the 
 nature of vanishing lines in general, and to shew their practical 
 application. The more scientific definition of a vanishing line 
 is, that it is a line described upon the picture hy a plane passing 
 from the eye through the picture, parallel to the plane whose 
 vanishing line is required. Thus upon the apparatus : if a plane 
 of pasteboard or card s be placed from the eye e (see PL 6. 
 Fig. 1,) parallel to the ground plane x, and continued to the 
 glass or picture, it will meet it in the horizontal line h l, 
 which is the vanishing line of all horizontal planes ; but if a 
 bent card representing the roof of a building, like a d b r t, 
 be placed upon the ground plane, then planes carried from the 
 eye to the picture parallel to the respective inclined sides, will 
 describe their vanishing lines upon the glass or picture above 
 or below the horizontal line, according to the inclination of the 
 original planes : the vanishing line of the plane r at p o, 
 
 above 
 
LECTURES ON PERSPECTIVE. 
 
 above the horizontal line ; that of the plane t at v w, below 
 the horizontal line. The plane a d b being perpendicular 
 both to the ground and picture, will have its vanishing line 
 pass through c, the centre of the picture, because a plane 
 from the eye parallel to a d b will cut the picture in n c m 
 The vanishing line of plane a (PI. 6, Fig. will be found at d f, 
 by the plane a passing through the eye and picture parallel 
 to it ; that of the plane b will be found at c i, by the parallel 
 plane b cutting the picture in that line, thus the vanishing 
 lines of all planes which ^re perpendicular to the ground, will be 
 perpendicular to the horizontal line in the picture. 
 
 In order to find the place of the vanishing line of any 
 original plane, a line must be drawn from the eye to the 
 picture, making an angle with the horizontal plane equal to 
 the angle made by the original plane with the ground plane, 
 as for example, the line en (Fig. l, PI. 6,) makes an angle 
 with the horizontal plane s, or line e c, equal to the angle 
 made by the line d b with a b, or the ground plane, and gives 
 N for the point through which p o the vanishing line of the 
 plane r is to be drawn; for the descending plane the same 
 angle must be made with the horizontal plane s that the 
 original plane makes with a parallel to the ground f d, as 
 F D A, thus the line e m makes the same angle with the plane s, 
 or line e c, that d a does with f d; and since m n is the 
 vanishing line of the plane a d b, n will be the vanishing point of 
 the line b d, and its parallel, and m the vanishing point of d a, 
 and its parallel, p o the vanishing line of the plane r, and v w, 
 that of the plane t, and hence we see that the vanishing points of 
 Imes must fall in the vanishing lines of the planes in which they 
 lay. 
 
 To 
 
LECTURES ON PERSPECTIVE. ;i 
 
 To put this into practice ; if a plane ascends in an ancle 
 of twenty-nine degrees, that is, makes such an angle with the 
 ground plane, we must make the same angle (ascending) at 
 the eye, but from necessity this angle must be made at the 
 point of distance transfemd upon the horizontal line, as in 
 PI. 6, Fig. 3, where e is the point of distance, c the centre of 
 the picture, and e upon the moveable plane when raised repre 
 sents the natural place of the eye, as in the apparatus ; raise 
 the plane e c d e and also the original plane e c d, and the 
 angle c e d is by construction equal to the angle c e d there 
 fore E D being parallel to e d, gives d for the vanishing 
 pomt of e d, and also the height of the vanishing line of the 
 P ane r, (F.g. 1.) Lay the moveable planes flat, and the an- 
 gles still remain similar, but the line e d is now drawn from 
 the transferred distance upon the horizontal line to the picture 
 and cuts It in the same point d upon the vanishing line of the 
 perpendicular plane c e d. From hence we have the means 
 of representing uphill or downhill views when regular build- 
 ings occur, for let the plane r, (Fig. ,,) be considered as an 
 ascending road, bounded by two walls upon the lines b d, 
 and Its parallel; the vanishing line of the plane r is p o 
 passing through n, and n is the vanishing point of the two 
 sides of the plane r, for e n is drawn parallel to b d In 
 practice let a b, (Fig. 4, PI. 6,) be the width of the road,' a 1 
 B 2 the height of the walls, and the angle the hill makes 
 with the ground plane equal to the angle a b c ; c is the cen- 
 tre of the picture, and e the point of distance, draw a line 
 Irom E through c, as e g, which is the vanishing line of 
 P anes perpendicular to the ground and picture ; transfer the 
 d^tance to the horizontal line at e, and draw e r, making an 
 angle with c e equal to the angle which b c makes with a b, 
 
 and 
 
12 
 
 LECTURES ON PERSPECTIVE. 
 
 and F becomes the vanishing point of the sides of the road, 
 or walls ; therefore draw from a and b to f, and also from 1 
 and 2 to f, and you have the representation of the two walls : 
 if houses occur, the lines which are in planes parallel to the 
 horizon, as the upper and lower parts of the window frames, 
 tops of the houses, kc. will vanish in the horizontal line; but 
 if it be required to represent a second house of equal height 
 farther up the hill, a line must be drawn from the highest 
 point of the first house to the point f, as in the figure, and 
 it will give the height of the second, kc. if the road inclined 
 either to the right or left, its vanishing point would be on 
 one side of f, upon n m the vanishing line of the ascending 
 plane or hill ; the same operation must be performed for a 
 descending plane, or down hill, the vanishing line being be- 
 low the horizontal line ; as for example, if the angle made by 
 the descent with the ground plane is equal to f g h, the same 
 angle must be made at e, the transferred distance, as c e g ; 
 through G draw a g b, and you have the vanishing line of the 
 descending plane. The proportion of the human figure, kc. 
 may be determined as before taught, except that the va- 
 nishing line of the plane upon which they stand, must be 
 substituted in the place of the horizontal line before used. 
 Thus in the ascending and descending views of Hay Hill, the 
 vanishing line of the hill must be used instead of the horizontal 
 fine but in Portland Place, and the Room, the horizontal line is 
 the 'vanishing line of the figures. In order to represent a circle 
 by means of the vanishing line of its plane, that vanishing 
 line must be drawn through the vanishing point of the line 
 upon which the plane stands, as for example, when the circle 
 is placed perpendicular to the ground and picture, as a wheel, 
 (Plate 6, Fig. 8,) c the centre of the picture is the vanishing 
 
 point 
 
LECTURES ON PERSPECTIVE. 
 
 73 
 
 point of the line a c, upon which the wheel stands, and e f is 
 consequently the vanishing line of that plane. After having 
 drawn lines from the vanishing point c, through the two ex- 
 tremities and centre of the given diameter a b, as in the case of 
 circles, (Plate 3, Fig. the process is simply to draw from 
 the eye or point of distance e, through the centre of the given 
 diameter, in order to obtain the square in Perspective, which 
 saves the trouble of finding the half of the diameter, kc. ac- 
 cording to the method when the horizontal line is the only 
 vanishing line; this will be very evident by turning the plate 
 so that the line e f may appear as the horizontal line. 
 
 It is not material where the vanishing point of the square 
 in which the circle is inscribied may fall, for through its va- 
 nishing point, the vanishing line of its plane must always be 
 drawn, the only difference in the process consists in the dis- 
 tance of the vanishing line, for instance, if c (Plate 7, Fig. I,) 
 be the centre of the picture, e the point of distance, and 
 G N the vanishing line of the plane of the square, raise the 
 moveable plane £ c g upon c g, then is e the natural place of 
 the eye or point of distance and the line e g the shortest line 
 that can be drawn to the vanishing line g n, consequently e g 
 is the distance of that vanishing line, which may be placed at 
 L, G L is now the distance, and if it be transferred to g n at 
 o, and a line drawn from o, through the centre of the diameter 
 A B, it will give the square as before. 
 
 Roofs of houses being inclined planes may be deter- 
 mined in like manner, for suppose a building to vanish in 
 the two points f and g (Plate 7, Fig. 5,) and if the angle made 
 by the roof at the gable end n is equal to the plan a c b, a va- 
 
 L nishing 
 
 I 
 
74 
 
 LECTURES ON PERSPECTIVE. 
 
 nishing line must be drawn through the vanishing point g, 
 perpendicular to the horizontal line^ because the plane n is 
 perpendicular to the ground, and it becomes the vanishing 
 line of the plane n ; transfer the distance of the vanishing line 
 from G to L by placing one foot of the compasses in the va- 
 nishing point G and the other at e, and make the angle g l d 
 equal to a b c, then d becomes the vanishing point of b c ; 
 draw p D ; then make the angle g l r equal to the angle x c a, 
 and R becomes the vanishing point of a c ; draw r o, and 
 continue it to q, and you have the point of the roof; draw 
 from Q towards f, the vanishing point of the side m, and from 
 s to D, the vanishing point of p q, and at t the roof is com- 
 pleated; or it may be done by drawing parallels to a o, b c 
 from L to the point of distance transferred. The vanishing line 
 of the plane q p t s is d t, for since f is the vanishing point 
 of p s and q t, and d of p q and s t, it follows, that the line 
 connecting or passing through those two vanishing points must 
 be the vanishing line of the whole plane. 
 
 Portions may be cut off from lines, whatever their situation 
 may be with respect to the picture, by means of their respec- 
 tive vanishing lines, in the same manner as by the horizontal 
 line. Lecture III, for let it be required to cut off a portion 
 from the line a b, (Plate 9, Fig. 1,) whose vanishing point is 
 at D, in the vanishing line of an ascending plane ; first, the 
 distance must be transferred to f g the vanishing line of the 
 plane in which the line a b lies; and in order so to do, a line 
 must be drawn from the centre of the picture perpendicular to 
 F G at M, the distance of the picture must next be transferred to 
 the horizontal line at h, and h m is the distance of the vanish- 
 ing line F G ; (the distance of a vanishing line being always 
 
LECTURES ON PERSPECTIVE. 75 
 
 that of the eye from its centre :) if the triangular plane c h m 
 be supposed to be raised upon c m till perpendicular to the 
 plane of the picture, h will represent the natural place of the 
 eye, and h m will evidently be the distance of the vanishing 
 line F G. This will appear still more clear by making use of 
 the apparatus, and applying the wire from the place of the eye 
 to the centre of any vanishing line ; this distance must then be 
 placed over m perpendicular to f g at n, and transferred from 
 D to F G at o, instead of transferring to the horizontal line; 
 draw a parallel to f g from a at pleasure, and upon it place 
 the given portion as a p, draw from p to o and it gives a r 
 for the perspective representation of a p. In this example the 
 vanishing line was parallel to the horizontal line. In the fol- 
 lowing it will be oblique as f g, (Plate 9, Fig. and the 
 only difference in the operation is, that the distance of the 
 picture c e must be placed upon c s parallel to the vanishing 
 line F G, in order to obtain the distance of that vanishing line 
 instead of using the horizontal line, and by substituting the 
 triangular plane c s m, in the preceding example, for ohm, 
 the truth of the method will be equally evident ; s will repre- 
 sent the natural place of the eye, and s m will be the distance: 
 from p to o gives a r for the perspective representation of a p, 
 and from t to o gives a v equal to at, or twice a p, kc. kc. 
 In both these examples the same letters of reference are 
 used. 
 
 The hand-rails of a flight of steps will vanish into the same 
 line and point with the ascending or descending plane of the 
 steps themselves, for example, the two lines d n, f m, (Plate 4, 
 Fig. 1,) touching the angles of the steps, if continued, would 
 meet in their vanishing point, which would be in the vanish- 
 
 L 2: ing 
 
76 
 
 LECTURES ON PERSPECTIVE. 
 
 ing line of the plane of their ascent ; to the same vanishing 
 point the hand rails s t u w must be drawn^ because parallel 
 to the ascent of the steps in reality, but w x and t v vanish in 
 the centre of the picture being parallel to the upper surface of 
 the step, which is a horizontal plane. The same of the oblique 
 steps, (Fig. 2,) the vanishing point of whose ascent will be 
 found over the point f, towards which point the ascending 
 hand rails must be drawn. 
 
 In cutting olF portions from a line in perspective it is some- 
 times convenient to take half the distance c e, (Plate 7, Fig. 4,) 
 as c d, and half the given portion a b as a b, and by drawing 
 from b to g, half the distance transferred, the same point n 
 will be obtained in the picture, as if drawn from b to e, the 
 whole distance transferred ; if a third, fourth, or any propor- 
 tion of the distance be taken, and the same of the given quan- 
 tity, it will answer the same end. 
 
 SHADOWS. 
 
LECTURES ON PERSPECTIVE. 
 
 17 
 
 SHADOWS. 
 
 The projection of shadows is frequently so useful, that 
 although the object of the present publication is merely to give 
 those examples which most commonly occur, yet the advantage 
 of devoting a few additional lines to the explanation of this 
 part of Perspective is obvious. 
 
 Shadows are bounded by lines like other objects, and there- 
 fore must be subject to the same laws of Perspective, and as 
 they often fall upon inclined planes, as the roofs of houses, 8cc. 
 the application of the respective vanishing lines will be found 
 indispensable. 
 
 Shadows are projected by the torch or candle and by the sun ; 
 it is with the latter that we are most concerned, but as those of 
 the torch will assist in the explanation of those of the sun, it will 
 be advisable to begin with them, and let a, (Plate 8, Fig. 1,) 
 represent the light of the torch, b the torch itself, c an object; 
 it is evident that the shadow of the object c would be projected 
 by the light a in the direction b d, that is, immediately from 
 the torch a b ; the length of the shadow will be easily ascer- 
 tained by a line representing a ray of light drawn from the 
 luminary a through the top of the object c, and where it cuts the 
 line or shadow b d, it gives e f for the length of the shadow of 
 the object c, when projected by a luminary thus high. Sup- 
 pose an object h on the other side of the torch, the shadow would 
 then be projected in the opposite direction, and its length de- 
 termined, as before, would be h l. If the objects are solids, 
 
 then 
 
78 
 
 LECTURES ON PERSPECTIVE. 
 
 then the point b may be considered as the vanishing point of 
 their shadows. If these objects are supposed to stand upon a 
 table, and others upon the ground, whose shadows are to be pro- 
 jected, it is evident, that the point b cannot be the point from 
 whence the shadows of the latter are to be drawn, but a perpen- 
 dicular, from the luminary to the ground, will give the point 
 at M, the whole length a m being considered as the torch and 
 M its base, and m n will be the line of shadow, but still its 
 length must be determined by the ray a o from the light a, and 
 p o is the shadow of the object k. 
 
 The distance of the sun from the earth is so great that its rays 
 may be supposed to fall upon it in parallel lines, and when 
 they come in a direction parallel to the plane of the picture, 
 have no vanishing point like other lines of that description ; 
 but when the sun is before or behind the plane of the picture, 
 its rays must have vanishing points. 
 
 First, suppose the rays to pass in a direction parallel to (he 
 plane of the picture, the sun's height thirty degrees, which 
 may be determined as in the ascending and descending views. 
 Let s (Plate 6, Fig. 5,) be the place of the sun, and a b an 
 object, since the light comes parallel to the picture, the shadows 
 will be cast parallel also, and neither the rays of light nor the 
 shadows have vanishing points. Draw a d parallel to the 
 ground line, and draw from s through b, and where it meets 
 A D in D, gives the length of the shadow of a b. 
 
 5. Let the sun be at s (Fig. 6, Plate 6,) behind the picture, 
 and consequently casting the shadows forwards ; as for ex- 
 ample, the shadow of a b must fall in the direction of a d ; 
 
 and 
 
LECTURES ON PERSPECTIVE. 
 
 79 
 
 and L the seat of the sun upon the horizontal line will be- 
 come the vanishing point of the shadows, for since all lines 
 parallel to each other in nature have the same vanishing 
 point, the vanishing point of d a must be the vanishing 
 point of all the other shadows of lines perpendicular to the 
 ground, which are cast upon the ground plane by the sun 
 at s, as for example, compleat the object a d g i and 
 proceed by the other lines of which it is composed, as 
 by the line a b ; thus draw from l through f and also through 
 I, then draw lines from s representing the rays of light pro- 
 ceeding from the sun, through b, e, and g, and where they 
 meet the lines drawn through a, f, and i, at d, n, and o, 
 is the length of their respective shadows ; join those points, 
 and you have the whole shadow compleat. 
 
 The point upon the horizontal line immediately under that, 
 chosen for the situation of the sun, will be the vanishing point 
 of all shadows cast upon horizontal planes; for lines forming 
 shadows upon the ground plane must vanish into the hori- 
 zontal line, and the vanishing point of such shadows will be 
 that point directly under the sun ; because a perpendicular, let 
 fall from the place of the sun, in the picture, may be repre- 
 sented by the body of the torch in the preceding example, and 
 consequently the shadows must be projected immediately from 
 that line, and if they fall upon the ground plane, or any other 
 horizontal plane, they must vanish into the horizontal line, 
 and from the situation of the luminary, their vanishing point 
 must be that part of the horizontal line in which the perpen- 
 dicular from the sun strikes it; and in every instance the va- 
 nishing point of the shadow will be found in the vanishing line 
 
 of 
 
80 
 
 LECTURES ON PERSPECTIVE. 
 
 ot the plane in which that shadow Hes, as in the case of Hnes in 
 general. 
 
 3. Suppose the sun to be placed before the picture, or be- 
 hind the spectator; in which case the vanishing point of its 
 rays, or sun's place in the picture, will be at s (Plate 6, Fig. 7,) 
 below the horizontal line, because a line drawn from the eye 
 parallel to its rays, will meet the picture below the horizontal 
 line, like the vanishing point of a line upon a descending 
 plane ; the shadow of a b will now be projected into the pic- 
 ture, and the lightest side of the object be next the specta- 
 tor: the seat of the sun upon the horizontal line will be at 
 H, which becomes the vanishing point of the shadows, and 
 by drawing from s to b, a h is cut in d, and a d becomes 
 the shadow of a b. By the same rule if the figure be com- 
 pleated, its shadow will be determined as in the preceding 
 case, by drawing lines from the bottoms of the respective 
 perpendicular forming the angles of the object to h, the va- 
 nishing point of the shadow, and then from the sun s to the top 
 of each perpendicular. 
 
 The cause of the sun being placed undfer the horizontal line 
 may easily be explained by means of the apparatus ; for if the 
 real place of the sun be supposed behind and above the spec- 
 tator, shining upon the face of the objects beyond the glass or 
 picture, its rays will descend to those objects, and a line drawn 
 from the eye parallel to any of those rays must of course fall 
 upon the picture below the horizontal line, and there give the 
 vanishing point of its rays. The nearer the sun is to the hori- 
 zontal line the lower it is in fact, for if it be placed at o a ray 
 
 from 
 
LECTURES ON PERSPECTIVE. 
 
 81 
 
 from thence will cut a h much nearer to h and consequently 
 give a greater length to the shadow of a b, which proves the 
 situation of the sun to be low^er in the latter than in the former 
 
 case. 
 
 By an attention to the three preceding examples, the shadows 
 of objects, which are apparently more complicated, may be pro- 
 jected with equal facility. 
 
 Let the shadow of the arch b c d e (Plate 8, Fig. 3,) be re- 
 quired^ the sun's place being at s, project the shadow of the 
 perpendicular a b by means of its vanishing point t, and the 
 shadow will take the direction of a f, and were it not for the in- 
 terruption of the building, x would proceed to h, but being now 
 compelled to fall upon the wall, it describes the line f g parallel 
 to the original a b, and by the ray from s continued through b, 
 F G is cut in G, and the shadow of a b is described by a f g, 
 the shadow of e d by e i and in order to obtain that of the 
 arch BCD, let fall a perpendicular from the point g to the 
 ground which it will find upon the line a f, project the shadow 
 of the line c m and it will describe the line m n o, and con- 
 sequently a curve drawn through g o k will give the shadow^ 
 of B c D with sufficient accuracy for common purposes. 
 
 Again, let the shadow of the projection z be required. 
 Let fall a perpendicular from b to the ground, which may be 
 found by drawing a line from d parallel to a b, as d e, and 
 where the perpendicular from b intersects it, is the ground 
 plane, as at e, project the shadow of b e as e f g, and g being 
 the projection of b, a line connecting a and g will give the 
 shadow of a b ; and for that of b h, if a line be drawn from the 
 
 M vanishing 
 
LECTURES ON PERSPECTIVE. 
 
 vanishing point of h b, through g, as g k, it will give the 
 shadow required. 
 
 The shadow of the plane a (Plate 8, Fig. 4,) is required upon 
 the plane b. The shadow of the perpendicular d e appears to 
 be E F G, and by the ray from the sun through d, g proves the 
 shadow of the top of e d, or of the point d, by joining h g, 
 that of H D is obtained, and thus the shadow of the whole plane 
 A is described upon the plane b by the line e f g h, but the 
 apperture i must be expressed, and may be done by letting fall 
 the perpendiculars k n m and o p s to the ground at m s, and 
 projecting the shadows of those perpendiculars, and also those 
 of the points k o p n, and the apperture will be represented at 
 w. The shadow of the whole plane b would fall upon the 
 ground at ^ and that of the window y (Fig. 3,) upon the side 
 of the building at l. 
 
 In the example, (Plate 8, Fig. 5,) the shadow of the plane x, 
 describes the line a b c d e f upon the steps, and passes over 
 the cylinder y, the tread of each step being a horizontal plane, 
 the shadows laying upon them, as c d e f, kc. must vanish in 
 the horizontal line immediately under the sun's place at t ; the 
 line A B upon the ground plane of course vanishes in the same 
 point, the length of the whole shadow is determined by the 
 ray from the sun to the top of the object as before: its ap- 
 pearance upon the ground after passing the steps, may be 
 ascertained by laying a ruler upon a d, and observing the 
 line it forms after passing the steps towards the cylinder ; or 
 it may be done by letting fall a perpendicular from the point e 
 to the dotted line representing the bottom of the farthest side 
 of the steps, and from the point of intersection draw to the 
 
 vanishing 
 
LECTURES ON PERSPECTIVE. 
 
 83 
 
 vanishing point t : the same may be done by the other line of 
 the shadow. 
 
 If the shadow of an object falls upon an inclined plane, as^ 
 that of a chimney upon the roof of a house, the vanishing point 
 of such shadow must be in the vanishing line of the roof, for it 
 is described by means of lines upon that roof, and it has al- 
 ready been shewn, that the vanishing points of lines are always 
 in the vanishing lines of the planes in which they lay. Now 
 the vanishing line of the inclined plane a b d k (Plate 8, Fig. 2,) 
 is F G, let the shadow of the line n o upon that plane be re- 
 quired, the sun's place being at s. In the first instance, a per- 
 pendicular was let fall from the sun's place to the horizontal 
 line for the vanishing point of the shadows laying upon the 
 ground or on any other horizontal plane, but in the present 
 instance, this perpendicular must fall till it reaches the vanish- 
 ing line of the inclined plane upon which the shadow lays, thus 
 it must be continued till it meets the line f g at m, then is m 
 the vanishing point of the shadow of n o, draw n m for the di- 
 rection of the shadow, and s o for the ray of light, cutting n m 
 in p, then is n p the shadow of the line n o, fold back the plane 
 X, and the inclined plane a b d k forms one side of the roof of a 
 house, N o the chimney, and n p that part of its shadow which 
 falls upon the roof The shadows of the other lines forming the 
 chimney may be obtained in the same manner, and the whole 
 compleated. The shadow of the whole building may be pro- 
 jected by that of each of the perpendiculars forming the angles, 
 and by letting fall perpendiculars from the highest point of the 
 roof, as in the example. 
 
 In the frontispiece, representing Portland Place, the shadows 
 
84 
 
 LECTURES ON PERSPECTIVE. 
 
 are projected upon the ground plane, and their vanishing point 
 upon the horizontal line, out of the picture, and the sun's 
 place higher than the top of the picture ; the shadows of the 
 wheels driven by a man, in an oblique direction, describe 
 straight lines, they being in the plane of the sun's rays. 
 
 In the representation of the room, the light of the window 
 upon the carpet is determined in the same manner, for the floor 
 being a horizontal plane, the vanishing point of the shadows 
 will be upon the horizontal line near the margin of the picture, 
 and the sun's place near the upper corner. 
 
 The shadows, in the ascending and descending views of Hay 
 Hill, will be found to vanish into the respective vanishing lines 
 of the hill, whether ascending or descending. 
 
 LECTURE 
 
LECTURE VII. 
 
 Containing the Perspective of Rivers, Reflections in Water^ 
 
 '&C. &c. 
 
 A River meandering through a vale, if truly drawn, will 
 considerably assist the apparent flatness and extent of 
 the country through which it flows. This appearance is 
 produced by keeping the most remote windings almost pa- 
 rallel to the horizontal line, and also nearly close to each 
 other : but as they approach nearer the eye, their windings 
 will be more evident, and less parallel to the horizontal line ; 
 for let D (Plate 4, Fig. 4,) be the vanishing point of a b, the 
 first reach of the river, and f the vanishing point of b c, 
 another reach of the river, and^ by way of example, let it 
 be supposed that the windings of the river are alternately 
 parallel to each other, as in the ground plan k : continue 
 the representation of the river from c towards d, the va- 
 nishing point of A B ; the next turn goes towards f, and the 
 next towards d, kc. kc. it plainly appears they become 
 more inclined to a parallel to the horizontal line, in propor- 
 tion as their distance from the eye increases. The course 
 
 of 
 
86 
 
 LECTURES ON PERSPECTIVE. 
 
 of a river is so capricious in its meanders, that it must not 
 be concluded they will vanish in any two given points, but 
 the inference to be drawn from what has been said, is^ that the 
 distant reaches of a river must take nearly the direction of 
 the horizontal line^ let the real direction be what it may ; 
 and that^ however great its distance^ it never can rise above 
 the horizontal line ; hence the means of giving to a lake its 
 apparent width without carrying it very high in the picture, 
 for if its extreme shores are represented nearly parallel to 
 the horizontal line, and the due proportion of objects (there 
 situated) attended to, the desired effect will be produced. 
 The eye being above the nearest part of the lake must also 
 be above every other part of it, a lake being a perfect 
 plane ; and therefore since the horizontal line is exactly the 
 heighth of the eye, no part of the lake can be represented 
 above it. Hedges, walls, kc. will be obedient to the same 
 rule, ai;id whatever their direction in nature when upon a 
 plain, they will appear to incline towards a parallel to the 
 horizontal line, in proportion as their distance from the eye 
 cncreases, and consequently be represented closer and closer 
 to each other in the picture. In the representation of lakes, 
 bays, kc. whose shores are curved, a recollection of the 
 figure described by the circle when seen in perspective may 
 be useful. The bases of mountains, rocks, kc. rising from a 
 plain obey, in some measure, the same principle as the rivers 
 and shores of lakes, but being like them, varied, something 
 must, of course, depend on correctness of eye. 
 
 REFLECTIONS 
 
LECTURES ON PERSPECTIVE. 
 
 REFLECTIONS IN WATER. 
 
 Nothing adds more to the transparency and clearness of 
 water, than the reflections of surrounding objects, which in 
 a tranquil day are almost as distinct as the objects themselves, 
 and appear nearly of equal length: for example, let a b (Plate 
 4, Fig. 5,) be the representation of an object whose reflection 
 in the water is required ; measure a b with compasses, and 
 with the same measure set off a c from a^ and the reflec- 
 tion of A B is obtained ; again, suppose the reflection of d e 
 required, a little removed from the brink of the water but not 
 upon rising ground ; measure d e, and from d with the same 
 measure mark the point e in the water at i, do the same by 
 G H and F, and the reflection is produced. In order to give the 
 reflection of the tree k, standing upon a bank, its elevation 
 above the level of the water must be added to the measure 
 of the tree ; as for example : from the bottom of the trunk 
 of the tree a perpendicular must be supposed to fall till it 
 meets the level or plane of the water continued, and from 
 that point, as l, measure to the top of the tree, and with the 
 same measure, from the point l, mark the reflection of the top 
 M in the water, and in order to know how much of the trunk 
 would be reflected, measure from l to o, and from l with the 
 same measure towards the water, and as it will not reach it ; 
 consequently the base of the trunk cannot be reflected. The 
 reflection of the inclined object x y will be obtained by letting 
 fall a perpendicular from y to the surface of the water at z, 
 measure z y, and make z r equal to z y, and r becomes the 
 
 reflection 
 
88 LECTURES ON PERSPECTIVE. 
 
 reflection of the point y; join x r, which is the reflection 
 of X 7. 
 
 The preceding rule depends upon a principle in optics, 
 namely, that the angle of reflection is equal to the angle of in- 
 cidence : for example, let ag (Plate 8, Fig. 7,) represent a re- 
 flecting surface, a b an object, e the eye, b o a ray from the 
 top of the object a b, reflected at o, and making an angle e o g 
 with the reflecting surface a g, equal to the angle of incidence 
 boa: to the eye e, the point b will appear at o, but will be 
 transferred to h immediately under a b, and a h will conse- 
 quently be equal to a b; but if the eye be raised to f the point 
 B will appear at l, for the angle of reflection f l g is equal to 
 the angle of incidence b l a, but the reflected image still ap- 
 pears equal to the original object. In the first instance the 
 spectator requires a space of reflecting surface equal to a o to 
 see the reflection of the whole object a b, but when elevated to 
 F the whole will be seen within a l. 
 
 The station or point of view comes next under consideration, 
 and in drawing from nature is of great importance, for the 
 same scene taken from different stations or points of view, 
 will frequently appear so unlike each other, as scarcely to be 
 recognized ; in one point many of its beauties are concealed 
 from the eye, but by altering the station a point may be 
 found from which it appears to the greatest possible advan- 
 tage. If a single building, as a church, be the object to be 
 drawn, care must be taken to remove to a sufficient distance 
 from the building or the angles will appear violent by va- 
 nishing too suddenly. Some writers are of opinion that 
 when a single building is the principal object of the picture, 
 
 it 
 
LECTURES ON PERSPECTIVE. 
 
 89 
 
 it ought to be viewed upon the angle ; if otherwise (say 
 they) a degree of distortion is the consequence; but we 
 have authorities of no less weight than Canaletti, Caspar, 
 and N. Poussin, Claude Lorraine, kc. for a contrary practice, 
 (i. e.) viewing the building with one side parallel to the 
 picture, whether the vanishing point of the lines perpendi- 
 cular to the picture falls in the centre of the horizontal line 
 or not. As examples: let Fig. 4, Plate 5, represent a church 
 viewed upon an angle, and consequently both sides will va- 
 nish in different points. Let b be the vanishing point of the 
 side A, and by the rule the vanishing point of the other side 
 c, will be found at d ; compleat the church, and nothing 
 distorted will be apparent ; let it now be viewed when the 
 end A, Fig. 5, has no vanishing point, but the side b va- 
 nishes into c the vanishing point of lines perpendicular to 
 the picture,':^ and the end a will have an appearance of not 
 standing at right angles, to b, but making rather an obtuse 
 angle with that side. When extensive scenes become the 
 subject of the picture, take the following example. Sup- 
 pose Fig. 1, Plate 5, a profile or section of a view in na- 
 ture: to the eye placed at v the wood d would conceal 
 the lake h i, and also every object, except that part of 
 the mountain between b and and the appearance of 
 that view when drawn, would be as under, at Fig. 2,, where 
 the mountain b would appear just above the wood d, and 
 no intermediate objects be introduced. Now let the eye be 
 placed upon an eminence at e, and as may be perceived, a 
 line passing from the eye touching the wood g, would meet 
 the lake at h, and the whole space from h to i be seen, the 
 
 N wood 
 
 * In this case the vanishing point of those lines is beyond the limits of the picture. 
 
90 
 
 LECTURES ON PERSPECTIVE. 
 
 wood I would also appear with the building k, and even the 
 plain beyond it ; the mountains would be seen rising from 
 their base, and n would appear above f, and discover ano- 
 ther line of hills, as appears at No. 3 ; the advantage of the 
 higher station in views of this kind is too evident to need 
 further explanation. In these scenes the horizontal line 
 would in the first case be only equal to a v, but in the latter 
 case A E will be its height. 
 
 If it be required to place the nearest angle of a building 
 at any given distance^ as five yards within (or from the bot- 
 tom of the picture a b, Plate 7, Fig. 6,) and ten yards from one 
 side, as the side a f, according to a given scale ; it is first 
 necessary to divide correctly the bottom, and one side of the 
 picture, according to the annexed scale ; draw a c,, measure five 
 yards from a, and draw 5 e, giving g for the five yards in the 
 picture ; from a set off ten yards, and draw 10 c, a parallel 
 from g, to 10 c, gives ten yards when removed five yards with- 
 in the picture ; with that measure from n mark o, which is the 
 place required for the nearest angle of the building, i. e. five 
 ^ yards within the picture, and ten from the side a f; if the 
 building is to be of a given height, as fifteen yards ; draw 
 from A and 1 5 to any point upon the horizontal line out of the 
 picture, as ?, and a parallel from o as o q, gives q r for the 
 fifteen yards high at o, (vide Lect. V. where the use of the 
 line of elevation is taught.) The side o s is to make an angle 
 of forty- three degrees with the plane of the picture ; through e, 
 the point of distance, draw m g, which line is called the 
 parallel of the picture ; at e make the angle m e x, equal to 
 forty-three degrees, and continue e x to the horizontal line, 
 and T is the vanishing point required ; for" the angle m e t is 
 
 equal 
 
LECTURES ON PERSPECTIVE. 
 
 91 
 
 equal to the angle b a v ; m g is parallel to a b, and i! t to 
 A v; consequently t is the vanishing point of a v, and a t 
 is its indefinite representation, of which o s is a part.>;< This 
 is therefore a convenient method of finding vanishing points 
 when the angle is given : the proportions of the sides of 
 buildings may be placed upon the ground line a b or upon its 
 parallel g r, but in the latter case the reduced proportion of 
 parts upon the line g r, removed further from the eye, must 
 be attended to ; the measures may then be determined for each 
 side of the building as before directed ; and the proportional 
 widths given to windows, or any other parts of known dimen- 
 sions, by marking those proportions, as is done by stronger 
 hues upon or, {Plate 7, Fig. 6,) and dividing the line o s 
 perspectively by the usual method. 
 
 In order to put the equilateral triangle a d b (Plate 3, Fig. 6,) 
 into perspective by the ground plan, with one side a b parallel 
 to the picture; continue d a and d b to their intersecting points 
 F and G, and find their vanishing points i and k, draw their 
 indefinite representations f k, g i, and find the representations 
 of the points a and b upon the picture at a and b, and a d b 
 will be the perspective representation of the triangle a d b. 
 
 The same by one side given in the picture as a d (Plate 3, 
 
 N ^ Fig. 
 
 * The use of this line will be more evident by applying it to the apparatus, when, 
 if the vanishing point of any original line, laying upon the ground beyond the picture, 
 be required, a line from the place of the eye parallel to such original line will give its 
 vanishing point, and it will appear that the line from the eye, or point of distance, by 
 which the vanishing point is found, will make the same angle with the line parallel to 
 the picture, passing cross the eye, that the original line makes with the picture 
 itself. 
 
LECTURES ON PERSPECTIVE. 
 
 Fig. 7,) continue a d to f its vanishing point, and from f 
 transfer the point of distance to the horizontal hne at draw 
 A B parallel to the bottom of the picture, and from g draw 
 through D till the line cuts a b, in b ; and a d b is the tri- 
 angle required. 
 
 The triangle, with every side oblique to the picture, as 
 A D B ground plan, (Plate 3, Fig. 8,) find the respective 
 intersecting and vanishing points of each side of the triangle, 
 either by making the same angle with the parallel of the 
 picture, that each side makes with the plane of the picture^ 
 or by drawing parallels to the respective sides from the eye, 
 and their intersection in the picture at a b d will give the 
 triangle in perspective as required. 
 
 To put a regular hexagon into perspective one side being 
 given. — Through the point b (Plate 7, Fig. 5.) of the given 
 line b d, draw a line a n parallel to the horizontal line, and 
 continue b d to its vanishing point h, from h transfer the 
 distance to l, and from l draw a line through d, cutting a n 
 in n ; then b n represents a line of which b d is a perspective 
 representation ; make a b equal to b n, then is a b the re- 
 presentation of one parallel side ; from d, draw d l, and from 
 a, draw a h, cutting d l in f ; then is f another corner, and 
 d f represents another side ; again from d, draw d i parallel to 
 the horizontal line, and a l cutting it in i, then i is another 
 corner, and a i another side; draw h i and the parallel f g, 
 which compleats the figure. 
 
 In the representation of extensive scenes it is almost im- 
 possible to produce a grand effect by giving to every object 
 
 a separate 
 
LECTURES ON PERSPECTIVE. 
 
 93 
 
 a separate light and shadow, therefore a general light and 
 shade adapted to the subject, considered as one whole, is to be 
 preferred. A partial light and shade may sometimes be ap- 
 plied with good effect by supposing the intervention of clouds, 
 whose shadows cover that portion of the scene where a shadow 
 would be useful, and a light diffused where required. A num- 
 ber of lights and shadows in the same picture will occasion 
 confusion, and should be guarded against by large masses of 
 shadow, produced by the supposed intervention of a cloud, as 
 before observed, or by any other natural means. 
 
 In sketching from nature, the paper or picture must be 
 prepared by drawing the horizontal line, and marking the 
 centre of the picture, as taught in the first Lecture; and as 
 the horizontal line is exactly the height of the spectator's eye 
 when looking straight forwards, it will of course pass 
 along those objects in the real view which are exactly the 
 height of the eye. All such objects must therefore be placed 
 upon it in the picture; and as the centre of the picture is 
 the point directly before the eye, that object upon which it 
 falls in the view, must be placed upon it in the picture : thus 
 the centre of the picture and horizontal line are of the 
 greatest use in determining the relative places of objects. 
 Those to the right of the centre of the picture, or point di- 
 rectly opposite the eye in nature, must be so placed in the 
 representation : and the same of those on the left ; and great 
 attention should be paid to the chusing a proper distance of 
 the picture, since it enables those who are not much in the 
 practice of drawing from nature to avoid the bad effects of 
 beginning with objects too near them. This was explamed 
 in the first Lecture, and a frame and glass supposed to be 
 
 held 
 
94 
 
 LECTURES ON PERSPECTIVE. 
 
 held before the eye, and the same scene traced upon it 
 when at different distances from the eye, shewing the 
 different representations produced by those different distances, 
 &c. &:c. The proper distance of the picture for landscape draw- 
 ing was considered to be at least equal to its longest diameter, 
 and that it generally should exceed it. A small frame, as in 
 Fig. Plate 7, made of tin, may be very convenient to carry 
 in a sketch-book or port-folio ; and, when a sketch is about to 
 be made, hold up the frame at a distance from the eye, equal to, 
 or exceeding its longest diameter, and in the position of the 
 picture (i. e.) perpendicular to the ground like a pane of glass 
 in a window ; then observe how much of the view is seen 
 within the frame, and put the same portion upon the paper. 
 If it should be necessary to hold up the frame several times, 
 attention must be paid to its coinciding with the same parts 
 of the scene ; it must also be held exactly at the same distance 
 from the eye ; and, in order to be correct as to the distance, a 
 thread may be fixed through holes at each end of the frame, 
 and, when the distance is determined, a knot tied, which, by 
 being brought near to the eye every time the frame is used, 
 will preserve the same distance. 
 
 The greatest attention to truth and correctness is strongly 
 recommended in making sketches from nature, with the ad- 
 dition of written notes, marking every peculiarity of effect, or 
 colour, deserving of notice in the scene ; if any alteration 
 should be necessary to the perfection of the picture as a com- 
 position, it may be made at a future opportunity, but not in 
 the original drawing. 
 
 If the foregoing pages have been carefully considered by 
 
 the 
 
LECTURES ON PERSPECTIVE. 
 
 95 
 
 the Student, he will have acquired enough of the science of 
 Perspective to apply its rules to all the general purposes of 
 drawing ; but, if he is desirous of enquiring into the intri- 
 cacies of the art, he must have recourse to more elaborate 
 Treatises, in which he may find enough both to gratify cu- 
 riosity and to exercise the most persevering industry. 
 
 THE END, 
 
Back of 
 Foldout 
 Not Imaged 
 
E 
 
 Flaie 2. 
 
 H- 
 
 1 
 
 K-,, - 
 
 A JV2. 
 
 C 
 
 H I 
 
 P 7W 
 
 J 
 
 jr2. 
 c 
 
 
 
 
 
Back of 
 Foldout 
 Not Imaged 
 
i . 
 
Back of 
 Foldout 
 Not Imaged 
 
S 
 
Back of 
 Foldout 
 Not Imaged 
 
4 
 
 % 0 
 
 / \ 
 
Back of 
 Foldout 
 Not Imaged 
 
Back of 
 Foldout 
 Not Imaged 
 
Back of 
 Foldout 
 Not Imaged 
 
Back of 
 Foldout 
 Not Imaged 
 
Back of 
 Foldout 
 Not Imaged 
 
\