EASY LESSONS 
 
EASY LESSONS 
 
 IN 
 
 PERSPECTIVE. 
 
 INCLUDING 
 
 INSTRUCTIONS 
 FOR SKETCHING FROM NATURE. 
 
 "The mo3t consummate master is tied to the observation of every one 
 of these rules, on pain of pleasing none but the ignorant." 
 
 BOSTON: 
 
 BILLIARD, GRAY, LITTLE AND WILKINS. 
 1830. 
 
DISTRICT OF MASSACHUSETTS, to wit : 
 
 District Clerks Office. 
 
 Be it remembered, That on the sixth day of October, A. D. 
 1830, in the fifty-fifth year of the Independence of the United 
 States of America, Hilliard, Gray, Little & Wilkins, of the said 
 District, have deposited in this Office the title of a Book, the 
 right whereof they claim as Proprietors, in the words following, 
 to wit : 
 
 Easy Lessons in Perspective. Including Instructions for 
 sketching from Nature. " The most consummate master is tied 
 to the observation of every one of these rules, on pain of pleasing 
 none but the ignorant." 
 
 In conformity to the Act of the Congress of the United States, 
 entitled " An Act for the encouragement of Learning, by secur- 
 ing the copies of Maps, Charts and Books to the authors and pro- 
 prietors of such copies, during the times therein mentioned:" 
 and also to an act entitled " An Act supplementary to an Act, 
 (entitled, An Act for the encouragement of Learning, by securing 
 the copies of Maps, Charts and Books to the authors and pro- 
 prietors of such copies, during the times therein mentioned ; 
 and extending the benefits thereof to the arts of designing, en- 
 graving, and etching liistorical and other prints." 
 
TO 
 
 JOHN RAPHAEL SMITH, 
 
 THIS BOOK 
 
 IS RESPECTFULLY DEDICATED. 
 
■7 
 
 PREFACE. 
 
 It is the object of this book to explain the elements of 
 Perspective, together with the art of sketching from nature, 
 in a familiar manner, so as to render them intelligible to the 
 young, and those not skilled in Mathematics and Geometry. 
 
 There are many learned and elaborate treatises on Per- 
 spective, but they are generally unintelligible to those who 
 cannot command the assistance of a teacher. 
 
 The subject is abstract in its nature ; an acquaintance 
 with its principles, and a facility in its practice, cannot be 
 gained without attention and labour, but with these, it is 
 believed that any one, having a competent skill in drawing, 
 may gain from this book all the knowledge requisite to 
 sketch from nature correctly. 
 
LESSONS 
 
 IN 
 
 PERSPECTIVE. 
 
 LESSON L 
 
 LINES. 
 
 A straight line is the shortest which can be made 
 between two given points : it is without curve or bend, 
 as A, Plate 1. 
 
 Straight hnes are horizontal, perpendicular, or ob- 
 lique. B, is a horizontal line ; C, a perpendicular line; 
 D, E, & F, are oblique lines. 
 
 Parallel lines are alike, and keep the same distance 
 from each other. A and B are parallel hnes. 
 
 ANGLES. 
 
 An angle is formed by two straight lines which meet 
 at a point. G R is an acute angle ; H, an obtuse angle ; 
 I, a right angle ; J, a triangle. A triangle has three 
 sides, and three corners or angles. 
 
 An angle is the space included in any of these lines. 
 
 The size of an angle is measured, not by the length 
 of its lines, but by the space included in them, and is 
 accordingly that portion of a circle which this space 
 contains. 
 
 2 
 
2 
 
 LESSONS IN PERSPECTIVE. 
 
 A circle, whether large or small, is by geometricians 
 divided into 360 parts, called degrees. A degree, 
 therefore, is not any precise measure, as an inch, a foot, 
 or a mile, but simply the three hundred and sixtieth 
 part of any circle. In a large circle, the parts or de- 
 grees are larger lhan in a small one. but the number is 
 the same (see Plate 2, circles A and D.) A hne which 
 passes through the centre of a circle, and divides it in 
 two equal parts, is called a diameter. Thus the half 
 of the small circle A, divided by the diameter B, is 180 
 degrees, as truly as the half of the larger circle D. 
 
 Any straight Hne drawn from the centre of a circle 
 to the circumference, is called a radius. In the circle 
 A are two radii E and F, proceeding from the centre ; 
 one a perpendicular, the other a horizontal line. These 
 two lines include one quarter of the circle or 90 degrees. 
 This is a right angle. If the circle were larger, as D, 
 a right angle would be but one quarter of it. There- 
 fore a right angle is a quarter of a circle, that is, 90 
 degrees, if it extend a thousand feet, or even to the 
 heavens, for its size is estimated only by the portion of 
 a circle which it includes. This is an idea of propor- 
 tion, not of actual measured space, and it is important 
 to perceive and maintain the distinction. An angle 
 which includes a portion of a circle less than 90 degrees, 
 is called an acute angle, and may be of any size from 
 90° to almost nothing. As E G (circle A, Plate 2) 
 which is about 45 degrees, and H F which is not more 
 than 10 degrees. 
 
 An angle which includes a portion of a circle larger 
 than 90 degrees, is called an obtuse angle, and may in- 
 clude any number of degrees, from 90° to 180°, as 
 K J (circle D) which is 135°, or K L which 155°. 
 
LESSONS IN PERSPECTIVE. 
 
 3 
 
 LESSON II. 
 
 PLANES. 
 
 Planes cannot be so well described as lines and 
 angles. Any even flat surface considered without re- 
 gard to its tliickness, is a plane. A table is a plane, the 
 floor is a plane, the side of the house, &lc. 
 
 Planes are perpendicular, horizontal, or oblique. 
 
 The wall of the house is a perpendicular plane. The 
 floor is a horizontal plane, and so is the ceiling a hori- 
 zontal plane, parallel with that of the floor. 
 
 Any even surface which varies or inclines from the 
 perpendicular, is an inclined plane ; as a writing desk. 
 
 A perpendicular plane is at right angles with a hori- 
 zontal plane. Thus, if you place a book upright on a 
 table, the book is a perpendicular plane, and the table 
 a horizontal one, and they make a right angle. 
 
 An inclined plane makes an angle less than a right 
 angle, with a horizontal or perpendicular one. For a 
 writing desk, which is an inclined plane, does not make 
 a right angle with the table on which it stands, as the 
 book when placed upright does ; but it makes a smaller 
 angle, and this angle is more or less acute (that is, small) . 
 according to the greater or less inclination of the desk. 
 
 Two or more similar planes are said to be parallel. 
 
 Planes may be of any extent, large or small. Some 
 really exist, as the floor or wall of a house, and some 
 are only imagined to exist, for the purposes of science. 
 
 If two balls (M and N Plate 2) were suspended from 
 a ceiHng by cords of the same length, and were revolv- 
 ing about, they would be said to move in the same plane, 
 though no plane or surface were actually under them; 
 we know that if one were put under them, they would 
 both touch it. Thus objects are said to be in the same 
 plane, when they are neither higher nor lower than 
 each other. 
 
4 
 
 LESSONS IN PERSPECTIVE. 
 
 All objects situate on the earth are, in perspective^ 
 said to be on the same plane, called the ground plane. 
 
 There are three planes especially to be attended to 
 in perspective, viz. 
 
 The ground plane, the horizontal plane, and the 
 perspective plane. 
 
 The ground plane is that on which the objects to be 
 drawn stand ; as trees, houses, figures, he. — And when 
 drawing an interior, the floor of the room is a ground 
 plane. 
 
 The horizontal plane, is an imaginary plane, sup- 
 posed to extend from the eye of the spectator, to the 
 verge of the horizon. 
 
 The perspective plane is also imaginary. It is a 
 transparent plane, hke a window or pane of glass, placed 
 between the spectator and the landscape, or object to 
 be drawn, standing perpendicularly. If the appearance 
 of objects seen through this plane, were traced on it, 
 as it might be on a window through which you were 
 looking, it would make a correct drawing or picture of 
 the view. 
 
 The paper on which you draw, in taking a view, is 
 the representative of this perspective plane : — Could 
 you hold it up in a perpendicular position, and see- 
 through it, as you do through a window, you would 
 draw the objects beyond it correctly. But as this is 
 impossible, you imagine it to be the case. 
 
 LESSON III. 
 
 VISION. 
 
 All objects are seen by means of rays of light pro- 
 ceeding from them to the eye. ^ 
 These rays proceed in straight lines. 
 
LESSONS IN PERSPECTIVE. 
 
 5 
 
 As they come in all directions, from every side of 
 the object, and enter so small a place as the pupil of 
 the eye, it is evident they must converge or draw 
 together, as in figure O, Plate 3. Having this idea 
 fixed and familiar in your mind, you will understand 
 that, whether the eye be nearer to or farther from the 
 object, the rays must converge to it ; they therefore 
 form an angle or cone whose apex or point is the eye, 
 and whose base is the size of the object. 
 
 Now it is plain that the size of this angle will depend 
 on the distance of the object from the eye. When 
 near, the angle is larger than when the object is far- 
 ther off. 
 
 Thus the rod P makes a smaller angle at Q than at 
 R, and the angle is still smaller at S. 
 
 For an angle, as has been already explained, (see 
 Lesson 1, Plate 2,) is a portion of a circle, and if you 
 take one side of the angle for a radius, viz. semi-diam- 
 eter, and draw a circle, making the apex of the angle 
 the centre of the circle, it will then be seen how many 
 degrees of this circle the angle occupies, and this 
 shows the size of the angle. 
 
 To ascertain the size of an angle, it is only necessary 
 to draw a quarter of a circle, that is, a right angle, 
 (when the angle to be measured does not exceed ninety 
 degrees, or a right angle). Take one side of the angle 
 for a radius, as either T R, T Q, or T S, (Plate 3,) 
 draw from the corner T a line perpendicular to it. The 
 angle R T P it will be seen, is more than half that quar- 
 ter, or about 50° ; at Q the rod makes an angle of 23°, 
 while at S it makes less than one fifth of a right angle, 
 or 170. 
 
 This difference in the size of the angles is caused by 
 a difference of distance. The size of the rod and the 
 position of the eye remaining the same in each instance. 
 
 This is called the angle under which an object is 
 2* 
 
6 
 
 LESSONS IN PERSPECTIVE* 
 
 seen. It is the angle which the two external rays of 
 light fronn an object make in coming to the eye. 
 
 Though somewhat technically expressed, it means 
 nothing more than, that the greater the distance of an 
 object, the smaller it looks. 
 
 In perspective, a line is always regarded as perpen- 
 dicular to another, when it is at right angles with it. 
 Thus, u is a line perpendicular to v, or v to u, (Plate 3,) 
 because it makes a right angle, i. e. an angle of 90 
 degrees with it. 
 
 It has been said that we see objects by means of 
 rays of light proceeding from them to the eye, and that 
 these rays converge, and form an angle or cone of 
 rays, whose apex is in the eye. 
 
 The side of a house w, (Plate 4,) is seen by rays 
 coming from it to the eye. The two exterior rays 
 form an angle, viz. a If, 
 
 In drawing a house, (or other object,) you may imag- 
 ine the perspective plane to be situate any where, 
 between the house and the eye, as at x or y. The 
 true drawing will be where the rays of light coming 
 from the house, enter (that is, intersect) the perspective 
 plane in their progress to the eye. 
 
 This point, where the rays pass through the perspec- 
 tive plane, is called the seat of their representation. 2 
 in the perspective plane y, and 3 in the perspective 
 plane x, (Plate 4,) are the seat of representation for 
 the rays abode and /, proceeding from the house w. 
 
 It will be perceived that when the perspective plane 
 is near the eye, as at the object must be drawn 
 smaller, than when it is farther off, as at x. 
 
 This rule must not be confounded with the one 
 already given, (see Plate 3,) that the angle under which 
 an object is seen, diminishes in proportion to the dis- 
 tance of the object ; for this regards the apparent size 
 
LESSONS IN PERSPECTIVE. 
 
 7 
 
 of an object, determined by its distance from the eye ; 
 but the other, only the drawing of the object, deter- 
 mined by the situation of the perspective plane. 
 
 Objects are drawn under their true angles, and pre- 
 serve their relative proportions, whether the perspective 
 plane is near or more remote ; as appears from the 
 figure, (Plate 4.) The house at ?/, is seen and drawn 
 under the same angle as at and the same proportion 
 of the windows and spaces between, is preserved in 
 each. 
 
 For, take 1,2 for a radius, and draw a circle or 
 right angle, and you will perceive that the house is 
 seen under an angle of 20°. So take I 3, or 1 4 ra- 
 dius, the circle is larger, but the size of the angle (that 
 is, the number of degrees) is the same. 
 
 The angle under which a« object is seen, determines 
 the size and nearness to the eye. 
 
 It will also be perceived, that the distance of the 
 perspective plane from the eye is important; and having 
 been once fixed, must not be varied in the same view. 
 
 To illustrate this still more, place a card between 
 the eye and an object, a house or tree for instance, if 
 the card is held near, say within a foot of the eye, it 
 will cover or hide the object, and if it were transparent, 
 this object could be traced on the small space of a card 
 of two or three inches size. But hold the same card 
 twice or three times as far off, and it will not cover 
 half the former object; and if you drew on the card at 
 that distance, you could not get all of the object in. 
 Tiiis card represents the imaginary perspective plane 
 on which objects are drawn, and by this experiment you 
 can understand, that when it is near you, you can put 
 more on the same space than when it is farther off, 
 though each object in the view will preserve the same 
 relative proportions in both cases. 
 
8 
 
 LESSONS IN PERSPECTIVE. 
 
 LESSON IV. 
 
 HORIZON LINE, AND GROUND LINE. 
 
 The horizontal plane in perspective, is a plane 
 imagined to extend from the eye of the beholder to the 
 horizon, or farthest verge of the earth which the eye 
 can reach, viz. where the sky appears to touch the 
 earth. 
 
 Suppose the perspective plane interposed between the 
 eye and the view, (like a window, as has been already 
 described, see Lessons 2 and 3,) the horizontal plane 
 would intersect it, or cut it through at right angles, and 
 the line formed on the perspective plane, by this inter- 
 section is the horizon line. — What is called the horizon 
 line on the paper or picture, is the representation of this 
 line. For if you suppose the perspective plane set 
 upright on the ground before you, higher than your 
 eye ; then the horizontal plane, to reach from your eye 
 to the verge of the sky, must pass through the perspec- 
 tive plane, and thus make a line exactly parallel with 
 the top and bottom line of your perspective plane. 
 
 Then draw such a line on your paper, and ;;his is 
 your horizon line. You will find, when sketching, that 
 some particular point of a tree or window of a house 
 comes just against it. The meeting of the sky with 
 the earth, and the distant hills will also be on this line. 
 
 It is evident that the height of this line (viz. how far 
 it is above the bottom line of the picture) depends on 
 the height of the eye : and this is the case whether the 
 spectator is standing or sitting, — is on the top of a 
 house, or mountain, or on the plain. 
 
 Could an actual plane extend from the eye to the 
 horizon, lines situate on the ground plane or earth 
 would be under it, and the ground plane would appear 
 to meet it in the horizon, and be inclined to it ; making 
 
LESSONS IN PERSPECTIVE. 
 
 9 
 
 with it an angle, whose size would be determined by 
 the height of the spectator. This is what is meant by 
 the phrase, " having a high cr a low horizon." The 
 figures A B and C (Plate 4) are of about the same 
 height. Their horizon varies in consequence of the 
 difference in their position. 
 
 Lines being here necessarily used to express planes, 
 the explanations are less clear than in experimental 
 teaching. Let E be a table, which is a horizontal 
 plane, representing the ground plane on which the spec- 
 tator and also the objects to be drawn stand, A, a small 
 figure stationed at one side of the table, representing the 
 spectator, — D, another horizontal plane, parallel to the 
 table, placed just as high as the eye of the figure A. 
 Then the plane D, would represent the horizon plane. 
 Now, if you had on the table objects to be drawn, models 
 of houses, trees, &c. — and threads attached to the top 
 and bottom of these objects, were brought through the 
 eye of the figure A, after the manner of rays of light ; 
 you would perceive, that the grjDund plane appears to 
 the eye to rise till it meets the horizon plane in the 
 distance. — As E rises to meet D, and the angle these 
 two planes make, as D E with figure A, or D E with 
 figure B, or with C (Plate 4) depends on the height 
 and position of the figures ABC, viz. the beholder. 
 
 The more distant the object, the higher up on the 
 perspective plane, and the smaller they appear. If, for 
 instance, the perspective plane were a window, the base 
 of a house or tree near it would be seen through the 
 panes at the bottom ; while that of a similar object a 
 mile or two off, would be seen through the upper panes, 
 or those more nearly on a line with the eye. 
 
 When you begin to take a view, you first fix your po- 
 sition, which must be stationary, and determine on the 
 height of your eye, and on the distance at which the 
 perspective plane is to be placed or imagined, keeping 
 
10 
 
 LESSONS IN PERSPECTIVE. 
 
 in mind that your paper is the representation of the 
 perspective plane. Then draw a line at the bottom of 
 the picture G, (Plate 5,) which is called the ground 
 line, and is the line formed by the intersection of the 
 perspective plane, with the original ground plane; or in 
 in other words, a line where the perspective plane rests 
 on the earth. This ground line is the boundary of the 
 bottom of the picture ; for the nearest object or point 
 which you design to include in your picture, must be 
 on the ground line."^ 
 
 Having drawn your ground hne, then draw the hori- 
 zon line H parallel with it, at the height of your eye ; 
 which line represents the place where the sky meets 
 the earth. 
 
 The space D between these two lines represents the 
 ground plane, or the earth on which objects stand. 
 The nearer an object is to the spectator, the lower down 
 it will be on the ground plane. I is nearer than J, and 
 J than K. (Plate 5.) 
 
 Remember that it is only such lines as are nearer the ' 
 ' ground plane than the eye, that are drawn under the • 
 horizon line. On looking at a tree or house, or any 
 object taller than yourself, you look down to see the 
 base, and you look up to see the top ; consequently the 
 base is below the horizontal plane, and the top is above 
 it. If you had three objects to draw at different dis- 
 tances, as I J K, (Plate 5,) the base of each would be 
 situate on the ground plane according to its distance, 
 while the top would come above the horizon line. 
 The more distant an object is, the smaller it looks. K 
 
 * It is best not to include in the picture any large object nearer . 
 than 100 feet, and even a small object, as a carriage, house, or man 
 at that distance, would occupy a considerable portion of a perspec- 
 tive plane, situate ten or fifteen feet from the eye. Of this you may 
 be easily convinced, by looking out at a window placed at this dis- 
 tance from the eye, and observing how large a portion of it such 
 small objects when very near will occupy. 
 
LESSONS IN PERSPECTIVE. 
 
 u 
 
 and J are not so far above, nor so far below the horizon 
 line as I ; this expresses at once that they are farther 
 off. 
 
 LESSON V. 
 
 POINT OF SIGHT. PARALLEL PERSPECTIVE. 
 
 There is a point in the horizon line exactly opposite 
 to the eye ; which is called the point of sight. It is 
 very important in perspective. 
 
 It is usually placed near the centre of the picture; 
 but it may be on either side, according to the position of 
 the beholder. You can, if you choose, put the objects 
 on each side of you, into your picture ; and then the 
 point of sight will be in or near the centre ; but if you 
 wish to drav/ only what is on one side, and omit the 
 other; then the point of sight will be near the extremity 
 of the picture ; because the object, which, in the position 
 you have taken, is opposite your eye, is the one at 
 which you will end your view. 
 
 The trees (Plate 5, L) are all on the left side of the 
 spectator, and he must stand at B, opposite to S, to see 
 them as they are drawn here ; and if he choose to omit 
 the objects on the other side, S will be his point of 
 sight, at the extremety of the picture. 
 
 If he prefer to take in the objects on his right, he will 
 have his point of sight in the centre of his picture. As 
 the picture M, (Plate 5,) where S is the point of sight; 
 because in this view are included the houses on the 
 right, as well as the trees on the left of the spectator. 
 Thus you perceive that you can have the point of sight 
 wherever you please : provided it be on the horizon 
 line, and opposite the spectator. 
 
12 
 
 LESSONS IN PERSPECTIVE. 
 
 The point of sight then is the point in the farthest 
 distance, exactly opposite the eye of the beholder, and 
 is always on the horizon line. Its use may be illustrated 
 by the drawing of a house. 
 
 This is usually a square or rectangular figure : sup- 
 pose it to stand exactly before you, opposite your eye. 
 It will then be correctly expressed by horizontal lines 
 for the top and bottom, and perpendicular hues for the 
 sides or wall. Its place on the ground plane, is deter- 
 mined by its distance from the perspective plane. You 
 will see the front, but nothing of either of the other 
 sides : as N. (Plate 5.) 
 
 But if the house is placed a little to the right or left 
 of the spectator, one end can be seen as well as the 
 front. — Look at a house from these two different posi- 
 tions. 
 
 (Plate 6) R. That part a of the end seen, adjoin- 
 ing the front, and next the spectator, is nearer than the 
 part 6, adjoining the back ; therefore a must look larger 
 than h. As this side (a h) actually recedes from the 
 eye, it must be drawn diminishing in size, after the 
 following manner. 
 
 Having drawn the front R, (Plate 6) exactly as in 
 N, (Plate 5) excepting that it is farther removed from 
 the point of sight, — draw tw^o lines, one from the top, 
 the other from the bottom of the house, meeting in the 
 point of sight 5, w^hich is the vanishing point, or that 
 where all the lines on this side, parallel with the top 
 and bottom, would meet. 
 
 The lines for the doors, windows, &;c. meet, that is, 
 vanish in this point. 
 
 When a house, or other rectangular object, stands 
 square before you, and not cornerwise or obliquely, two 
 sides, viz. the front and back, are parallel with the 
 ground line, and the other two are exactly at right 
 angles with it. 
 
LESSONS IN PERSPECTIVE. 
 
 13 
 
 Lines which in the original object are parallel with 
 the ground line, are drawn parallel.* 
 
 Lines at right angles with the ground line, vanish or 
 terminate in the point of sight. 
 
 Perpendicular lines which are parallel with the per- 
 spective plane, like the sides of a house, are drawn per- 
 pendicular and parallel. 
 
 Parallel lines (whether horizontal like the top and 
 bottom lines of the front of the house, in Plate 6, R, or 
 perpendicular, like the sides of the same house) are 
 shorter than their originals, in proportion to their dis- 
 tance from the perspective plane. Thus the top, bottom, 
 and sides of R, though parallel, like their originals, are 
 shorter ; because they are at some distance from the 
 perspective plane, and the beholder. And if the house 
 were farther off they would be still shorter, in exact 
 proportion to their distance; which means no more than 
 that the house would look smaller, if it were father off. 
 Still, however, they preserve the same direction, and 
 are parallel like their originals ; but the lines on the side 
 a b are smaller than their originals, and they take a 
 different direction ; instead of being drawn parallel, 
 like their originals, they tend to, and meet in the point 
 of sight. — In parallel perspective therefore, there are 
 but three sorts of lines to be considered. 
 
 J St. Those which are parallel with the ground 'line, 
 and are horizontal lines in a pfcture. 2d, Those which 
 are parallel with the perspective plane, and are perpen- 
 dicular Hnes in the picture. 3d, Those which are at 
 right angles with the ground line, and when drawn, vanish 
 in the point of sight. The length of all these lines, that 
 is, how much smaller they are than their originals, de- 
 pends on their distance. 
 
 This is parallel perspective, and these rules comprise 
 
 * Original lines are such as really exist in contradistinction to the 
 <lrawing of them. 
 
 3 
 
14 
 
 LESSONS IN PERSPECTIVE. 
 
 all that is requisite for the sketching of rectangular fig- 
 ures, placed parallel with the spectator. Further instruc- 
 tions for the drawing of circles and curves in parallel 
 perspective, will be found in the lessons on circles, 
 bridges, and interiors, he. 
 
 In taking a view out of doors, you will be able to 
 determine the apparent size, situation, and relative pro- 
 portions of objects, with sufficient accuracy, by holding 
 up a pencil or ruler before your eye, in a horizontal 
 and perpendicular position, and comparing the object 
 with this measure. If you nearly close your eyes while 
 looking, it will facilitate the operation ; for if you look 
 at a house with your eyes shut as near as can be, and 
 see, and hold a pencil before them, you can with your 
 finger mark exactly how much of this measure the 
 house occupies to your eye. By looking in the same 
 way, at a house more distant, you will see how much 
 less of the pencil this occupies than the first 5 you have 
 only then to make this difference in their sizes when 
 you draw them. 
 
 By the same method you can form a correct judg- 
 ment, how much taller one tree is than another, or than 
 a house or other object ; how much higher one hill 
 rises against the sky than another ; or how large a 
 space a sheet of water occupies on your ground plane. 
 This space for water, fields, or any level surface on 
 the earth or ground plane, will be much less on your 
 picture, than you would believe, till you have made the 
 experiment, and measured it in this way. You may 
 observe, also, that the hues for the banks of rivers, 
 lakes, he. vary less from the horizontal, than you 
 would be disposed to draw them, if you judged merely 
 from your eye, without comparing them with your 
 measure, or some horizontal line. 
 
 Observe that your measuring rule or pencil, must be 
 held at the same distance through the whole sketch ; 
 
LESSONS IN PERSPECTIVE. 
 
 15 
 
 for an object which would occupy the whole at a dis- 
 tance of three feet, would not be equal to half of it, 
 when held near the eye. 
 
 It is easy to preserve the same distance for the 
 measure, by means of a cord fastened to its centre and 
 held in the mouth. 
 
 Novices in sketching, are often at a loss to determine 
 on the place for their horizon line, and think that 
 because they see no such line in the landscape before 
 them, they need not and cannot draw one ; but it is 
 difficult, if not impossible, to get a correct likeness 
 without one, and it is easy to determine on its place. 
 
 Suppose you were out of doors, and looking at the 
 view 4, (Plate 6) with a design to sketch it. 
 
 If you were on level ground, your horizon would be 
 low ; and the horizon line must be drawn about as far 
 from the ground line, as it is in the sketch, — wherever 
 you draw it, on the paper, would be the place for that part 
 of the picture, where the sky meets the earth. Then 
 observe by holding up a pencil, or other straight stick 
 in a horizontal position, exactly at the height of your 
 €ye, what this line passes across. The distant hill 6, is 
 on the right hand, and there is another hill on the left ; 
 consequently S between them is opposite your eye, and 
 is the place to mark the point of sight on the horizon 
 line. 
 
 The hill h rises a little above this line, and comes a 
 little below it, — the hill d rises higher and comes farther 
 down on the ground plane : draw them so. Then notice 
 the cedar tree c, — two thirds of it are above the horizon 
 line, (that is, two thirds of it appear above any hne 
 held horizontally across your eye,) and the root is one 
 third below. The elm tree e being nearer the specta- 
 tor, its base approaches almost to the ground line, 
 while its top reaches far above the horizon, to the top 
 
16 
 
 LESSONS IN PERSPECTIVE. 
 
 of the picture. The horizon line passes near the inser- 
 tion of the lowest branch. 
 
 Next draw the house /; observe where the base 
 comes above the foot of the tree, e, the horizon line 
 passes near the middle, just above the lower row of 
 windows ; therefore you must draw these windows 
 below the line, and the other row above it. 
 
 Thus this line helps you to ascertain the situation of 
 every object you wish to draw, — and the observation of 
 the relative position of these objects enables you to 
 determine the place of the horizon line. 
 
 After a httle practice, and with the help of these 
 rules, no difficulty can be experienced in sketching any 
 common view in parallel perspective. 
 
 The spectator in this view is placed at J, opposite to S. 
 
 Lines from the side of the house, to the point of 
 sight, S, determine the drawing of the side w, which is 
 at right angles with the ground hne, and vanishes in the 
 point of sight. The side / being parallel with the 
 ground line, must be drawn parallel, according to the 
 rules already given. 
 
 Throughout the book the following references are 
 invariable : — H, horizon hne ; G, ground line ; S, point 
 of sight; D, point of distance. 
 
 LESSON VL 
 
 OBLIQUE PERSPECTIVE. 
 
 Oblique perspective teaches the drawing of objects 
 situated obliquely to the ground line, as when a house 
 or other object stands with the corner towards you, like 
 W, (Plate 6). 
 
 As no side of the object W is parallel with the ground 
 line G, no lines can be drawn parallel with it 5 since as 
 
LESSONS IN PERSPECTIVE. 
 
 17 
 
 has been said in lesson 5, original lines parallel with the 
 ground line, are drawn parallel with it, but no others. 
 
 Each of the sides makes an angle with the ground 
 line, and must have a vanishing point. This cannot be 
 the point of sight, that being the vanishing point for 
 such lines only as are at right angles with the ground 
 line. They must have another vanishing point or 
 points. 
 
 These are on the horizon line, and are thus ascer- 
 tained. 
 
 Prepare your paper as before with a ground line G, 
 (Plate 7, Figure I,) horizon line H, and point of 
 sight S. 
 
 Rule a perpendicular hne through the point of sight : 
 this is called the prime vertical line. Mark on this 
 line the point D, called the point of distance. 
 
 This space from S to D, represents the distance of 
 the spectator from the perspective plane : in other 
 words, the distance at which you stand when taking 
 a sketch, from the nearest object you intend to put into 
 your picture. It may be arbitrary, but the distance here 
 marked is a good proportion. It is rather more than 
 twice the distance from the ground Hne to the horizon. 
 If you refer to Lesson 3, Plate 4, you will see the use 
 and importance of the distance point. The distance D 
 (Plate 7, Figure I) is set off, or marked on the prime 
 vertical line. In other cases, which will be hereafter 
 explained, it is measured on the horizon line. 
 
 Having proceeded thus far, look at the building, if 
 you are sketching one, and estimate as well as you can 
 (by means of your measuring stick held in a horizontal 
 position) the angle which the bottom Hne makes with 
 the ground line, and draw this from the ground hne to 
 the horizon G V. Where it intersects the horizon at V, 
 is the vanishing point for this side. Draw a Hne from 
 3* 
 
18 
 
 LESSONS IN PERSPECTIVE. 
 
 the point of distance D, to the vanishing point, mak- 
 ing D V. 
 
 Draw the line D W so as to make up the comple- 
 ment of a right angle ; that is, if the first line D V 
 make an angle of 60^ with the vertical line, let the 
 second D W make an angle of 30° ; or if one is 45° 
 let the other be 45°, both being equal to 90°, and D V 
 and D W form a right angle. 
 
 If you have not the necessary instruments at hand for 
 taking angles, you can easily obtain a right angle, by 
 cutting a bit of card exactly square, place one side on 
 the line D V, letting the corner touch the point D ; then 
 the other side will give you the line which you are to 
 produce from D to the horizon, to find the point W for 
 the vanishing point of the second side of the building. 
 
 If the object you are drawing is rectangular, the hues 
 to determine its vanishing points must form a right 
 angle. 
 
 The point W is the vanishing point for the second 
 side of the house, and for all lines, as doors, or win- 
 dows on it. 
 
 Determine the nearest point in the base of the house, 
 as A, by your eye, or measure. The line A V for the 
 first side of the house is already drawn. Draw the 
 other side to its vanishing point, making A W. 
 
 Raise the perpendicular A B I to the height the 
 house appears to be. A little practice will enable you 
 to judge of this height, with sufficient accuracy for all 
 the purposes of sketching. Compare it with the objects 
 in the view, or compare the height with the length. 
 Draw C and F from the point I to their vanishing 
 points V and W. 
 
 Draw the perpendiculars L and M, determine their 
 place by your eye and the aid of your measuring stick. 
 
 Observe that windows and other parts, diminish in 
 apparent size as they are drawn nearer the vanishing 
 
LESSONS IN PERSPECTIVE. 
 
 19 
 
 point. This rule applies also to the vanishing side, in 
 parallel perspective, viz. the v^^indows, doors, he. of 
 that side which vanishes in the point of sight. The eye 
 is generally sufficiently correct to judge of this propor- 
 tion ; but the lessons in drawing from a ground plan 
 will very much assist the scholar, who after having 
 studied them, will be in possession of the principle upon 
 which they are diminished, and can apply it with ease 
 to any case, without making all the measurements re- 
 quired in drawing from a ground plan. 
 
 The point of the roof E, which in the original, is 
 exactly over the centre of that side, must in the drawing 
 be placed a little beyond ; because that half which is 
 farthest from the spectator, appears smaller than the 
 other. 
 
 Further directions for drawing roofs will be given in 
 Lesson 9. 
 
 The Hne E V for the top of the roof vanishes at V, 
 because it is parallel with the bottom line of the house ; 
 and so would all the lines for the doors and windows, 
 parallel with the base hne. These are omitted, in 
 order that the figure may not be too complicated. 
 
 If there are several buildings in the view you wish to 
 take, some standing parallel, others oblique, you need 
 not be puzzled by this circumstance, but regard them 
 as so many different sketches. Thus, Plate 7, Figure 
 2, N O P are three houses standing in different posi- 
 tions, O is parallel, N and P oblique. 
 
 Having drawn the ground line, horizon line, point of 
 sight, prime vertical line, through it and the point of 
 distance ; draw the parallel house O, the end q vanish- 
 ing in the point of sight, because it is at right angles 
 with the ground line. 
 
 The house N must have two vanishing points of its 
 own, (R and g, on the horizon line,) because it stands 
 obliquely. These are to be found, as already directed, 
 
20 
 
 LESSONS IN PERSPECTIVE. 
 
 in the house above, figure 1, and the lines for the top, 
 the roof, and the doors or windows, must all be ruled 
 to these vanishing points ; for these lines are in the 
 original, parallel with the base line of the house, and 
 lines which are parallel, if they vanish, have the same 
 vanishing point. 
 
 Having found the vanishing point for one side, noth- 
 ing is easier than to draw all parallel lines on that side 
 to this point. You cannot fail of getting them right by 
 this rule ; whereas if you trust to your eye alone, it 
 would be scarcely possible that your drawing should be 
 correct. 
 
 The house P standing obliquely, must also have 
 its own vanishing points, found as already directed, by 
 means of the distance point D on the vertical hne, and 
 making the complement of a right angle of both sides. 
 These points are V for the side T, that for the side P 
 extends beyond the plate. This often happens in 
 oblique perspective, therefore the paper must be larger 
 than the picture, and the horizon hne extended far 
 enough beyond the boundary of the picture, to receive 
 the vanishing points. The side which makes the 
 smallest angle with the ground line, is that whose van- 
 ishing point will be farthest from the point of sight. If 
 it makes a very small angle, that is, stand nearly square, 
 this vanishing point will be very remote, and the lines 
 of that side will be almost parallel. In this case, the 
 vanishing point for the other side will be very near to 
 the point of sight, and vanish more suddenly. You 
 will see less of this side, or rather the representation of 
 it, will take up less space in the drawing than the other. 
 
 This can be easily proved by drawing houses with 
 various degrees of obliquity, according to the foregoing 
 rules ; which will be very useful practice. 
 
LESSONS IN PERSPECTIVE. 
 
 21 
 
 LESSON Vll. 
 
 GROUND PLAN, OR ICHNOGRAPHY. PARALLEL 
 PERSPECTIVE. 
 
 If you desire great accuracy in your view, or have 
 occasion to draw from description, you will make use 
 of a ground plan. This is called taking the ichno- 
 graphy of objects. 
 
 First make a scale or measurement, divided into 
 equal parts, in which inches, or parts of inches are taken 
 for feet or other dimensions. As A, (Plate 8) which 
 is a scale of 40 feet, or other measures. 
 
 Adhere to your scale in all your measurements for 
 the same picture. 
 
 Draw the ground line, horizon line, vertical line, and 
 point of sight. 
 
 Measure the distance at which the spectator is sup 
 posed to stand from the perspective plane, and set it 
 off in this instance, on the horizon line, from S. The 
 point D thus ascertained is the distance point. Its use 
 will presently appear. It is necessary to keep in mind, 
 what has already been explained of the perspective 
 plane, viz. that it is imaginary, and represented by the 
 paper on which you draw, that it is a transparent plane 
 held up before the eye, at some distance, on which you 
 delineate the objects beyond, as they are seen through 
 it ; and that the drawing of each part or point is pre- 
 cisely where the rays of light pass through it, in their 
 passage from the object to the eye. Though not visi- 
 ible as straight lines, these rays actually move in straight 
 lines, and form an image of the picture in the eye, 
 where, small as this image is, the relative proportions of 
 every part are exactly preserved. 
 
 It is desirable for one who is learning perspective, to 
 know something of the theory of vision, and a few hours 
 
22 
 
 LESSONS IN PERSPECTIVE. 
 
 Study of any treatise on optics, with a plate of the eye, 
 would be sufficient for the acquisition of all the knowl- 
 edge requisite. 
 
 The objects to be drawn are always beyond the 
 perspective plane, that is, this plane is between these 
 objects and the eye ; the nearest point coming just up 
 to the plane, and the place where this nearest object 
 comes, is the place for the ground line. All this has 
 been repeatedly said, but it is necessary to call it to 
 mind, and render the ideas famiHar by repetition, that 
 what follows may be fully understood. If the objects 
 to be drawn are beyond the perspective plane, they 
 may be at different distances, and it has been already 
 explained, that the lines of light coming from the object 
 to the eye form an angle, the size of which depends on 
 the size- of the object, and its distance from the eye. 
 The drawing of it is also affected by the distance of 
 the perspective plane : see Lesson 3. Now if you 
 make the object of the same size and distance from the 
 eye, and put the perspective plane in the same place 
 as the original, (that is, the same proportion, measuring 
 by a scale,) you will obtain the same angle as the origi- 
 nal makes, and this angle will intersect the perspective 
 plane precisely as the original angle would a pane of 
 glass, at the given distance from the eye. 
 
 The use of a ground plan is to give these proportions 
 and angles, with perfect accuracy, and of course to 
 enable you to obtain a correct drawing of any object 
 thus described and laid down. 
 
 It may be the case, that you cannot place yourself 
 at a convenient distance from the object you wish 
 most to include in your sketch ; but you may imagine 
 yourself there. 
 
 With a ground plan you can select any distance, 
 which the situation of the objects warrants ; and if you 
 adhere to your points of distance, sight, &ic. and your 
 
LESSONS IN PERSPECTIVE. 
 
 23 
 
 measurements, the drawing will always be in good per- 
 spective. 
 
 Having fixed the distance point on the horizon line 
 D, you proceed to draw a plan of the object. Let B 
 (Plate 8) represent the ground floor of a house, meas- 
 ured accurately by your scale, and placed at the same 
 distance from the ground line as the original. Carry 
 up, or as it is expressed technically, produce the two 
 lines N O and K J, till they intersect the ground line. 
 These lines are at right angles with the ground line, 
 and therefore vanish in the point of sight. 
 
 From F and I, the points of their intersection, draw 
 two lines to the point of sight, making I S and F S ; 
 I S is the true representation of I O and F S of F J. 
 
 Measure the distance at which the house stands from 
 the ground line, viz. from K to F, and set this off on 
 the ground line from the point of intersection F to M, 
 and then the actual size of that side, and set it off to L, 
 M L being equal to K J ; from the points M and L 
 draw" two lines, meeting in the point of distance D, 
 making the angle M D L, which angle is precisely the 
 same that two rays of light would make, proceeding 
 from an object of the same dimensions as that in the 
 plan, and at the same distance from the eye and the 
 perspective plane. The space F K influencing the 
 size of the angle precisely in the same degree, when 
 • transferred to the ground line at F M, as it would do in 
 the original. 
 
 Suppose a perspective plane, and an object of the 
 same dimensions as B, placed at the same distance 
 beyond it, that B is now placed before the perspective 
 plane in Plate 8. Let the eye be stationed in front, 
 just as high above the ground line, as S the point of 
 sight is, and at the same distance from the perspective 
 plane, that D is from S. Two threads from the side 
 K J, carried in straight lines to the eye, as rays of light 
 
24 
 
 LESSONS IN PERSPECTIVE. 
 
 come, would form this same angle at M D L, and 
 would pass through, or intersect the perspective plane 
 in their passage to the eye, exactly at the points h and a. 
 These are the points required, and give the apparent 
 size on the perspective plane, of that side which is at 
 right angles with the ground line, and vanishes in the 
 point of sight. 
 
 h is the point which corresponds to K, rule h d par- 
 allel with the ground line, which represents N K. 
 Then from the other point o, rule a c, which answers 
 to O J, and the figure is complete ; a b c d being the 
 true drawing of K J N O. 
 
 From the points d b and a raise perpendicular lines 
 for the sides or walls of the house. In order to ascertain 
 the apparent height, raise a perpendicular from the 
 point I, this is the point at which the line O N, when 
 produced, intersects the ground line ; for could the house 
 be moved up to the perspective plane, it would touch 
 it at I F. Measure on this perpendicular, by means 
 of your scale, the actual height of the house (of which 
 it is presumed you have on your plan an exact des- 
 cription) set this off, from I to m, from u rule u S, 
 which intersects the perpendicular d e, at e, this gives 
 the apparent height. — You ascertain by this process 
 precisely how much the house diminishes, in conse- 
 quence of its distance N I from the perspective plane. 
 Rule ef parallel with d b, because these lines are in 
 the original parallel with the ground hne. Rule /, S, 
 which being parallel with b a, has the same vanishing 
 point. The perpendicular from c, which would com- 
 plete the four walls of the house, is not drawn, because 
 it is not seen. 
 
 The height of the roof is set off from u to v. Draw 
 w at the true angle, viz. making the same angle with 
 the line e f as in the original. Draw v S ; where it 
 intersects at x is the apparent height for the roof. The 
 
LESSONS IN PERSPECTIVE. 
 
 25 
 
 point y, which, in the original is the centre of that side, 
 appears a little beyond, in the perspective representa- 
 tion, because the half of this side which is farthest off 
 looks smallest. To ascertain the precise place, divide 
 M L exactly in halves at rule a hne from z to the 
 distance point D. Where this intersects at g raise a 
 perpendicular till it intersects the line a? y at y; this 
 gives the place y for the centre. For h a correspond 
 with M L, and g with z. 
 
 If the house were nearer the ground line, or farther 
 off, you would proceed as above ; only remember to 
 produce the two lines which are at right angles with the 
 ground line, (as O N and J K,) till they touch the 
 ground line, and rule them to the point of sight. Set off 
 the distance F K, whatever it may be on the ground 
 line, as F M ; and from M set off the true measure- 
 ment of the side at right angles, viz. K J. This is the 
 side which vanishes in the point of sight, and therefore 
 is next the point of sight. 
 
 If the plan B were on the other side of the point of 
 sight, then ONI would be laid down or measured off 
 on the ground hne, as F M L are now. 
 
 This figure is a sufficient rule for the drawing of any 
 rectangular building, placed parallel or square before 
 you, let the dimensions and distance be what they may ; 
 provided these are accurately laid down on the ground 
 plan. 
 
 LESSON VIII. 
 
 GROUND PLAN. OBLIQUE PERSPECTIVE. 
 
 If you wish to put a house, or other figure, in oblique 
 perspective, by a ground plan, you first prepare your 
 paper with the ground hne, horizon hne, point of sight, 
 4 
 
26 
 
 LESSONS IN PERSPECTIVE. 
 
 and prime vertical line through it, and the distance 
 point, set off on the vertical line from the point of sight, 
 as in Lesson 6. Leave space enough below the ground 
 line to draw your plan, of the same dimensions, position 
 and distance as the original : see Plate 9, O. 
 
 Obtain the vanishing points A and B by means of 
 parallels ruled from the distance point D, on the vertical 
 line to the horizon, D B being parallel with d b, and 
 D A with d a. 
 
 Produce the lines which mark the four sides of the 
 house, d b c, c a, a d, till they intersect the ground 
 hne. 
 
 At the points of intersection efgh, rule lines to the 
 vanishing points. A is the vanishing point for the line 
 a d g, and therefore for c b A, because they are parallel; 
 and you must keep in mind the rule, viz. parallel lines 
 if they vanish, have the same vanishing point, fdb and 
 e a c are parallel and vanish at B; therefore make e B 
 and/B. The intersection of these lines on the per- 
 spective plane, make the figure ij k Z, which is the 
 perspective representation of a d b c m the plan : be- 
 cause, these points of intersection on the perspective plane 
 are the same which would be made by the rays of light 
 coming from the points in the original to the eye, pro- 
 vided the dimensions and position correspond to those 
 in the plate, as has been shown in Lesson 7. 
 
 From the points kj Z, raise perpendiculars for the 
 sides or walls of the house. 
 
 Ascertain their height by the following method : Rule 
 perpendicular hnes from the points of intersection, with 
 the ground line g and /. If you look back to Lesson 
 7 you will find you did the same thing, and the reason 
 is there given, excepting that there you ruled one line, 
 whereas here you have two. As has been said in a 
 former lesson, oblique perspective is twice as much 
 
LESSONS IN PERSPECTIVE. 
 
 27 
 
 work as parallel, because both sides have a vanishing 
 point. 
 
 On these perpendiculars raised from g and/, measure 
 by means of your scale, the actual height from the 
 ground line. 
 
 Thus if the side a c is thirty feet, and the height of 
 the house forty, make / m and g m one third more 
 than a c. 
 
 Rule the lines m B and m A ; they intersect on the 
 perpendicular k, giving the top of the wall for each 
 side.* 
 
 The point of the roof n is exactly over the centre of 
 the house O, in the ground plan ; to find which, rule 
 diagonals across the perspective representation of the 
 floor of the house, making i k and i j. These lines 
 cross at the centre o which represents O in the plan.f 
 
 From 0 raise a perpendicular o n. Produce m to P, 
 which is the height of the roof: rule from this to its 
 vanishing point making P B, where it intersects at n is 
 the point of the roof, rule lines from n to the corners of 
 the house. 
 
 If the roof is not pointed, rule the lines for the ridge 
 to their vanishing points. In the original, they are 
 parallel with the top and bottom lines of the house, and 
 therefore vanish at A and B. 
 
 If much accuracy is required, measure the space to 
 be cut off from the peak on the line m P, and by ruling 
 from this to the vanishing point, you get the precise 
 place for the ridge. 
 
 * The line m g is not drawn all the way, but only at its com- 
 mencementj at m. n o is not carried beyond S, as these lines come so 
 near those for the nearest window. 
 
 I By producing the lines 5 7 and 6 8 (Plate 9) to the ground line, 
 and ruling them to their vanishing points, as you have done the 
 outside lines ad, d b, &c., you will find the centre as truly as by 
 ruling the diagonals i k and I j ; but this last method is more simple. 
 
28 
 
 LESSONS IN PERSPECTIVE. 
 
 % 
 
 Divisions for the doors and windows are ascertained, 
 as may be seen from the Plate, by being marked on the 
 ground plan, produced to the ground line, and then 
 ruled to the vanishing point A. 
 
 From the points at which these lines intersect the 
 base lines of the house, raise perpendiculars, which will 
 give the perspective place for all the windows and 
 doors. 
 
 For as the sides of the house recede, the farther 
 part looks smaller than the nearer, and you perceive 
 that the method given shows this gradation with ex- 
 actness. 
 
 When the ground plan is so large that the lines to be 
 produced to the ground line (as c b produced to h) 
 would extend beyond the paper, and thus be inconvenient 
 to draw, the following method of making divisions, or 
 measuring lines may be used ; and perhaps it will be 
 thought preferable in every case where there is a ground 
 plan. If you wish to find J (the representation of the 
 point b) on the line k B, (Plate 9) which is the point 
 where the house terminates, lay your ruler from the 
 distance point D, on the prime vertical line, to the point 
 b in the plan, making D 6. — You perceive that it cuts 
 the line k B (which is the base line of the house) at J, 
 precisely as the line from A to A, and answers the pur- 
 pose of measurement equally well. And if you lay the 
 ruler from D to a, you get the point /, previously obtain- 
 ed by ruling a line from e to B. 
 
 In the same manner places for the windows may all 
 be found, by ruling lines from D to 1 2 3 4, which 
 lines are not drawn on the Plate, to avoid confusion. 
 
 The angles are the same in the last method as the 
 first, and both correspond exactly with the angles, which 
 rays of light proceeding from the house to the eye (of 
 the given dimensions and position) would make : see 
 Lesson 15. 
 
0 
 
 LESSONS IN PERSPECTIVE. 
 
 29 
 
 A t^ird method of marking divisions in oblique per- 
 spective, somewhat more intricate than either of the 
 above, but which dispenses with the necessity of a 
 ground plan, will be given in the Lesson on bridges. 
 
 LESSON IX. 
 
 FURTHER INSTRUCTIONS FOR ROOFS. 
 
 In giving the true slant to all the lines of a roof, no 
 two of which are drawn parallel, a knowledge of the 
 rules of perspective is requisite ; and this knowledge 
 cannot be acquired without some labour, especially 
 when the pupil is learning from books ; the constant 
 reference to plates, making the process far more tedious 
 than when he has the assistance of a teacher. It is the 
 object of this work to enable those who cannot obtain 
 the services of a teacher, to acquire a knowledge of 
 perspective by their own efforts. But it is not pre- 
 tended, that this mode of learning, can be made as easy, 
 or even as intelligible, as the instructions of a competent 
 teacher. 
 
 The rules now to be explained, belong more properly 
 to a future lesson, but their application to the drawing 
 of roofs is here given, because this is necessary to 
 render the instructions for drawing a house complete. 
 
 In Plate 7, figure I is a house B, standing obliquely ; 
 V and W are the vanishing points for the two sides. 
 It will be remembefi'ed, that a perpendicular line ruled 
 through the point of sight, as D S in this figure, is called 
 the prime vertical line. It represents a ray of light 
 coming straight from the perspective plane through the 
 eye, and marks the point of sight as S, and also the 
 distance of the spectator as D, and it is plain that the 
 
30 
 
 LESSONS IN PERSPECTIVE. 
 
 farther off the spectator is placed from the perspfctive 
 plane, the longer would be this ray. 
 
 The learner must not be puzzled by the situation of 
 this line in the plate. If a spectator were actually 
 placed before a window, a ray of light coming straight 
 from the object exactly opposite his eye, through the 
 perspective plane or window wouldT be a horizontal 
 line, and not perpendicular, as it is in this figure. But 
 such a line cannot be expressed on a flat sheet of paper, 
 nor is this necessary ; for the angle under which an 
 object is seen, and the distance of the perspective plane, 
 can be measured with the same accuracy when they 
 are laid down on a flat sheet ; as is done in Plate 7, 
 and this is all that is requisite to obtain a correct per- 
 spective representation. 
 
 This subject, however, will be further illustrated in 
 Lesson 15. To return to the prime vertical line, figure 
 1, Plate T. This ray coming straight to the eye, on 
 which the distance D is marked, is sometimes called the 
 visual ray. A similar line drawn through the vanishing 
 points of oblique planes, (viz. sides of houses, he. 
 standing obliquely,) as W in this figure, is the vertical 
 line, or visual ray for these points, called also the 
 radial or vanishing line. 
 
 Therefore the line drawn through W, viz. W X, and 
 through V, figure 2, Plate 7, are the radials, or van- 
 ishing lines of these same points W and V. The roof 
 of the house in figure 1, Plate 7, is a prism, whose 
 base vanishes at W and V, and its sides must vanish at 
 some point on the radial of one or the other of these 
 points, as X. This point is deterR:;ined by the angle 
 of the slant line with the base, as E I, which being pro- 
 duced, till it intersects the radial, gives the vanishing 
 point X, to which point draw the other line for the 
 roof, as g ; for g being parallel to E 1, must if it van- 
 ishes, have the same vanishing point. All lines have 
 
LESSONS IN PERSPECTIVE. 
 
 31 
 
 a vanishing point, except such as lie on planes, parallel 
 with the perspective plane or the ground line. The 
 wall of a house which stands parallel or square before 
 you, is a plane parallel with the perspective plane, or 
 the window through which you look ; but the roof is 
 not, it makes an angle more or less large, with the 
 perspective plane, consequently any lines lying on it, 
 (viz. the outline of the roof,) have a vanishing pointy 
 found according to the directions given above. 
 
 In figure 2, Plate 7, the roof of the house P vanishes 
 at y, (see figure 1,) on the the radial of its own vanish- 
 ing point V, that is, on the perpendicular drawn through 
 V, and the point y«is ascertained by producing the line 
 of the roof r to y. 
 
 In the house O, standing parallel, the peak of the roof 
 is ascertained, by finding first, the centre of the ground 
 floor of the house. This ground floor is an oblong rec- 
 tangular figure, the perspective appearance of which 
 may be found without the aid of a ground plan. 
 
 From the point j?, rule a line to the point of sight, 
 which will give the end not seen, parallel with and 
 through the upper corner of q rule a horizontal line, 
 and you have the floor of the house, as it would appear 
 if the house were transparent, and you could see it all. 
 To find the centre, rule diagonals from each corner, 
 and the point of their intersection, as you see by the 
 figure, is the apparent centre. Raise a perpendicular 
 from this centre to the height required, and you have 
 the point h for the roof: let the slant lines meet here, 
 and cut them off by ridge poles if required. 
 
 The roof of the house N (Plate 7) is obtained in the 
 same way, by drawing a radial through R, one of its 
 vanishing points. 
 
 In Plate 8 the house is parallel, and the vanishing 
 point for the roof is found on the prime vertical line, 
 because the base of this roof, viz. the line / S vanishes 
 in S, the point of sight. 
 
32 
 
 « 
 
 LESSONS IN PERSPECTIVE. 
 
 LESSON X. 
 
 CIRCLES. 
 
 A circle may be circumscribed by a square, and if 
 tliis square is put into perspective, the circle can be 
 drawn v;ithin this perspective representation, or if accu- 
 racy is required, the square can be divided, and the 
 corresponding parts in the representation will be a suf- 
 ficient guide for drawing the circle. The larger the 
 circle is, and the greater the degree of accuracy re- 
 quired, the more numerous must be the divisions of the 
 square, put into perspective. All this, however, is only 
 putting into perspective, horizontal, perpendicular, or 
 oblique lines : the rules for doing which, have been 
 fully given. 
 
 But as some difficulty may be found in applying these 
 rules to new cases, the following illustrations are offered. 
 
 Plate 10, figure 1, represents a circle put into paral- 
 lel perspective. 
 
 H, horizon line ; S, point of sight ; D, point of dis- 
 tance ; G, ground line, sometimes in works on perspec- 
 tive, called intersection line, because it is the line form- 
 ed by the intersection of the perspective plane with the 
 ground plane. 
 
 The circle C, in the ground plan is circumscribed by 
 a square, diagonals and diameters are ruled. The 
 points at which the diagonals strike the circumference, 
 make equal divisions on the circumference, though not 
 on the square. Through these points are ruled lines, 
 called sines and cosines. 
 
 Put all these lines into perspective, according to the 
 rules already given in Lesson 7 ; this being a case in 
 parallel perspective. 
 
 The lines A B F E L must be produced till they 
 intersect the ground line : from the points of intersection 
 
LESSONS IN PERSPECTIVE. 
 
 33 
 
 rule them to the point of sight, because they are lines 
 at right angles with the ground line. 
 
 Measure the distance of the circle from the ground 
 line, viz. M L, set it off on the ground line, making M 
 N, then the distances of the points K and I, which are 
 equal to O P ; rule lines from N O P to the point of 
 distance D. The object of these lines is merely to 
 mark the perspective size of the square, by means of 
 the points of their intersection with the line M S, drawn 
 to the point of sight ; therefore at these points of inter- 
 section, rule the lines u v t parallel with the ground 
 line, corresponding to A L, V K, W I in the ground 
 plan. 
 
 Rule diagonals through the points r t u w, repre- 
 senting the diagonals in the plan. 
 
 Observe the points of intersection in the perspective 
 representation, which correspond with those in the plan, 
 and draw the circle through them. You perceive that 
 the perspective circle is divided into parts like that in 
 the plan, but in the former they are not equal, although 
 they are so in the latter. The upper half of the circle 
 is smaller than the lower half; this circumstance gives 
 the figure a peculiar character, which you will, with 
 a httle practice, be able to draw with sufficient accuracy 
 for the common purposes of sketching, without all these 
 lines, or even without any, although you never could 
 arrive at this, except by a knowledge of these rules. 
 
 Portions of circles, as arches, doors standing more or 
 less open, (which describe portions of circles on the 
 floor, by the movement which opens them,) are drawn 
 on the same principles, and will be further illustrated. 
 
 Plate 10, figure 2 represents two circles in obhque 
 perspective. 
 
 The ground plan is first made ; then the vanishing 
 points are obtained by drawing parallels. From the 
 distance point D, (which in obhque perspective is 
 
34 
 
 LESSONS IN PERSPECTIVE, 
 
 always set off on the prime vertical line,) draw D B 
 parallel with c W, and D A parallel with c q. The 
 points of intersection with the horizon line, give A B 
 vanishing points for the sides c W and c q. 
 
 The lines c K L M W are produced till they inter- 
 sect the ground line, also c e N f q, and from these 
 points of intersection lines are ruled to each vanishing 
 point. O A P ^ c to B, and R T w V to A, and the 
 circle is drawn through the points of intersection as in 
 the original. 
 
 As the line W, if produced to the ground line would 
 extend beyond the picture, the rule is laid from D to 
 W, which gives the point y with equal correctness as by 
 the other method, as has been shown in Plate 9 : see 
 D b and D a. 
 
 LESSON XI. 
 
 BRIDGES. 
 
 It is nearly impossible, with the most accurate eye, 
 in taking a sketch, to draw a bridge of several arches 
 correctly, without a knowledge of the rules of per- 
 spective ; more especially if the bridge stand ob- 
 liquely. 
 
 The following method with the figure is given, to 
 to illustrate the application of the rules of perspective to 
 the drawing of bridges ; though somewhat elaborate, it 
 has been made as clear and simple as the subject 
 permits. 
 
 If this figure be studied faithfully, and the rules 
 applied to new designs made by the pupil, he will meet 
 
LESSONS IN PERSPECTIVE. 
 
 35 
 
 with no difficulty afterwards, in sketching with sufficient 
 accuracy, without the necessity of laying down all the 
 lines and points in these figures. With the principles 
 of perspective familiar to his mind, he will never make 
 any glaring mistakes, even in the most rapid and care- 
 less sketching ; while without this, his most laboured 
 productions would be wanting in truth of expression. 
 To this, every one acquainted with perspective, will 
 readily assent. 
 
 Plate 11 represents abridge in oblique perspective. 
 Having drawn the horizon and ground lines, points of 
 sight and distance, rule the line E F, making the angle 
 with the ground line, which you presume the bridge to 
 make. Of this you will judge by holding up your 
 measuring stick. From F draw F D, F is one van- 
 ishing point ; draw also the line D L at right angles 
 with D F, which gives L for the other vanishing point, 
 (as it is oblique, both sides vanish.) The angle F D L 
 is a right angle. Select by your eye, with the aid of 
 the measuring stick (described in Lesson 5) the nearest 
 point in the bridge J, raise the perpendicular J i to 
 the height at which the bridge appears to be ; which 
 you can determine, by observing how near it comes to 
 the horizon : then rule i F for the top, because the 
 top and bottom are parallel, and must have the same 
 vanishing point. 
 
 Draw a line through the point J, parallel with the 
 ground line ; set off on this line the measurement of the 
 size of each arch. This you may ascertain by com- 
 paring the size of the nearest arch with the height of 
 the bridge. Perfect accuracy is not requisite, but the 
 spaces for each arch must be equal. You thus get the 
 points J K M N. Measure the space F D, (with com- 
 passes if you have them,) and lay it on the horizon 
 from F, by describing the arc, making the point R. 
 
36 
 
 LESSONS IN PERSPECTIVE. 
 
 This is called the radius* of its own vanishing point, 
 and answers the same purpose as the distance point 
 (set off on the horizon from the point of sight, in paral- 
 lel perspective) for taking measurements. 
 
 Rule lines from the points K M N to R, they inter- 
 sect the line for the bottom of the bridge J F, at the 
 points O P Q, and give the apparent size of each arch, 
 viz. the place for the foot of each arch. Then divide 
 the space for each arch, viz. J K, K M, and M N 
 equally, and rule lines from these divisions to R. 
 These lines are not ruled in the figure ; they intersect 
 the line J F at T m the places for the centre of each 
 arch. Raise perpendiculars from t u v to the top hne 
 of the bridge : draw a guide line A F for the tops of 
 the arches, which line being parallel with the top and 
 bottom of the bridge, has the same vanishing point. 
 
 Draw a straight line from each of the points W X Y, 
 to the points J O P Q, like the dotted lines in the plate. 
 Describe arches on these lines. The arches may be 
 drawn without these straight lines, but you will not 
 probably do them as well. 
 
 Draw the line J L, which gives the other side of the 
 bridge, L is the vanishing point for all lines parallel to 
 J L ; therefore rule O L, P L, and Q L, which lines 
 represent the under part of the arch, as it leaves the 
 water, and are, as you will perceive by a little observa- 
 tion, parallel in the original bridge, with the end J L. 
 
 You have now ascertained the direction of these 
 lines, but not their size. Each arch, as you observe in 
 
 * A radius is the semidiameter of a circle, that is, a straight line 
 drawn any where from the centre to the circumference. If you take 
 F (Plate il) for a centre, and putting one foot of the compasses in 
 this point, and extending the other to D for the size, and draw a 
 circle ; F R would be a radius of this circle, as well as F D, and it 
 is called the radius of its own vanishing point, because it is the 
 radius of a circle, of which this vanishing point F is the centre, and 
 F D the radius. 
 
LESSONS IN PERSPECTIVE. 
 
 37 
 
 the figure, shows more of the under part, as it recedes 
 farther from R its distance point. Measure by the 
 scale you have used for your other measurements, on 
 the line J, the space J Z, being the real size for the end 
 of the bridge, then take the radius of the vanishing point 
 of this side L, viz. L D, (as you did for the other side,) 
 and lay it on the horizon line to r, making L r. Rule 
 Zr, the point of its intersection at a is the size of this 
 end ; raise a perpendicular at a, rule i L parallel with 
 a J, in the original, therefore, having the same van- 
 ishing point ; from h rule b F, the top of the further side 
 parallel with i F, for, as the whole bridge is below the 
 horizon, you see this line, otherwise you could not. 
 Rule a line from a to the vanishing point F, this line 
 represents the base line of the further side of the bridge, 
 parallel in the original with J F, therefore having the 
 same vanishing point. The hues for the under part of 
 the arches, viz. O L, PL, Q L, are already drawn. 
 a F intersects these at / j k, giving the perspective 
 finishing of the arches. 
 
 Observe the dotted lines continued from I m n, they 
 show how each arch would appear, if the bridge were 
 transparent, and they could be seen. Unless you un- 
 derstood the true drawing of the whole of each arch, you 
 could not draw correctly the part which is visible, and is 
 represented by the darker line, for each differs from the 
 other, and to draw them all ahke (as is frequently done, \ 
 even in sketches otherwise correct,) is bad perspective. j 
 
 Plate 12 represents a bridge in parallel perspective, 
 which is easier than oblique. 
 
 The exterior arches are all alike, and are therefore 
 drawn without the aid of any other rule than that of 
 making them equal ; lines ruled from the foot of each 
 arch to the point of sight, give the direction of the lines 
 for the under part of the arch, A B C E. These lines 
 are at right angles with the ground line, and vanish at 
 5 
 
38 
 
 LESSONS IN PERSPECTIVE. 
 
 the point of sight : draw a hue at the foot of the bridge 
 parallel with the ground line, passing through the foot 
 of each arch as it leaves the water : mark on this line 
 the size of each arch, making the points F M N O, 
 from these rule lines to the distance point D, viz. F D, 
 M D, N D, and O D, cutting the base line of the arches 
 at P Q R T. This gives the size for the under part of 
 each arch, and also for the end T. Draw arches like 
 those in the figure. The dotted lines show the true 
 drawing for the arches, on the further side, (if they 
 could be seen.) In this way, you get the true appear- 
 ance of the under part of each arch of a bridge, situate 
 as this is, with regard to the point of sight. As may be 
 seen by the figure, each arch differs from the other in 
 the drawing, although in the original they are alike. 
 
 LESSON XII. 
 
 INTERIORS. 
 
 Interiors are drawn in perspective by the rules 
 already given, for they must consist of lines either 
 parallel, at right angles, or oblique to the ground line.* 
 
 After having drawn the horizon and ground lines, and ) 
 points of sight and distance, observe what lines are par- 
 allel with the ground hne, and draw them parallel, their 
 place being determined by their distance from the 
 ground hne. 
 
 Note what lines are at right angles with it, whether 
 they are on the walls of a room or any articles of fur- 
 niture ; the vanishing point for all such lines is the point 
 of sight. 
 
 * Except lines inclined to the ground plane, for which see Les- 
 son 14. 
 
LESSONS IN PERSPECTIVE. 
 
 39 
 
 If any objects or lines are oblique, you will determine 
 their vanishing points on the horizon line, by their angle 
 of obliquity, that is, by the angle they niake with the 
 ground line. 
 
 To illustrate this, see Plate 13. Make the requisite 
 lines and points. S being equal to S, because 
 you need a distance point for each side. In parallel 
 perspective, you may set off the distance point on the 
 horizon line, on either side of the point of sight. 
 
 Determine the size of the room by a scale, or your 
 eye, and draw the boundary lines N E and O I. Meas- 
 ure the length of the sides which are at right angles 
 with you, and lay it down on the ground line, making 
 E F for one side and I J for the other ; draw E S and 
 I S. Draw F D^, and also J (not drawn in the 
 Plate.) These give the points of intersection K and M, 
 which show the apparent length of the sides. Draw 
 N S and O S for the top lines of these sides ; draw the 
 line K M parallel with the ground line ; raise perpen- 
 diculars from the points K and M till they strike O S and 
 N S ; draw P Q, thus you get the back wall of the 
 room P Q K M. 
 
 The lines for the top and bottom of the windows, 
 with the bars which are parallel, go to the point of sight. 
 The dimensions of the windows are marked on the 
 ground line. R T for the first ; U I for the second : 
 rule lines from these points to D^, making the points r t 
 u V ; at these raise perpendiculars, which gives the 
 space for each window, u v being the smallest, because 
 it is the most distant ; mark the length of the windows 
 on the boundary line of the side N E, and rule the 
 lines X S and y S, also the lines for the window bars, 
 vanishing at the point of sight. Divide the space R T 
 and U I exactly in halves, and rule to D^ for the middle 
 line of the window :* smaller divisions are made in the 
 
 * In the Plate the larger window only has the middle line. 
 
40 
 
 LESSONS IN PERSPECTIVE. 
 
 same way, but are not drawn on this figure, lest it should 
 be confused. The same rule also answers for pictures 
 or pannels, on the walls of a room. 
 
 On the opposite side of the room is a door. Mark 
 its dimensions and place on the ground line a U, and 
 rule to D^, mark the top at d, and rule to S, getting 
 efg h ; this is the door frame. The door stands open. 
 A door in opening describes on the floor an arch or 
 portion of a circle, of which the hinge is the centre, and 
 the bottom of the door a radius or semidiameter. Open 
 a door quite back to the wall, and you will find that it 
 describes a semicircle ; open it less, and the bottom of 
 the door makes an angle (more or less large according 
 to the opening) with the sill of the door, which remains 
 stationary while you are moving the door. When you 
 have ascertained this angle ; in other words, when you 
 have opened the door as wide as you wish, you have 
 only to draw the door in your sketch at the same angle, 
 by drawing a line through the hinge g parallel with the 
 ground line, and letting the hne for the door make with 
 it the angle required. Produce this to the horizon hne 
 to obtain the vanishing point ; thus g 3 produced, gives 
 4 for the vanishing point. Draw a line from / to 4 for 
 the top ; that being parallel with the bottom, must have 
 the same vanishing point. The door, now it is open, 
 is no longer a plane at right angles with the ground line, 
 as it would be if shut, and as the wall of that side of 
 the room is, but it becomes a plane standing obHquely 
 to the ground line, and therefore has its own vanishing 
 point, viz. 4, as already shown. 
 
 In order to obtain accurately the point 3, from which 
 the perpendicular 3 9 is raised to finish the outline of 
 the door, you must keep in mind, that the door in open- 
 ing, describes a semicircle, ^ A is the radius. This 
 circle, or a quarter of it, must be put into perspective^ 
 
LESSONS IN PERSPECTIVE. 
 
 41 
 
 which is very easy, since this is only to put a square in 
 perspective. 
 
 Lines drawn from D^, passing through the points 
 g and h to the ground, give the dimensions of the radius 5 
 they are identical with the space for the door, viz. the 
 very radius in question. 
 
 Draw a line from U to S, which gives one side of the 
 figure in which the quarter circle is to be contained, 
 while g h already drawn, is the other. The figure in 
 which a quarter of a circle may be comprised, is a 
 square, one fourth less than the square by which the 
 whole circle may be circumscribed: see Plate 10, 
 where each circle is divided into four squares. 
 Having drawn the line U S, draw a line through h, and 
 another through g, both parallel with the ground line, 
 and intersecting U S at 5 and 6. The square is then 
 complete 6^5^. Describe within it the quarter 
 circle from h to 5, (which you can do, by inspecting 
 Plate 10, figure 1, without making any more lines,) 
 and where the line for the bottom of the door strikes 
 the edge of the circle, as at 3, raise the perpendicular 
 till it intersect (at 9) the line for the top of the door. 
 
 The two doors in the back side of the room are also 
 open. Their vanishing points are found as in the door 
 described above ; 1 vanishes at 7, and 2 at 4. 
 
 LESSON XIII. 
 
 TO PUT FURNITURE AND OTHER SMALL OBJECTS FOUND 
 IN INTERIORS, INTO PERSPECTIVE. 
 
 If you wish to put furniture, &c. into your picture, 
 this also must be drawn according to the rules already 
 given, as will be further illustrated. Keep in mind 
 5* 
 
42 
 
 LESSONS IN PERSPECTIVE, 
 
 what has been taught with regard to the vanishing 
 points for parallel and for oblique objects ; and remem- 
 ber that for every obhque object, whether doors, tables, 
 chairs, he, you must have distinct vanishing points, 
 which are all found on the horizon line, except in cases 
 where the planes are elevated above, or depressed 
 below^ the parallel of the ground plane, for which in- 
 structions will be hereafter given. 
 
 You must first determine what rule the object you 
 are drawing requires, by observing vvhether it is parallel 
 or oblique ; elevated or depressed. When this is done, 
 the difficulty vanishes, and you cannot fail in applying 
 the rule, if you have become famihar with its use. 
 
 Very great practice is necessary to insure facihty. 
 Accustom yourself to regard the diflierent aspects or 
 sides of objects as planes. A chair for instance, may 
 be viewed as composed of planes, perpendicular, hori- 
 zontal or oblique. The floor on which the four feet 
 rest, is one plane, the seat is another, parallel with the 
 former. The back is another plane at right angles 
 with the seat, or perhaps oblique to it. The four sides 
 reaching from the seat to the floor, where the cross 
 pieces are placed, are four upright planes, at right 
 angles with each other : for if the chair were box^d up 
 from the floor to the seat, this box would form the four 
 planes or sides. Thus in a chair, you have only hori- 
 zontal, perpendicular, or oblique planes to put into 
 perspective, which, it is presumed, you can now do. 
 
 It may be well to mention, that in oblique perspective, 
 the distance point is always marked on the prime verti- 
 cal line, viz. that drawn perpendicularly, through the 
 point of sight ; and it is from this point that angles are 
 taken, and parallels ruled for determining the vanishing 
 points, and vanishing lines in oblique perspective. 
 
 Plate 14 represents several articles of furniture which 
 afford further illustrations of the rules already explained. 
 
LESSONS IN PERSPECTIVE, 4S 
 
 The chair A is in parallel perspective, and the lines 
 vanish at S, the point of sight ; as will be seen by laying 
 a ruler from them to this point. The boxes B and C, 
 and also the footstool E, are parallel. The chair F is 
 oblique : vanishing points N and M. It will be found that 
 d and the lines parallel with it, vanish at M, and that A, 
 and its parallels vanish at N. The table T is oblique, 
 vanishing points V and W. The opening of the hd of 
 the box C, is determined on the same principle as the 
 opening of doors. The lid in opening describes the arc 
 of a circle, of which e a is the radius, the hinge being 
 the centre. Put this circle into perspective by means 
 of a square. The circle being put into perspective 
 shows w^here to draw e i, which must terminate at the 
 circumference. Draw /. 
 
 If you did not understand the principle, you would 
 be likely to make the line for the lid, e i of the same 
 length as e a, it being so in the original ; but in the per- 
 spective representation, you observe, that no radius 
 which may be drawn in this circle is of the exact length 
 of e a, for even the continuation of that line, as e n 
 must be shorter than e a, because that half of the circle 
 is farther from you, than the half in which the radius 
 e a lies, and consequently must appear smaller. 
 
 Neither can the line m for the opening of the other 
 end of the hd, be drawn parallel wath i, for it is the 
 corresponding radius to e i, of a circle nearer than the 
 circle e, and must therefore look larger than that : m 
 must also differ from r, in the same proportion, and for 
 the same reason, as e a from e i. 
 
 The two circles or rather parts of circles, are given 
 for the purpose of illustrating the importance of a thor- 
 ough knowledge of the rules of perspective, in order to 
 draw the most common or simple object with truth. 
 
 Having once understood the principle on which an 
 open box is drawn, you will, without the necessity of 
 
44 LESSONS IN PERSPECTIVE. 
 
 putting circles into perspective, be able to draw the 
 parallel sides of the opening with correctness. 
 
 You will observe that the two circles partly described 
 on the plate, for the purpose of determining the open- 
 ing of the box, are circles standing upiight on the 
 ground plane, and not laying on it, as are the circles in 
 Plate 10. They are situate like picture frames on the 
 walls of a room. The wheels of a carriage are drawn 
 in the same way ; each included in a square, put into 
 perspective, according to its position, (whether parallel 
 or oblique,) and its distance from the ground line. The 
 spokes are so many radii, not one of which you could 
 draw correctly, without an acquaintance with the rules. 
 
 As you have learned to draw squares, whether stand- 
 ing upright as windows, picture frames, &ic., or lying 
 on the ground plane, as the floor of a house : (see Plates 
 8 and 9,) you will have no difBculty in drawing the 
 squares in which to describe your circles, whatever may 
 be their position. After having gone through this book, 
 you will, it is presumed, be able to understand more 
 elaborate works on perspective, in which you will find 
 a greater variety of cases. 
 
 Another method of obtaining the line m, for the second 
 side of the lid of the box C, will be given in the expla- 
 nation of Plate 16. 
 
 LESSON XIV. 
 
 LINES AND PLANES NOT PARALLEL WITH THE 
 GROUND PLANE. 
 
 Lines and planes which are not parallel with the 
 ground plane, but have an elevation above, or depression 
 below it, find their vanishing points above or below the 
 
LESSONS IN PERSPECTIVE. 
 
 45 
 
 horizon line, determined by the angle of their elevation 
 or depression. 
 
 A book lying flat on a table, and a house on level 
 ground, are parallel with the ground plane, whether 
 placed obliquely or parallel with the ground line : but 
 houses on the side of a hill, a book with one end ele- 
 vated, slanting sides, as roofs of houses, desks, prisms, 
 or lines laying on them are inclined to the ground plane, 
 and their vanishing points are found on the vertical line 
 of the vanishing point of their base, either above or 
 below the horizon. 
 
 The directions for drawing roofs in Lesson 9, contain 
 the rules required for the drawing of planes and lines 
 oblique to the ground plane ; but it is thought that a 
 further illustration of the subject is needful. 
 
 In Plate 1 5, the base line of the row of houses A makes 
 an angle of 20° with the ground plane. This row also 
 stands obliquely to the ground line, and the angle of its 
 obliquity is 31*^. This angle is taken from the distance 
 point D, by the line D V ; V is the vanishing point for a 
 line laying on the ground plane, and inclined to the 
 ground line, at an angle of 31°. Thus if the row of 
 houses A stood on level ground, at its present degree 
 of obhquity, it would vanish at V. Draw the radial or 
 vertical line of the vanishing point V, which is (as has 
 been shown in the instructions for drawing roofs) a per- 
 pendicular line drawn through this point. 
 
 Now you may mark on this radial, from V, the 
 degree of elevation you determine on for the houses, as 
 W : or if you would be exact, you can measure it by 
 an angle, after the following manner. 
 
 Take the space V D and set it off on the horizon line 
 from V, making the point y ; this is the radius of the 
 vanishing point V. From ?/ as a centre, make the true 
 angle of elevation which the row has, in this case 
 
46 
 
 LESSONS IN PERSPECTIVE. 
 
 20^*. Where it strikes the radial of V, viz. at W, is 
 the vanishing point of the houses A. And all lines 
 parallel with B W, as the roof, windows, and the 
 street, vanish at W. 
 
 You will seldom find it necessary to take angles. 
 Draw a line from the bottom of the houses to the hori- 
 zon, at the degree of obliquity, you judge right, and 
 then make a point as W, directly over the vanishing 
 point, at the elevation you choose. Make all parallel 
 lines vanish at W ; this will be sufficient for the common 
 purposes of sketching. 
 
 The row of houses C is in parallel perspective, and 
 stands at right angles with the ground line, therefore the 
 vanishing point is on the prime vertical line. The 
 angle of its elevation is 20°. The distance S D being 
 laid on the horizon line to X, the angle J X S gives J for 
 the vanishing point. The row M is parallel, and has 
 an angle of depression below the horizon. The distance 
 S D transferred to the horizon hne at Z, gives the angle 
 S Z P. P is the vanishing point for all lines parallel 
 with the base line O P. 
 
 The row K is level and parallel, and vanishes at the 
 point of sight. 
 
 Plate 16, figure 4 represents an inclined plane. A 
 is a desk standing parallel. The drawer or base is 
 level, and the side a vanishes at the point of sight S^. 
 But as the plane A is elevated at an angle of 17°, its 
 vanishing point is at P, and the sides h and c are ruled 
 to P. 
 
 If you wish to determine the size of the desk by 
 measurement, set the real dimensions of the side a on 
 the line h i, and from h rule to the distance point D^. 
 
 * The line from V to W is the tangent of this angle. A tangent 
 is a line drawn from the point where a radius touches the circum- 
 ference, at right angles with this radius, and measures the angle^ 
 W V is the tangent of the angle W y V. 
 
LESSONS IN PERSPECTIVE. 
 
 47 
 
 Where this intersects at d is the apparent size of this 
 side, because it is parallel with the ground plane. 
 
 But in order to measure the inclined plane A, you 
 must take another distance point, because you have 
 another vanishing point. 
 
 Draw a horizontal line through P, (not entirely drawn 
 in the figure, to prevent confusion, but should be drawn 
 by the pupil in copying the figure,) which will be the 
 horizon line for the inclined plane A. On this new 
 horizon set your distance, viz. the space from P to D^, 
 making R. PR being equal to P D^. R is the 
 distance or measuring point for all lines vanishing at P. 
 Lay a rule from h (the true measurement, on the ground 
 line for the desk) to R, it intersects at T. This is the 
 apparent size of the desk at this elevation, and which if 
 laid flat and parallel with the drawer, would be of just 
 the same size as the drawer ; for the space from P to R 
 is the radius of the vanishing point P, set off on its own 
 horizon. Rule the line T r parallel with i n, to finish 
 the desk. 
 
 Unless you have a perfect acquaintance with these 
 rules, you perceive that you would be very unlikely to 
 draw the desk correctly, even if it were before your 
 eyes. Were the desk a little more or less open, that is, 
 were the elevation of the plane A a little more or less, 
 the line T r could not be drawn as it is now; whereas, 
 with the present elevation, if it were not drawn precisely 
 as it now is, it would not belong to the bottom part of 
 the desk. The measurement h n is the same for the 
 drawer and for the desk : but for the drawer, the dis- 
 tance point is fixed on the horizon line ; and for 
 the plane A, on a point (R) as much above that, as P 
 is above the horizon. 
 
 Plate 16, figure 3 is a desk elevated at an angle of 
 15°, and placed obliquely to the ground line. V and 
 W are the vanishing points for the two sides of the 
 
48 
 
 LESSONS IN PERSPECTIVE. 
 
 part which stands level. X is the vanishing point for 
 the sides k and /, which are elevated. being the 
 point of sight for the desk figure 3. above it is 
 the distance point on the prime vertical line, whence 
 angles are taken. Make V u equal to V D^. The 
 radius u is the measuring point of the side o of the 
 desk, which is level ; and the point above it Z, the 
 measuring point for the elevated part of the desk. 
 Lines 1 2 3 are parallel, and vanish at W ; 4 5 are 
 parallel, and vanish at V ; and k and I are parallel and 
 elevated above the ground plane, and vanish atX; lines 
 from Q to w give the point 6, and from Q to Z the 
 point 7. 
 
 The open box C, Plate 14, affords an example of 
 lines depressed below the ground plane. 
 
 After one side of the lid, as e i is found by means of 
 the circle, the other as m, may be ascertained by finding 
 the vanishing point of the first. As the box stands 
 parallel, this must be on the prime vertical line helow 
 the point of sight, because it is an example of depres- 
 sion, and not of elevation. 
 
 Produce i e till it intersect the prime vertical line 
 below the point of sight, which is at y, and this is the 
 vanishing point required. Rule a Hne from the point 
 y through the edge or hinge g, till it intersect the line 
 /, and it will give the line m with the same exactness as 
 the circle does, and with less trouble. 
 
 For i e and m g are parallel in the original, therefore 
 must have the same vanishing point, which point you 
 ascertain by producing i e to the prime vertical line at y. 
 
 The lid of the box is a plane not parallel with the 
 ground plane, as the bottom is, nor perpendicular to it, 
 as the sides are, nor parallel with the perspective plane, 
 as the front and back are ; but it is inclined to the 
 ground plane, and also to the perspective plane, having 
 an angle of depression below the ground plane. 
 
LESSONS IN PERSPECTIVE. 
 
 49 
 
 The base or edge of this inclined plane, (viz. the 
 line e at which it touches the top of the box, where 
 the hinge is,) is parallel with the ground plane, and the 
 side e a at right angles with the ground line ; therefore 
 the vanishing point for the inclined lines e i and mg 
 must be sought on the prime vertical line, that being 
 the vanishing line for all planes at right angles with the 
 ground line, as this end of the box is. 
 
 If the box stood obliquely as the desk, (in Plate 16, 
 figure 3,) this point would be sought on the radial of 
 the vanishing point of its own plane, and below the 
 horizon line. 
 
 If you have any doubt whether any plane (as the Hd 
 of the box C, Plate 14) is depressed below or elevated 
 above the ground plane, and therefore, whether its van- 
 ishing point must be sought above or below the horizon 
 line, you have only to observe whether the bottom or 
 the top of the plane is farthest from you ; if the top, as 
 the upper line of the roof of a house, or of a desk (like 
 T r and 1 7, figures 3 and 4, Plate 16) recedes, then the 
 vanishing point is above the horizon, for it is the re- 
 ceding part which looks smallest, and the fines of 
 course converge to produce this diminution. But if the 
 bottom is the receding part, (as the line e ^ in the box 
 C, Plate 14,) then the vanishing point is below the 
 horizon. 
 
 LESSON XV. 
 
 COLONADES AND STEPS. 
 
 Plate 16, figure 1 represents a colonade or row of pil- 
 lars, on each side the point of sight, that is, on the right 
 and left of the spectator. The lines which vanish go to the 
 point of sight, therefore, it is parallel perspective. It is 
 6 
 
60 
 
 LESSONS IN PERSPECTIVE. 
 
 thought that this figure, and an inspection of Plate 11, 
 where the arches of a bridge, in obhque perspective, 
 are exhibited, will be sufficient to enable the pupil to 
 apply the rules to colonades and arches in oblique per- 
 spective. The divisions are made, and the measure- 
 ments taken for a colonade viewed obliquely, in the 
 same manner as for a bridge or a single arch of a bridge 
 viewed obliquely. 
 
 The columns appear shorter and narrower as they 
 approach the vanishing points. 
 
 The floor in figure I is divided into squares to rep- 
 resent the figure of a carpet, or a pavement, after the 
 following manner. Draw hnes from the divisions on the 
 ground line to S, the point of sight. Draw the diagonal 
 E D from the first square to the distance point. This 
 diagonal intersects each line, showing the size of each 
 row of squares. Draw parallel lines through the points 
 of intersection. By this process, you find (as appears 
 by figure 1, Plate 16) the exact proportion in which 
 each square diminishes as it recedes from the eye. It 
 will be easy to draw any figure (a circle for instance) 
 within the square, as is done in two of the nearest 
 squares on the figure. The diagonals of each square 
 will give the centre, through which centre rule a line 
 for the diameter. If it is parallel perspective, the line 
 for the diameter is parallel with the ground line ; if 
 oblique, it goes to its vanishing point. 
 
 This diameter will show how much larger the nearer 
 half of the square appears, than the more remote. If 
 the figures are of an oval shape, you must put parallel- 
 ograms into perspective, instead of squares, which you 
 can easily accomplish by observing Plates 8 and 9, or 
 by the help of a ground plan. 
 
 Figure 2, Plate 1 6, shows the manner of drawing 
 steps in perspective. E two steps parallel, F two ob- 
 lique. It is in fact only putting so many boxes, or 
 
LESSONS IN PERSPECTIVE. 
 
 solid rectangular objects placed one on top of another 
 in perspective. You could easily draw one box as c, 
 in true perspective, and why not another as A, imntiedi- 
 ately below it ? The parts E and a correspond with 
 the tops of the boxes, as they appear seen below the 
 horizon : see also the box B, Plate 14. If they were 
 above the horizon, you could not seethe tops. By this 
 rule, in looking at an object, you may ascertain at once, 
 whether any part of it is above the horizon, that is, 
 above the height of your eye. When you are on level 
 ground, you cannot see over the top of a house ; but 
 when you are on a high hill, you can see over the tops 
 of the houses on the plain below. If you are in a room 
 you cannot see the top of a piece of furniture which is 
 higher than your head, while those articles which are 
 lower than your eye, as a table, show their upper sur- 
 faces, occupying more or less space, (viz. looking wider 
 or narrower) as they are nearer to or farther above the 
 floor. Therefore, if in a view, the tops of houses are 
 drawn, the horizon must be a high one, for it would be 
 apparent to any one acquainted with perspective, that 
 your sketch was taken from a height. 
 
 The steps F, Plate 6, figure 3, are, as it regards their 
 drawing, two boxes, one on the other, placed obliquely, 
 and having their vanishing points on the horizon line at 
 and W2. 
 
 That the rules given in these lessons will give the 
 true perspective drawing of objects, may be experimen- 
 tally proved by the following method. Provide a large 
 table ; this is a horizontal plane, and will represent the 
 ground plane, viz. the earth, on which objects are situate. 
 Station at the edge of one side of this table, a little figure 
 to represent the spectator, or person taking the view. A 
 
52 
 
 LESSONS IN PERSPECTIVE, 
 
 Stick of four or six inches in height, with a hole in the 
 top for the eye, vAW answer the purpose, it must be 
 securely fastened to the table. 
 
 At a suitable distance from the spectator, (say two or 
 three times, the height of the figure) set up a frame like 
 a picture frame without a glass, at right angles with the 
 table, that is, standing upright upon it. This is to rep- 
 resent the perspective plane. Put a line across the per- 
 spective plane horizontally, at the same height as the eye 
 in your figure. This line represents the horizon. 
 The best way to fasten this line is to attach a small 
 weight to each end of it, insert pins into the frame at 
 the proper height, and lay the line across. The weight 
 hanging down over the pins will keep the cord tight. 
 If you wish a higher or lower horizon, elevate or shorten 
 the figure, and alter the pins and line accordingly ; 
 always remembering that the line must be at the same 
 distance from the table or ground plane as the eye. 
 
 Mark the point in this horizon line directly opposite 
 the eye, whether it be the centre of the frame, or 
 nearer to one side than the other. This is the point of 
 sight. It is convenient to be able to move the figure to 
 the right or left, as this changes the point of sight, and 
 enables you to vary your experiments. 
 
 Through this point of sight pass another cord perpen- 
 dicularly, and fasten it. This is the prime vertical line, 
 passing through the point of sight. Plate 14, H W the 
 horizon line, and D S ^ the prime vertical line, repre- 
 sent the two lines here described. Prepare a model of 
 a house, box, bridge, or any object, the true drawing of 
 which you wish to ascertain ; place it behind the 4)er- 
 spective plane, to the right or left of the point of 
 sight, and at any distance you choose. 
 
 Attach threads to the corners, and to the top and 
 bottom of the sides next the perspective plane, which 
 
LKSSONS IN PERSPECTIVE. 
 
 53 
 
 are the only parts that can be seen ; bring all these 
 threads through the perspective plane, converging to 
 the eye of the figure, and fasten them securely at the 
 back. These represent rays of light in their passage 
 from the object to the eye. 
 
 It will appear that the points at which the threads 
 enter the perspective plane, in coming to the eye, give 
 the same drawing which the measurements, points and 
 angles do, in a drawing from a ground plan : provided 
 the proportions, size, distances, &ic. correspond. 
 
 If you look through the hole designed for the eye, at 
 the same time placing a pencil or small rod on the per- 
 spective plane, so as to conceal the lines in the original 
 object from the eye, you will find that it strikes just 
 where the threads enter the perspective plane. 
 
 Lay a ground plan of a floor of a house, or of circles, 
 like those in Plates 8, 9, and 10, on a table, behind the 
 perspective plane, so as to have this plane between the 
 eye and the ground plan. Substitute for the vacant 
 frame, one with a plate of glass in it, as a perspective 
 plane ; you can trace with a pencil on this glass, or 
 measure with compasses, the appearance of the figures 
 beyond. By placing your eye in the hole for the eye 
 of the figure, you will see that the drawing is the same 
 as that resulting from the measurements, angles, he* 
 already given in the rules of perspective, the proportion 
 and distances being preserved. 
 
 Objects may be placed in any position, and be of 
 any shape, and their true perspective dehneation can be 
 ascertained by attaching threads to their outline or 
 edges, and bringing them to the eye, after the manner 
 detailed in the above description. — The proportions 
 must be exactly preserved. 
 
 Your figure or spectator, which is presumed to be 
 about six feet high, affords a good scale, A complete 
 6* 
 
54 
 
 LESSONS IN PERSPECTIVE, 
 
 model of a person taking a sketch, with all the objects 
 in their true situation may thus be made. The threads 
 attached to each, and carried to the eye, will show the 
 angles under which every object is seen, and thus de- 
 termine the true drawing. 
 
 The diminishing of figures in a landscape according 
 to their distance from the ground line, may be experi- 
 mentally proved, by fastening one thread to the head, 
 and another to the foot of each of the figures, placed at 
 different distances on the ground plane. It will then 
 appear how much smaller the angle is (viz. how much 
 nearer the threads approach each other in passing to 
 the eye) when the figure is far off, than when it is 
 near. A figure of a man placed at six inches from the 
 ground line, will in this experiment, be seen under a 
 much larger angle than a similar figure twelve or twenty 
 inches distant. 
 
 It will also appear that such figures never rise 
 above the horizon line, unless they are on elevated 
 ground. If the spectator is sitting on the level of the 
 ground plane, a figure standing up will rise above the 
 horizon, or if the spectator is on a hill or the top of a 
 building, the figure will appear below his horizon. 
 
 It is evident that if a plane were extended horizontally 
 from the eye to the verge of the horizon, every object 
 on the ground plane, not higher than the eye, would be 
 under this horizontal plane. 
 
 LESSON XVI. 
 
 RECAPITULATION. 
 
 The rules of perspective are not numerous or diffi- 
 cult to comprehend, but as they include ideas which 
 are abstract, they should be practically applied to a 
 variety of cases, by a course of drawing in perspective. 
 
LESSONS IN PERSPECTIVE. 
 
 The pupil having once made himself familiar with 
 the principles which these rules involve, will find no 
 difficulty in sketching with truth and expression, any 
 object within his sight, without having recourse to many 
 of the elaborate methods described in this book. Let 
 him not expect, however, to arrive at this facility, by 
 any more expeditious course than that of copying the 
 figures in the plates, and making practical applications 
 of the rules here given. 
 
 To such it is believed, that the following brief enu- 
 meration of the rules and principles of perspective may 
 be acceptable ; although they may be scarcely intelh- 
 gible to those who have no previous acquaintance with 
 the subject. 
 
 1. Objects are seen by means of rays of light, pro- 
 ceeding from them in straight lines, and converging and 
 entering the pupil of the eye. 
 
 2. These rays form a cone whose apex is the eye. 
 
 3. The true drawing of objects is at the points 
 where these rays would intersect a perpendicular trans- 
 parent plane, if such were interposed between them 
 and the spectator. 
 
 4. The object, the rays of light, and the eye, form 
 a triangle or cone, whose base is the object. The 
 size of this angle is determined by the size of the 
 object, and its distance from the beholder. When 
 similar angles are made on a flat surface, a true linear 
 representation is obtained ; this is what perspective 
 teaches. 
 
 5. The distance point represents the distance of the 
 eye from the perspective plane. Lines drawn to it, 
 from dimensions laid down on the ground line, form 
 
56 
 
 LESSONS IN PERSPECTIVE. 
 
 the same angle as is made by the rays of light in the 
 original. 
 
 6. Lines parallel with the ground line in the original, 
 are drawn parallel : They have no vanishing point. 
 
 7. Original lines which are parallel, if they vanish, 
 have the same vanishing point. 
 
 8. Original lines at right angles with the ground 
 line, have iheir vanishing point in the point of sight. 
 
 9. Original lines oblique to the ground line, have 
 their own vanishing and distance points. 
 
 10. These points are ascertained by means of par- 
 allels drawn from the point of distance on the prime 
 vertical line to the horizon. The intersection of these 
 parallels with the horizon gives the vanishing points, 
 and the radii of these vanishing points, transferred to 
 the horizon line, give the distance points, or as they are 
 also called, the measuring points. 
 
 11. Circles and arches are drawn by means of 
 squares, sines and cosines put into perspective, by the 
 foregoing rules. 
 
 12. Planes and lines on them, which are inclined 
 to the ground plane, find their vanishing points on the 
 radial of their own vanishing plane. The place for these 
 vanishing points is determined by the angle of their 
 inclination, and their measuring points, are found by 
 the radii of their own vanishing points, and have the 
 same level above or below the horizon as these vanish- 
 ing points. 
 
LESSONS IN PERSPECTIVE. 
 
 57 
 
 LESSON XVII. 
 
 SHADOWS. 
 
 Every one has observed that the higher up the sun 
 gets, the shorter the shadows of objects become. This 
 fact teaches, that in making the shadows of a picture, 
 regard must be had to the position of the hght, which 
 must be the same for every object in the same picture. 
 You must not therefore put into your view a figure 
 with a long shadow, as if the sun were not more than 
 an hour high, and a tree or a house with a shadow no 
 longer than it would cast, with the sun at three or four 
 hour's height. 
 
 As light comes to us in straight lines, it is evident, 
 that when any opaque object is in the way, it will inter- 
 sect such rays as meet it in their progress. And there 
 will be a space beyond the opaque object, which will 
 receive no light from the luminous body, although it 
 may receive some reflected light from surrounding 
 objects, which will lesson the darkness of the shadow. 
 This space of shade will bear a definite relation to the 
 shape of the object ; but it will not always assume pre- 
 cisely the same shape, because the shadow may be 
 longer or shorter, according to the height of the light, 
 and broader or narrower, according to the position of 
 the beholder. 
 
 The first thing then to be attended to in projecting 
 shadows, is the position of the light. 
 
 If the luminous body is larger than the opaque, the 
 shadow will diminish as it recedes from the opaque 
 body which casts it ; but if the opaque body is larger, 
 then the shadow will increase in width as it recedes. 
 
 There are three different positions of the sun to be 
 attended to in sketching from nature. 1st, When it is 
 
58 
 
 LESSONS IN PERSPECTIVE. 
 
 before the perspective plane or picture ; 2d, when it is 
 behind, and 3d, when it is in the plane of the picture. 
 
 If you imagine a window or perspective plane before 
 you, on which the objects beyond may be drawn, and 
 the sun is beyond the window and the objects, so that 
 its light strikes on that side of them which you do not 
 see, then the light is said to be behind the picture, and 
 the shadows will be thrown towards you, and will appear 
 larger than when cast from you. 
 
 2d, If the sun is behind you, and strikes on that side 
 of objects which you see, and the spectator is situate 
 between the sun and the perspective plane, then the 
 sun is said to be before the picture, and you will see 
 less of the shadow, which will be cast from you, than if 
 the sun were behind the picture. 
 
 3d, If the sun is on a line with the perspective plane ; 
 that is, so placed, that were the perspective plane ex- 
 tended till it reached the sun, it would go neither before 
 nor behind, but just through it, then the sun is in the 
 same plane as the picture, and the shadows fall in a 
 line parallel with the ground line. 
 
 The general remarks already made, may be sufficient 
 for the common purposes of sketching ; but further 
 illustrations of the subject are given, for the use of such 
 as desire to be accurate in the forms of their shadows. 
 To understand these illustrations requires some study 
 and attention ; they are however rendered as clear and 
 simple as the subject permits. 
 
 To obtain the precise shadow cast by a given opaque 
 object, first determine the position of the sun, whether 
 it is before, behind, or in the same plane as the picture, 
 and also its height, or altitude, as it is technically called. 
 
 In order to do this, draw a ground line, horizon line, 
 point of sight, and prime vertical line, and the object 
 whose shadow is required, which object must be drawn 
 in true perspective. 
 
LESSONS IN PERSPECTIVE. 
 
 59 
 
 The sun appears to be over some point of the horizon, 
 either on your right hand or your left. You can select 
 this point according to your judgment, but if you wish 
 any particular place, as 40^ from the point of sight, 
 make an angle of 40° (Plate 17) from D, the distance 
 point on the prime vertical line, obtaining the point C. 
 This is called the angle of the sun's declination, through 
 this point, C, rule a perpendicular, the sun's place is 
 somewhere on this perpendicular. You can fix on any 
 height, but if you wish to do it with exactness, take the 
 radius, that is, the distance C D,* and set it off on the 
 horizon line from C, making the point E. From E 
 make the angle of the sun's altitude, (in this case 30°,) 
 and the point where this angle intersects the sun's per- 
 pendicular, as at F, is the height of the sun. Thus you 
 can determine with precision any given altitude, and 
 position of the sun, by means of angles from the distance 
 and radius points. 
 
 Having fixed on the point for the light, if you wish to 
 find the exact shadow of any given object, as K, regard 
 must be had to the perpendicular lines, or sides of the 
 object, as a 6 c. C is a point on the horizon line, per- 
 pendicularly under the sun, called the seat of the light. 
 Draw a straight line from C through the bottom of the 
 side a, and another straight line from F the sun him- 
 self, through the top of the side a. They intersect each 
 other at d, and thus determine this point. Then draw 
 a line from C, passing through the bottom of the side b, 
 and one from F, through the top, they cross at c, which 
 gives this point. Then take the bottom and top of the 
 side c, after the same manner, which gives g, and join- 
 
 * It cannot be made too familiar to the pupil, that the radius of 
 any point, is the distance of that point, (as C,) from the distance 
 point, (as D on the prime vertical line,) set off from the vanishing 
 point on the horizon line, as C E Plate 17. 
 
60 
 
 LESSONS IN PERSPECTIVE. 
 
 ing these points, viz. d e the whole figure of the 
 shadow is determined. 
 
 Now if the sun were situate lower, that is, nearer the 
 horizon, as at L, the lines from C through the base of 
 the perpendiculars ah c must be produced, and lines 
 from L, the sun's place, drawn through the tops, making 
 h i j. Observe how much farther the shadow extends 
 when the sun is low, and also that the shape is differ- 
 ent. This plainly illustrates the necessity of fixing a 
 height for the light in all pictures, into which shadows 
 are introduced. Mathematical exactness may not al- 
 ways be required, but without a knowledge of these 
 principles, you might be liable to incongruities. 
 
 In this example, the sun is behind the picture, and 
 the shadows fall towards the spectator. 
 
 If the sun is before the picture, continue the perpen- 
 dicular from C, (the sun's seat in the horizon,) below 
 the horizon line. Let M be the sun, (figure 2, Plate 
 17,) C his seat on the horizon line. Draw lines through 
 the top and bottom of the perpendicular sides of the 
 solid P, as before. Those from C to the bottom, and 
 those from M to the top. The lines from the light 
 itself always go to the top, and those from the seat of the 
 light, to the bottom of all perpendiculars of which you 
 seek the shadows, C m for the base m of this side, and 
 M n for the top intersecting at O. You must also 
 ascertain the shadow of the side not seen, (but which 
 is drawn in dotted lines.) The lines for this side inter- 
 sect at^. Join p 0, the shadow is then complete. 
 
 If the sun is lower than at M, mark its place nearer 
 the horizon line, as at R : if higher, farther from the 
 horizon line. The shadow is obtained correctly by 
 this mode, because the lines or angles drawn, are the 
 same which the rays of light proceedin-g from the sun, 
 at the given height and position, and arrested by the 
 given object, would make ; and all rays within the two 
 
LESSONS IN PERSPECTIVE* 
 
 BXterior ones drawn in the figure, are intercepted, and 
 do not reach the ground. 
 
 When the sun's place is beyond the picture, it is 
 truly represented by a point above the horizon line ; and 
 when it is before the picture by a point on the other 
 side, that is, below the horizon line. 
 
 3d, When the sun is in the plane of the picture, 
 Plate 18, figure 1, draw horizontal lines through the 
 base of the object, as a b and c d. Intersect them by 
 lines touching the top, and making the same angle with 
 the horizon, as the angle of the sun's elevation. The 
 dotted line b gives a less elevation than the dark lines, 
 consequently a longer shadow. 
 
 The opaque object A (figure 1, Plate 18) is oblique 
 both to the horizon and the ground plane. Draw hori- 
 zontal lines from the base of its perpendicular sides i 
 and /, intersected by lines through the tops of these 
 sides, drawn at the angle of the sun's elevation. This 
 gives the points g h; from g draw a line to the lowest 
 point in the object e, and you have the shadow. For 
 the shadow of every other perpendicular line in the 
 object taken in the same way, would fall within this 
 figure. 
 
 LESSON xvm. 
 
 SHADOWS. CONTINUED. 
 
 If the light proceed from a lamp or other luminous 
 body on the earth, situate in a room or out of doors, it 
 must be perpendicularly over some place in the ground 
 plane. This is called its seat ; whereas the seat of the 
 sun's light by reason of his immense distance, is always 
 supposed to be on the horizon line. 
 
 Mark this point (Plate 18, figure 2, C) on the ground 
 7 
 
62 
 
 LESSONS IN PERSPECTIVE. 
 
 plane of your picture, viz. the floor or earth on which 
 objects stand. Rule a perpendicular through it, and 
 mark the height of the light on this perpendicular. 
 
 Draw lines from the seat of the light C, on the ground 
 plane, through the foot of the object, as the lines m n o 
 on the solid o ; and lines from the light through the top 
 P r S. The points of their intersection t u mark the 
 extent of the shadow. The only difference between 
 this light and the light of the sun, is, that the sun is 
 always supposed to have its seat on the horizon line ; 
 but when the light is stationed on the earth, its seat is 
 on the ground plane. In both cases, the seat is always 
 perpendicularly under the luminous body. In the case 
 of the sun's being before the picture, his position is 
 marked below the horizon, as figure 2, (Plate 17.) 
 This method is resorted to, because all the hnes are 
 drawn on a flat surface, as a sheet of paper ; but the 
 sun is nevertheless supposed to be above the horizon 
 line, although on the nearer side of it. 
 
 Thus in projecting shadows, you have only to mark two 
 points, the one perpendicularly over the other, viz. the 
 seat of the light, either on the horizon or ground plane, 
 and its height. From these points, rule straight lines 
 to the top and bottom of every side of the object, re- 
 membering that those to the top of the object, must 
 always proceed from the luminous body ; those through 
 the bottom, from its seat."^ 
 
 If the object which casts the shadow is oblique, as B, 
 figure 2, (Plate 18,) rule a horizontal line M through 
 the seat of the light, and a line from the height of the 
 light N, passing through the top of the oblique object. 
 W, the point where these lines intersect, is the extent 
 
 * Unless the light be below the object, as when it is suspended in 
 the air, or a room, and strikes the under part of the object, in which 
 case, lines from the light go to the bottom, and from its seat, to the 
 top of the object. 
 
LESSONS IN PERSPECTIVE. 
 
 of the shadow. From this point, draw a straight line 
 to its extreme base, or lowest point, and this gives the 
 exact form of the shadow, as W X. 
 
 Shadows take the form of the objects on which they 
 fall ; thus the shadow of a line on a circular object will 
 be curved. 
 
 If shadows are intercepted by objects, draw them 
 first, as if nothing were in the way, and then raise per- 
 pendiculars from the points of interception to the top of 
 the intercepting object, and continue the shadow across. 
 
 The reflection of objects from the water is an exact 
 image of the object reversed. 
 
 Draw this image reversed from the foot of the object, 
 and of the same dimensions, and that part which ex- 
 tends over the water, will be the part reflected. (See 
 Plate 18, figure 3 ; 2 being farther from the water than 
 either 4 or 1.) 
 
64 
 
 LESSONS IN PERSPECTIVE. 
 
 CONCLUSION. 
 
 Many more illustrations of the rules of perspective 
 might be given, which would be useful to the learner, 
 but they would too much increase the size of this vol- 
 ume. It is hoped that any one, after a faithful study of 
 what is here explained, may be able to understand more 
 scientific treatises, and obtain from them any additional 
 know^ledge he may require. A few hints are added 
 as to the finishing up of sketches. 
 
 Linear perspective, which regards the drawing and 
 outline of objects, is scarcely more important than ariel 
 perspective, or their tinting and shading. An object 
 must be drawn smaller and coloured fainter, in propor- 
 tion to its distance. The lights should be less bright, 
 and the shadows less strong, as they recede from the 
 foreground. 
 
 The observation and study of nature, is the best guide 
 for the composition of light and shade in a picture. 
 Beautiful effects of light and dispositions of shadow, may 
 at times be seen to lend a new and indescribable charm 
 to the landscape. These should, if possible, be secured 
 as soon as they are observed, by sketching the scene, 
 and putting it in the same light and shade. 
 
 It is also of advantage to consult fine engravings and 
 paintings, and when a happy composition occurs in any 
 of these, imitate it in one of your own sketches as 
 nearly as the difference of the subjects will permit. 
 
LESSONS IN PERSPECTIVE. 
 
 65 
 
 Let the shadows be broad and in masses, and the 
 lights sparing, and not scattered indiscriminately. The 
 most common fault with beginners, is to have too many 
 hghts, and these equally bright. The brightness of a 
 light depends on the depth of the shade with which it 
 is contrasted. White paper in the distance, shaded by 
 a faint tint, will look remote, but the same white in the 
 foreground, opposed to very dark touches, will be bril- 
 liant and near. Aim at simplicity of effect. This will 
 render imperfect execution agreeable, but what is elab- 
 orate must be skilful to please. 
 
 As the light comes in one direction, the picture will 
 have a light and a shadow side. Be careful not to dis- 
 turb the shadow side by introducing into it bright lights, 
 but let the light parts of this side be of a darker tint 
 than some of the shadows on the other. Determine on 
 the disposition of your light and shade before you com- 
 mence, and pass a tint over that part of your picture 
 designed to be in shadow. This will secure you from 
 leaving bright lights here, and produce breadth of effect. 
 
 Objects situate between the eye and the light, look 
 dark. The sail of a vessel, so placed, looks darker 
 than the sky or the water. A tree in the foreground, 
 with a similar disposition of light, may receive a deep 
 tint, and contrasts finely with the sky and the lights 
 which catch on the distance or nearer objects. 
 
 A landscape usually looks best in a morning or even- 
 ing light, when the shadows are long. 
 
 On many accounts, India ink is the most suitable 
 medium for a beginner to use in finishing up a sketch. 
 Having disposed the light and shade, as directed above, 
 begin with a hght tint (your pencil being well filled 
 with the colour) and make out the sky, doing the clouds 
 first, let these assume generally a horizontal charac- 
 ter. Next put in the blue sky, leaving out the lighter 
 edges of the clouds. This you will do with more grace 
 
* 
 
 66 LESSONS IN PERSPECTIVE. 
 
 and freedom if the cloud is already designed. With 
 the same light tint, pass over the mountains or any dis- 
 tant parts, leaving out such lights as the sun, striking on 
 the hills, buildings or water, would produce. Cover 
 every other part of the picture with this tint, except the 
 brightest lights of the foreground. Then take a tint 
 somewhat darker, and finish those parts next the most 
 distant ; carry down this tint like the first, over every 
 other part of the picture, leaving out such parts only as 
 are to be lighter than the tint in your pencil, and so 
 proceed with as many tints as you have distances. 
 
 If the distant parts look too strong, pass a sponge 
 wet with pure water, over them ; this will give them 
 softness. When you commence, after having made the 
 outline, wet the paper with a sponge, and press it with 
 a cloth or blotting paper. This gives a little dampness, 
 which makes the ink work favourably. 
 
 With regard to fohage it m^ay be observed, that the 
 more distant it is, the less distinct and the smaller is the 
 character of its touch. Each tree should have a touch 
 of its own, by which its species is expressed. A hill 
 covered with foliage is represented by a touch which 
 resembles a set of curves with indented edges ; the 
 more distant such foliage is, the nearer the curve ap- 
 proaches a horizontal character, and the closer are the 
 lines or touches. 
 
 END. 
 
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