Digitized by the Internet Archive in 2014 https://archive.org/details/newmanualofperspOOwhit INTERIOR OF A CATHEDRAL. A NEW MANUAL OF PERSPECTIVE: CONTAINING 3ftemarlt£i on tije Cljearg *>f ^tt, AND ITS PRACTICAL APPLICATION IN THE PRODUCTION OF DRAWINGS : CALCULATED FOR THE USE OF STUDENTS IN ARCHITECTURAL AND PICTURESQUE DRAWING, DRAUGHTSMEN, ENGRAVERS, BUILDERS, CARPENTERS, ENGINEERS, ETC. ETC. ILLUSTRATED BY NUMEROUS ENGRAVINGS. BY N. WHITTOCK, AUTHOR OF THE OXFORD DRAWING BOOK, DECORATIVE PATNTERS* GUIDE, ILLUSTRATIONS OF YORK, SURREY, SUSSEX, ETC. LONDON : ARTHUR HALL & CO. 25, PATERNOSTER ROW. 1849. LONDON : CLAY, PRINTER, BREAD STREET HILL. INTRODUCTION. Books professing to convey instruction on various branches of art have become so nume- rous, that authors at the present time usually think it necessary to apologize for adding to the number. In introducing the New Manual of Perspective to public notice apology would be superfluous, as it is an endeavour to render a most useful branch of knowledge intelligible to all persons of ordinary capacity and confined education, to whom it has hitherto been a sealed book, from the prolix, pedantic observa- tions, obsolete technicalities, and complicated diagrams, used by most authors that have written upon the Art of Perspective. Even modern professors pre-suppose that those who require instruction in the art have attained 6 INTRODUCTION. some mathematical knowledge ; and, acting on that supposition, use terms and figures that render their works useless to those who most require information. All persons desirous of producing correct delineations of natural objects, artists, archi- tects, engineers, machinists, builders, uphol- sterers, and others, absolutely require a know- ledge of perspective. Without some proficiency in this art, the industry, genius, and talent of the artist are comparatively useless. The archi- tect that would produce a representation of the building that has taken him many hours to plan, finds great difficulty in doing so if he is unac- quainted with the means of drawing his plans according to the rules of perspective. Mechani- cal draughtsmen may be enabled to convey their ideas to their workmen by means of sections and elevations of their inventions, but can give no general idea of their utility and beauty unless they can make a perspective drawing of the machine they are anxious to submit to INTRODUCTION. public notice. Carpenters, builders, uphol- I sterers, outfitters, and other artizans, who are required to give sketches of the work they are desirous of executing, will find the great utility of becoming acquainted with the practical details of the Art of Perspective contained in this Manual. The remarks on the progressive operations are made in plain, familiar language, divested as much as possible of technical terms; and where they are unavoidably used, they are pro- perly explained. The Author confidently anti- cipates that the numerous diagrams contained in this work will be the means of removing many difficulties that impede the progress of young artists in their early efforts in drawing objects that require a knowledge of the Art of Perspective. A MANUAL OF PEBSPECTIVE. CHAPTER I. Writers on perspective have generally dis- gusted the juvenile student by their lengthened observations on the theory of perspective, describing the effect of the rays of light pass- ing through the pupil of the eye, and forming figures on the retina, by numerous complicated diagrams, explained by terms and figures which can only be understood by mathematicians. It is not at all necessary for thoroughly under- standing the Art of Perspective to become versed in optics : all that the draughtsman requires, is to know if there are any rules by which objects which present themselves to the eye may be 10 MANUAL OF PERSPECTIVE. properly drawn upon canvass or paper, so that every part may appear in its proper position, as it appears in nature ; for there is no person of common understanding that can see, but is aware that objects present themselves to the sight larger or smaller, distinct or indistinct, ac- cording to the distance we are placed from them: for instance, on first entering the nave of West- minster Abbey, we observe the piers and arches of the nave and chancel all appear to become smaller the farther they are from the eye ; and that they not only appear smaller, but the width of the nave and chancel seems gradually to contract until the distant piers and arches seem to approach each other. Now we know by admeasurement that the piers and arches at the east end of the chancel are really as far apart from each other as those at the west end of the nave, and that there must be some law in the science of optics, or light, to account for this appearance. Again : if we stand at the end of Portland- place, or any long, regularly-built street, we MANUAL OF PERSPECTIVE. 11 shall find the same effect : the houses that are nearest the eye will be seen distinctly; the windows and the architectural decorations are clear and perceptible ; but as the houses recede from the sight, they become gradually smaller, and the two sides of the street seem to meet each other. This effect is seen more completely at night, when the lamps are lit, where, how- ever distant from each other, they appear close to the eye; at the farther end of the street they appear so close to each other as to form one line of light. Any person well studied in the science of optics could explain the cause of this appearance, and he would be acquainted with the theory of perspective ; but unless he knew how to apply his theoretical knowledge to pro- duce rules for placing points and lines on paper, so that the objects may be drawn as truly as they appear to the sight, he knows nothing of practical perspective. All that the reader of this Manual will require to know of the theory of perspective may be explained in a few words. We are told 12 MANUAL OF PERSPECTIVE. by theorists that all objects in nature are seen through an atmospherical medium, which forms the perspective plain: this is true. Not one reader in a thousand could understand this theorem without explanation. The perspective plain will be easily under- stood by referring to the annexed engraving. Fig. 1. The student must suppose one side of the room to be taken away, to allow the interior to be seen. The man seated at the enclosed desk is looking through a hole in a square piece of MANUAL OF PERSPECTIVE. 13 wood, towards a window in the opposite wall. At some distance from the window an obelisk is seen standing upon a hill; lines are drawn from several parts of the obelisk to the sight hole in the square piece of wood : the lines run directly through the glass ; and the obelisk appears to the sight, not the real size, but the size it appears upon the glass, which represents the perspective plain. . When we look at objects in the streets or the fields, the air that intervenes between the eye and the object before us, forms the per- spective plain, and supplies the place of the glass in the square window. Rays of light pass from every object to the eye exactly as the lines run from the obelisk to the sight hole in the square piece of wood. By the first diagram we see how the rays of light pass to the pupil of the eye; and by the second will be seen the rays passing through the pupil of the eye to the retina, which is a beau- tiful net-work of nerves, acting like a mirror, at the back of the eyeball. In diagram 2, the circle 14 MANUAL OF PERSPECTIVE. represents the eyeball ; the projection at J, the pupil, or sight point. The objects immediately before the eye are two boats placed at a dis- tance from each other. At the back of the Fig. 2. t 3 inner surface of the circle is the retina, upon which is formed a picture of every object that is seen. The rays of light pass from the ends of the boat 1, 2, through the pupil J, to 1 and 2 on the retina. In like manner, the lines, or rays, are drawn from the second boat through the point J, to the retina. The angle is con- siderably reduced, and the second boat will appear on the retina the length of the line 3 and 4. If twenty boats were placed at equal distances from each other, they would decrease MANUAL OF PERSPECTIVE. 15 in size as the angle became smaller, until the last boat would appear like a small dot. The reader, if he refers to the first diagram, will recollect that the glass forms the medium through which the rays pass from the object seen to the eye. If there were four glasses instead of one, the rays would have a thicker and less transparent medium to pass, and would of course be more indistinct. This will also account for the difference of colour in objects near or distant from the sight; but we will reserve our remarks on this subject till we speak of Aerial Perspective. Before we proceed to the practical rules of the art of perspective, it will be necessary for the learner to become acquainted with the names and forms of the various lines, points, and figures, that will constantly be required in producing the examples contained in this Manual. 16 MANUAL OF PERSPECTIVE. CHAPTER II. PRACTICAL PERSPECTIVE — LINES, POINTS, FIGURES, ETC. ETC. A straight unbroken line, drawn directly from one point to another, is called a right line. Lines are named according to the direction in which they run : thus a line drawn in the direc- tion of the level line of the horizon is called an horizontal line : thus the line from a to b, in Fig. 3. the above example, is a right line drawn in a horizontal direction. The line from c to d is drawn in a slanting, Fid. 4. or oblique direction. It is called an oblique line. MANUAL OF PERSPECTIVE. 17 A perfectly upright line is called a perpendicular line. The line drawn from d to e is a per- pendicular line. A line leaning from the per- pendicular towards the ground line, as at f c, is called an in- clined line. F Lines that appear bent, or wavy, are called curved lines. 1 is a part of a circle, and is a curved line; 2 is also a curved line; but as it is an irregular curve it is called a wavy line. Lines running at equal distances from each other are called parallel lines. Fig. 8. A point is always represented by a small dot, thus (.) A point has in reality no form, B 18 MANUAL OF PERSPECTIVE. Fig. 9. and the speck, or dot, is used to show the place to which lines that are to be drawn towards a certain point may be taken. Points have different names, ac- cording to the place they occupy, which will be repeatedly seen in the succeeding examples. Figures used in geometrical or perspective drawings are formed with lines taken in different directions. We will commence with angular Fig. 10. figures. Two right lines drawn across each other form an angle at the place where they cross, or intersect each other. This is called the angular point, as the intersec- tion at i. If a perpendicular line is drawn from an horizontal line, as in the annexed example, it forms a right angle. If the line falls, or inclines towards the hori- jVy. 12. zontal line, it forms an acute >\ angle. Fig. 11. MANUAL OF PERSPECTIVE. 19 If it declines the other way from the horizontal \ line, it forms an obtuse \ angle. We shall have to return to angles again ; but before we do so, it will be necessary to describe the circle, and the way in which it is divided. A circle is a curved line con- tinued at an equal distance round a point. A right line drawn directly through the point in the centre, from one side of the circle to the other, shows the diameter. The admeasurement round the circle is called the circumference. One half of a circle is called a semicircle. The annexed diagram is a semicircular figure. The circle, be it large or small, is always divided into 360 parts, called degrees. To avoid placing so many figures on the circumference of the circle, it is usual to measure a space of ten degrees. In the semicircle annexed, the black space, from 360 to 10, includes ten degrees; 20 MANUAL OF PERSPECTIVE. the white space, from 10 to 20, also contains ten degrees. It will be seen that the quadrant, or quarter of the circle, contains ninety degrees: Fig. 15. these will be sufficient to show the division of the circle. All angles are measured by the degrees in the circle. We have shown, in Example 10, that any two lines approaching each other till they meet, form an angle. Thus within the semicircle before us, the lines drawn from f and c meet at the centre g. This is called the angular point. It is of no conse- quence how T long or short the lines forming the angle may be ; it is measured by the space at the widest part of the angle. Thus a line drawn from f to c includes thirty degrees, or G © MANUAL OF PERSPECTIVE. 21 three of the spaces of ten degrees on the semi- circle. This angle is a triangle of thirty- degrees. The lines drawn from a b to the centre g, include six of these spaces. This is an angle of sixty degrees. To prove that the size of the angle has nothing to do with its admeasurement, the angle dge 3 on the small circle, is also an angle of sixty degrees. The right line running from a to b is said to be a chord of sixty degrees. The same num- ber of degrees measured on the circumference is an arc of sixty degrees. We have been rather particular in explain- ing this diagram, as the degrees in a circle are used in measuring all matters connected with architecture, geography, geometry, and per- spective. The juvenile student who has made himself thoroughly acquainted with the remarks on the semicircle, will no longer be at a loss to know what a builder means when he speaks of a wall inclining ten degrees from the perpen- dicular, or that a bridge which he is construct- ing was an arc of ninety degrees. 22 MANUAL OF PERSPECTIVE. All the following angular figures are formed by taking degrees of a circle. It will only be necessary for the student in perspective to know their forms and the names that are given to them. Fig. 16. Equilateral triangle, or angle of three sides, all the same length. Fig. 17. ^^^^^^ Quadrangle, or square. Pentagon, or angle of five sides. Fig. 19. Hexagon, or angle of six sides. Fig. 18. MANUAL OF PERSPECTIVE. 23 Tig. 4>\j. Septagon, or angle of seven / sides. \ I ) Fig. 21. Octagon, or angle of eight / sides. \ Fig. 22. A line that touches the cir- cumference of the circle with- / out passing through it, is /( called a tangent. ^ Geometrical angles can be formed of a great many more sides; but in speaking of angles beyond the octagon, it is usual to call such figures polygons, or many-sided angles. It does not follow that all angles are formed in circles ; those having / \%. 23. sides of different lengths / cannot be so formed. The / 24 MANUAL OF PERSPECTIVE. preceding cut is a triangle, all its sides being of different lengths. The lines and points that are indispensable in making drawings in perspective are seen in the annexed engraving. The square is the form Fig. 24. :xy~\ // // r • of the picture. It is in fact the perspective plain. The bottom line of the square is called the base line. The line that runs across the picture parallel to the base line, is the horizon- tal line ; the point at e is the point of sight ; that at f the point of station. The points at MANUAL OF PERSPECTIVE. 25 either end of the horizontal line are called points of distance. Simple as these points and lines may appear, the accuracy and beauty of a perspective drawing entirely depend upon the above lines and points being placed in their true position. It may be necessary to inform the juvenile student that he will require a drawing board, upon which he can either strain or fasten the paper he intends to draw upon. A board about twenty inches long and twelve inches wide will be the most convenient size; the edges of the board must be smooth and per- fectly square. If the student is not provided with a case of drawing instruments, he will, at least, require a pair of ordinary compasses, and also another pair having a movable leg, which will contain a pencil or ruling pen, for drawing circles and other figures. He will also require a T square, and two flat rulers of different lengths. Both square and rulers must be thin at their edges, or what is called feather-edged. As all the operations in perspective have cer- 26 MANUAL OF PERSPECTIVE. tain points from which a number of line3 are drawn, the learner will find it convenient to insert a needle in those points for the ruler to rest against when drawing lines from the points of sight or distance. The T square and the smooth edges of the drawing-board will enable the learner to pro- duce perpendicular lines with great facility; but it is proper that he should be able to raise a perpendicular line without the use of the square, which may be easily executed by copying the above diagram. First draw a line parallel to the bottom of the paper ; then place the sharp point of the compasses at a ; make Fig. 25. MANUAL OF PERSPECTIVE. 27 points at equal distances from it on the line ; mark those points b and c. Remove the sharp point of the compasses to b, and extend the pencil point to c; then draw the curved line c d ; reverse the legs of the compasses, placing the sharp point on c and the pencil on b ; draw the curve b d, letting the two curved lines cross, or intersect each other; then place the flat ruler upon point a, and at the intersection at d draw a line from a through the intersection, and the perpendicular will be obtained. Fig. 26. A drawing seen directly in front, where all the lines running in an horizontal direction are 28 MANUAL OF PERSPECTIVE. parallel to the base line, is said to be an eleva- tion of a building. Only one side of a building can be shown in elevation, as may be seen in the preceding engraving of the drawing of a house in elevation. When both the front of the house and the side can be seen at the same time, the drawing is in perspective. Wig. 27. j MANUAL OF PERSPECTIVE. 29 CHAPTER III. OPERATIONS IN PRACTICAL PERSPECTIVE — FIGURES ON THE GROUND PLAIN. Operation 1. — To draw the perspective appear- ance of a square, one side of it being on the base line. First draw the square; then place one foot of the compasses on the angle of the square at c ; take that foot containing the pencil to and draw a curved line beyond the centre of the square. Then reverse the process : place the foot of the compasses on and that leg of the compasses which Fig. 28. 30 MANUAL OF PERSPECTIVE. holds the pencil on c, and draw a curved line as before. Where these curves intersect at e will be the point of the angle dec. By drawing lines from e to d and c, the angle will be complete ; and as the student is aware, from example, that an equilateral angle is always an angle of sixty degrees, he will, if he make the point e the point of station, of course see the end of the square under that angle ; and as this distance is the most proper for all large objects, most of the following diagrams will be drawn at that angle ; or, in other words, the station point will always be the angular point of an angle of sixty degrees. Draw this diagram over and over again before you proceed to put the square in perspective. You will find it of great use in all our future lessons, in determining the point of distance. We will now proceed to draw the perspective appearance of this square. First draw the base line ; upon which draw that end of the square that is nearest the eye, d c. (We will suppose MANUAL OF PERSPECTIVE. 31 the angular point f found as directed in the last diagram.) Next draw the horizontal line, taking care that it is parallel to the base line ; then, directly above the point f, at the point of station, make the point f on the horizontal line. (This is always the true position of the point of Fig. 29. sight.) Then place one leg of the compasses on the point of sight, and the other on the point of station ; draw a curved line from the station point to the horizontal line, and where the 32 MANUAL OF PERSPECTIVE. curved line intersects, or touches, the horizontal line, will be the true point of distance c. Then from the angle of the square c, on the base line, draw a line to the point of distance." This will of course intersect, or cross, the line running from d to the point of sight. From this intersection to the line c f draw a line parallel to the base, and the square as seen in perspective will be obtained. Most writers on perspective have no fixed principle for placing the point of distance; and this it is that makes the drawings of streets, churches, and other objects look so out of drawing. If the square had been seen under a smaller angle than sixty degrees, the point of distance would have been at h ; and if at a still less, at i. Any- common observer will see that, if a line had been drawn from c to h, the intersection on the line d f would have made the square on the ground plain much too long; and if it had been drawn from c to i, the sides of the square seen in perspective would have been much longer than the side of the square seen MANUAL OF PERSPECTIVE. 33 on the base line, which is, of course, in- correct. The square properly drawn a b c d is shaded in the diagram, to distinguish it from the square drawn from the wrong point of distance; but if the learner, in working this diagram, take the trouble to shade the other squares, the dif- ference will be more perceptible. The annexed diagram (Fig. 30) shows three squares running in an oblique direction to the Fig. 30. point of sight. The process is the same as in the preceding lesson, with the exception that the side of the square measured on the base is placed some distance from the point of sight, instead of immediately under it. The author of this Manual is aware that nothing is more tedious to the juvenile student c 34 MANUAL OF PERSPECTIVE, than the early lessons in any branch of mathe- matics ; but the difficulty is greatly lessened if the student will make himself perfectly ac- quainted with the names and forms of the lines, points, and figures, and also repeat the drawing of these operations till he thoroughly com- prehends them. This will render every suc- ceeding lesson comparatively easy. Operation 2. — To draw diamond-shaped squares in perspective, the angle of the square being on the base or ground line. This will be found nearly a repetition of the last operation. A circle is first drawn, enclosed in a square of the size required; then draw a line through the centre of the circle from d to e, and another from c to b. If chords are drawn from one letter to the other, the diamond-shaped MANUAL OF PERSPECTIVE. 35 square will appear. Proceed, as before directed, to find the point of station, a. Having ascertained the size of the square, and the point of station, proceed to draw the base line and the horizontal line. On the base line mark the width and centre of the square. Place one foot of the compasses on point k, and the other on l, and draw the curved line l a. Fig. 32. \ \ \ 1 / \ \ x Next draw the curve k a. The intersection will give the point of station a. Next draw a perpen- dicular line from a to the horizontal line. Where 36 MANUAL OF PERSPECTIVE. these lines meet, is the point of sight b. Place one foot of the compasses on the point of sight, and extend the other to the point of station a, and draw the curved line to the horizontal line at c. This is the point of distance; and, as before remarked, the point of distance is always placed on the horizontal line exactly as far from the point of sight as the latter is from the station point. The student will see that in working this operation there would be no necessity for letting any of the curved lines appear, as the mere movement of the compasses, without mak- ing the line, would give the point required. We now proceed to obtain the perspective of the diamond-shaped stones, by drawing lines from l d k on the base line to the point of sight b. From d draw a line to the point of distance c. Where this line intersects the line running to the point of sight, it gives one side of the square e. Draw a line parallel to the base from e to f. The student will see that the lines of intersection are drawn beyond the line k b, to show that if required to mark points MANUAL OF PERSPECTIVE. 37 of distance on each side of the point of sight, these lines would all run to it, as they do to the point c. The line f c again intersects the line from l to b, and another line parallel to the base, gives two angles of the second square. In working this operation, we have endea- voured to describe the whole process, line by line ; but for the future we shall presume that the student knows how to place the base and horizontal lines, and also the points of station and distance; and we shall have no further necessity for verbal direction for placing them in their proper places. Operation 3. — Squares and diamond-shaped pavement, both seen obliquely. In the preceding operations, the squares have been immediately in front of the spectator. In this example the point of station is of course opposite the point of sight a; consequently the spectator will see both the diamond and square 38 MANUAL OF PERSPECTIVE. shaped paving stones in an oblique direction. In this and the succeeding examples the point of station will be omitted. The student is aware that it is only required to ascertain the true place for the point of distance on the horizontal line ; and as that has been so thoroughly explained in working the preceding examples, it will save time, and simplify the diagrams, by its omission. In the diagram before us, first draw the base and horizontal lines, and on the latter Fig. 33. g C D E F mark the point of sight A. On the base line mark the size of the squares e f, and from those points draw lines to the point of sight a. Then from e draw a line to the point of dis- tance j; where this line intersects the line from f to a, draw a line parallel to the base — MANUAL OF PERSPECTIVE. 39 it will give the perspective of the first square. The second square is at an irregular distance from that last drawn ; but it is as easily found by drawing a line from the lower side of the square (which is always parallel to the base line) to the point of distance, and where it intersects the line running from f to a draw a short line parallel to the base — and that will give the second square. We will now proceed to draw the diamond- shaped stones on the opposite side. Mark the points bcd on the base line, and from them draw lines to the point of sight a ; from the point c draw a line to the point of dis- tance J ; and where this line intersects the line running from b to a, draw a short line parallel to the base; then from c draw a diagonal line to the short line last drawn — and one half the diamond is formed. From the ends of the short lines, where they intersect the lines b d running to a, draw lines to the point of distance J, and as many diamond-shaped stones may be formed as the space will admit. 40 MANUAL OF PERSPECTIVE. Operation 4. — A pavement of squares in perspective. The student may suppose he is required to show the pavement of a hall seven yards square, being paved with slabs of marble each a yard square. He would of course draw the ground, or base line, and the horizontal line; and on Fig. 34. the latter, place the point of sight ; then mark points of distance in their proper places on the horizontal line, at an equal distance from the MANUAL OF PERSPECTIVE. 41 point of sight ; then proceed to set off the size of one end of a square block on the base line, immediately opposite the point of sight, and draw lines from each end of the square to the point of sight; then mark the lower end of three squares on the base line on each side of the square first drawn. You will then have the lower end of seven squares of a yard each. From each of those points on the base line draw lines to the point of sight ; then draw from the angle of the outside of the squares last formed on the base, diagonal lines to each point of distance; and where they intersect the lines running from the base to the point of sight, draw lines parallel to the base, — and the hall will be covered with forty-nine square stones, seen in true perspective. The student will observe in this diagram we have not marked the points with letters, as we presume that by this time the point of sight, and point of distance, have become so familiar to him that letters of reference are not re- quired. 42 MANUAL OF PERSPECTIVE. Operation 5. — A pavement of diamond or lozenge shaped stones, of alternate colours. This operation will be found very similar to the last. Here the student may suppose him- self to have a hall of any dimensions to cover with lozenge-shaped stones alternately grey and Fig. 35. white. He will of course proceed to draw the base and horizontal lines, and the points of dis- tance. Next draw a perpendicular line from the point of sight to the base line, and on each side of this line mark the size of four squares. MANUAL OF PERSPECTIVE. 43 This will give eight white stones. From the points on the base line draw diagonal lines to the points of distance, and they will, without further trouble, show the whole space covered with diamond-shaped stones in proper perspec- tive : then colouring the rows of diamonds alternately black and white, the operation will be completed. The student will see from the example, that it is of no consequence what area is required to be covered. It would be quite as easy to draw a pavement for Westminster-hall as for the passage of a private residence. Operation 6. — To draw a circle in per- spective. To show the perspective of a circle, it will first be necessary to draw a circle the size required, and enclose it in a square. Divide 44 MANUAL OF PERSPECTIVE. this square into compartments, as seen in the annexed diagram. It will be found that the circle intersects the lines that divide the square at regular intervals, so that but a small part of the circle is seen in each division. Diagonal Fig. 36. lines are also drawn from each angle of the square, to increase the intersections, in the diagram before us. The upper part of the square that contains the circle forms the base line of the perspective drawing. From the MANUAL OF PERSPECTIVE. 45 ends of the upright lines forming the divisions of the square, draw lines to the point of sight a on the horizontal line ; then from the left angle of the square forming the base draw the diagonal line b to the point of distance, which is of course on the horizontal line, though not seen in this diagram. Where the diagonal line b intersects the lines running from the base to a, draw lines parallel to the base, and the same number of divisions will be seen in the perspective square as in the square below the base line ; and as the divisions are so small, it will be easy to draw by hand that part of the circle that is seen in each division. Operation 7. — To draw irregular figures in perspective. The process of drawing irregular figures in perspective is the same as in the preceding lesson. If the student is required to make a 46 MANUAL OF PERSPECTIVE. perspective drawing of the ground plan of a city, the walls of which form the irregular figure seen in the annexed diagram, he would proceed to enclose the plan in a square ; then Fig. 37. draw diagonal lines from the angles of the square, and also divide the square into sixteen compartments. The upper side of this square is the base line of the perspective drawing. Next draw the MANUAL OF PERSPECTIVE. 47 horizontal line ; and from the centre division of the square marked on the base line draw a per- pendicular line to the horizontal line, which will give the point of sight a. Draw lines from all the divisions marked on the base to a, and draw diagonal lines from the angles of the square on the base line to the points of distance on the horizontal line, which in this diagram are out of the picture, but which the student can easily supply in working this diagram on the drawing-board. Where the diagonal lines intersect the lines running to the point of sight, draw lines parallel to the base, and the divi- sions of the square will be seen in perspective. Draw that part of the plan of the city that is seen in the divisions on the square below the base, on the corresponding divisions of the square in perspective, and the operation will be performed. The preceding examples will be quite suf- ficient to enable any intelligent student to put figures on the ground plane in perspective, 48 MANUAL OF PERSPECTIVE. particularly as every succeeding subject will commence by forming their outline on the plane. In this chapter we have been anxious to make the learner fully understand the Point of Station and the Points of Distance. There is another point frequently used, called the Acci- dental Point, which will be explained in the next chapter. MANUAL OF PERSPECTIVE. 49 CHAPTER IV. OBJECTS RAISED ABOVE THE SURFACE. Operation 8. — To draiv a transparent cube in perspective. To the student that has made himself con- versant with the preceding subjects, this will be an easy lesson. We have supposed the cube Fig. 38. 9 to be of glass, that the six sides may be seen, which could not be the case if the cube were 50 MANUAL OF PERSPECTIVE. opaque. The lowest line in this drawing is the base line ; upon it one side of the square of the cube is measured ; and from each of these points lines are drawn to the point of sight. From the left angle of the square a diagonal line is drawn to the point of distance. This intersects the line drawn from the right angle of the square, on the base, to the point of sight. At the intersection a line is drawn parallel to the base, and the lower part of the square is formed on the ground plane, as in the preceding operations. The student will next proceed to raise two perpendicular lines of the same length as the lower line of the square, marked upon the base line ; and from each end of the line of the square, on the base, the perpendicular lines being drawn, draw a line parallel to the base from the top of one perpendicular line to the other, — and the square of the cube towards the spectator will be complete. From the upper angles of this square draw lines to the point of sight; and then proceed to draw two perpen- dicular lines from the ends of the short line MANUAL OF PERSPECTIVE. 51 forming the outer side of the square upon the ground plane ; the perpendicular lines will touch the lines running to the point of sight, — and the cube will be represented in perspective. The student will observe that the accuracy of this figure entirely depends upon the true position of the square on the surface ; for if that had been wrong, every part of the cube would have been thrown out of drawing. Operation 9. — Square blocks of marble rising above the horizontal line. In this operation we commence as before, by finding the squares of the three upright blocks on the surface. The lower side of the first square of the three upright blocks is used as the base line ; and lines drawn from it to the point of sight, on the horizontal line. From the angle of the first square draw the diagonal 52 MANUAL OF PERSPECTIVE. line b till it touches the horizontal line at some distance out of the picture. A line drawn from the intersection of this line with that running to the point of sight, will give the first square a. Next draw perpendicular lines from the angles of the square on the base to the height required ; join them by a line even with the line at the base ; and we have a long square upright figure, forming one side of the block of stone. From the angles at the top draw lines to the point of sight; from each of the angles of the squares on the ground draw perpendicular lines to the lines above the horizon running to the point of sight, — and the three upright blocks will be produced. The figure near the centre of the ground plane is a trough, open at the top. The square of this is drawn first; but as it is a long irregular figure, no lines are required to the point of distance, but merely a short line drawn parallel to the horizon, touching the lines that run to the point of sight. From the line nearest the base draw two short perpendicular MANUAL OF PERSPECTIVE. 53 lines, and connect them at the top by a line drawn from one to the other,— and the square of the trough nearest the eye will be drawn. Fig. 39. From the upper angles of this square draw lines to the point of sight ; — short upright lines from the farthest angles of the square on the plain will give the other three sides of the trough. The large square block on the right side of this diagram is drawn as directed for the 54 MANUAL OF PERSPECTIVE. three opposite blocks, and will require no direction. As this is the first operation in which we have placed the point of distance out of the picture, it may be necessary to say, that where there are many objects in one drawing, the whole together are seen under one angle, which is consequently larger than those required for single objects ; and the point of station and point of distance are too far off the point of sight to be seen within the square of the pic- ture ; but of course must be properly placed in working the operation on the drawing- board. Operation 10. — Four piers supporting beams above them; the columns standing on a pave- ment of squares. In this, as in the preceding operation, we have left the outlines of the subject without light MANUAL OF PERSPECTIVE. 55 and shade, as if the beam was supported merely by iron rods rising from the angles of the squares of the pavement. This is done to show the student all the lines of the drawing. Commence this subject by marking the num- ber of squares required on the base line ; and from the divisions draw lines to the point of sight. Next draw a diagonal line from the last division on the left side to the point of distance. This line will of course intersect the lines run- ning to the point of sight ; and if lines parallel to the base are drawn from every intersection, the pavement will be completed. Next draw perpendicular lines, of the requisite height, from the lower angles of the outside squares of the pavement, and above them a long line even with the horizontal line. The lower line of the beam projects a little beyond the perpendicular lines. From the ends of this projection draw two short upright lines for the ends of the beam, and connect them with another line run- ning in a horizontal direction. The sides of 56 MANUAL OF PERSPECTIVE. the piers nearest the eye, and also the front of the beam, are now drawn. From the upper angles of the piers draw lines to the point of sight ; and from the angles of the second and Fig. 40. sixth squares, on the pavement, draw perpen- dicular lines to the lines above the horizon running to the point of sight ; then draw the square of the beam in the distance, — and the drawing is complete. MANUAL OF PERSPECTIVE. 57 Fig. 41 shows the way in which the centre of the square figure in perspective is found, let the size of the square be what it may. The base and horizontal lines being drawn, and the point of sight marked upon the latter, draw a perpendicular line the length of one side of the square, and from each end of this line draw lines to the point of sight ; then draw a shorter perpendicular line at the proper distance from the first, and the square will be formed. Then draw lines from the angles of the square, cross- ing each other as in the annexed diagram. Where the lines cross, or, to use the proper Fig. 41. 58 MANUAL OF PERSPECTIVE. term, intersect, is the perspective centre. A perpendicular line drawn through the intersec- tion, will give the correct place of the point of a gable, spire, or pediment, in any subject that may come under the notice of the student. MANUAL OF PERSPECTIVE. 59 CHAPTER Y. THE HORIZON IN NATTJKE AND PERSPECTIVE . In all the drawings we have made, we have drawn an horizontal line and a base line, with- out any fixed principle, or reason why they should be placed as we have hitherto drawn them. Before we enter upon more elaborate subjects, it will be necessary that the student should be aware of the proper place for the horizontal line, by studying the natural horizon. If the reader were standing on the sea-shore, looking over the ocean, he would find that, in the extreme distance, the water and sky appear to touch each other; and if he happen to be looking towards the west as the sun sets, he will find it seems gradually to sink beneath the 60 MANUAL OF PERSPECTIVE. mass of water in the distance, or, to use a com- mon phrase, it has sunk below the horizon. If, while contemplating the distant waters, the spectator were to hold up a stick directly across his eyes, it would, at a short distance from them, intercept his views of the natural horizon, which is always of the same height as the eye of the spectator, stand where he may. And he will also find that all the objects in the expanse before him commence at some distance from the place on which he is standing, and cannot go beyond the horizon. In the marine view, ships of various sizes sail past, but they all sail upon the liquid plane bounded by the horizon. Looking steadily forward towards the place where the water and sky appear to meet, he finds that he cannot see objects ten or fifteen feet away from him without looking down upon them, and thus lose the view of the distance; but at a certain point the objects in the foreground present themselves distinctly. This is the natural base line, and, of course, the place where he stands is the point of station. MANUAL OF PERSPECTIVE. 61 The line formed by the meeting of the sky and water, is the natural horizontal line, and upon it, directly before his eyes, the point of sight. It will follow, that in copying nature we must observe her laws. If, in commencing a marine view, we make the horizon too low, we must suppose it to be taken by a person sitting on the sand. The same effect is observable in a picture where the horizon can be seen. In the little sketch annexed, the Arab is sitting on a stone in the midst of the ruins of Palmyra, look- ing towards the horizon where the edge of the Fig. 42. 62 MANUAL OF PERSPECTIVE. desert and the sky seem to meet together. In this case the plane of the picture would be too confined to allow him to see objects dis- tinctly. In the next sketch (Fig. 43) the man is stand- ing up, looking towards the sea. This is the Fig. 43. natural horizon. If the spectator is standing on level ground, all the objects on the ground plane are seen distinctly, and sufficient space is allowed for detail, and light and shade. The perspective of a picture will show to the greatest advantage under and above the natural horizon, which, as will be seen in the sketch, is MANUAL OF PERSPECTIVE. 63 the height of the head of the Indian in the foreground. If a person makes a drawing from the top of a house, or from an eminence, he will of course have a greater extent of view, but the hori- zontal line will be so high, if much foreground is allowed, that one side of every object will appear to be lifted up, and quite out of its usual position. This is the case with objects when the horizon is placed as high as the figure seen from a projecting turret of the castle. In the fourth sketch (Fig. 45), the horizontal Fig. 44. 64 MANUAL OF PERSPECTIVE. line is near the top of the picture. An hori- zontal line this height is only allowable in what is called a bird's-eye view. Many of our readers have doubtless seen in old books, views of gentlemen's seats, drawn exactly in this manner, before the Art of Perspective was practised. It was the only means the artist Fig. 45. had of getting space for a foreground. In this the figures are seen walking over each other : the house, gardens, and trees, appear all out of drawing. From this examination of the appearance of the natural horizon, the horizontal line in a MANUAL OF PERSPECTIVE. 65 drawing may generally be placed about one- third the height of the picture ; in some in- stances it will require to be rather lower, but seldom above that height. The student will also observe, that in what- ever part of the picture figures may be intro- duced, if they are standing on a level sur- face 3 their heads should never be much above fig. 46. the horizon. The annexed engraving will show how figures appear in perspective that are standing on the same plane. It will be seen that the head of the Bedouin Arab in the fore- E 66 MANUAL OF PERSPECTIVE. ground, looking towards the point of sight, is a little higher than the horizontal line. The Arabs that are marching one after the other, all have their heads the same height : so have the rest of the figures. If this rule is observed, figures may be placed at any distance without appearing to walk over the heads of others in the foreground, which they invariably do in old street views, or other subjects where, in order to obtain great distance, the horizontal line is placed near the top of the picture. We will close our remarks on the horizontal line by showing that the horizon is not altered by objects being placed on an eminence. In the above diagram, the horizontal line will MANUAL OF PERSPECTIVE. 67 be seen to be the height of the figure in the distance as well as of that nearest the eye. The cottage on the left of the picture is stand- ing on the ground plane ; the lines all run regularly to the point of sight in the horizon. The house on the right is on a high bank ; but the lines all run from it to the same point of sight. The lines of every subject below the horizon run upwards to the sight point ; while the lines of all objects above the horizon are drawn downward to the same point. Operation 11. — Three arches springing from piers. Commence by drawing the base line and the horizontal line; then mark eight points, at equal distance from each other^ on the base line. Draw lines from the points on the base line to the point of sight a; then draw a diagonal line to the point of distance b. The 68 MANUAL OF PERSPECTIVE. intersection of the lines running to a will point out the place of the lines running parallel to Fig. 48. the base. Mark the two first outside squares atfd the two fifth. The student will find he MANUAL OF PERSPECTIVE. 69 has not squares enough on which to place the piers of the third arch. From the outer angle of the seventh square he must draw another diagonal to the point of distance b, and from the intersections of the lines running to a draw parallel lines as before. By this means forty- nine more squares will be obtained. Count from the squares marked for the second piers ; and on the fourth from them, mark the squares for the piers of the third arch. Having drawn the ground plane, or pavement, from the an- gles of the two outside squares marked upon the base, raise the perpendiculars c c, c c : form the top of each pier by drawing a line with the pencil directly across the drawing over both piers ; then from the angles c on the piers draw lines to the point of sight. From all the squares upon which piers are to be placed, draw perpendicular lines to the lines last drawn ; and , form the tops of the piers by drawing lines parallel to the horizon directly across the drawing, as at c c, c c. All the piers being raised, proceed to form the arches that spring 70 MANUAL OF PERSPECTIVE. from them. For this purpose, find the centre of the line taken across the drawing, and placing one leg of the compasses on the centre point, extend the pencil point to c on the right side of the drawing, and make a semicircle to c on the left. Draw another smaller semicircle from the inner side of the pier : draw it lightly, and with a fine-pointed pencil. Arches may be drawn over the remaining piers in the same way. Next draw lines parallel to the horizon from the upper angle of the piers : and drawing a line from the centre point first formed be- tween the piers to the point of sight, will give the centre of all the other "arches. The joints of the stones with which the arch is built are all drawn towards the centre of the semicircle. From the ends of the lines on the inner semi- circle draw lines to the point of sight, and they will give the markings for the stones on all the arches. The operator will find that the whole drawing is by this time nearly covered with lines; he will therefore take a fine pen and Indian ink, and go over the outline of the piers MANUAL OF PERSPECTIVE. 71 and arches, leaving all the perspective lines to be removed by the Indian-rubber when the ink outline is dry. The piers and arches are afterwards put in shade with a wash of Indian ink. Operation 12. — An arcade of eight arches over a pavement of square stones, the point of sight not being in the centre of the drawing. There are no subjects where errors in per- spective are so immediately perceptible as in the interior of long-vaulted buildings. In the preceding operation we had three arches, the spectator standing exactly in front of them ; but in drawing the interior of a church it is usual to make the point of sight out of the centre, so that the spaces between the arches and the whole of one side of the church may be larger than the other: not only that it is more picturesque, but it enables the draughts- 72 MANUAL OF PERSPECTIVE. man to show objects beyond the piers on one side of the church, and also the architectural ornaments of the piers and arches to greater advantage. We commence this operation, as all others^ by drawing the base and horizontal lines. Next draw the square about the picture to determine its size, letting the base line form the lower side of the square. The point of sight is on the horizon at a, and, for the reasons before stated, it is not placed in the centre of the pic- ture. The method of forming a pavement of squares has been so repeatedly shown, that we may merely observe that there are three diagonals intersecting the lines running to the point of sight, giving 192 squares. The first perpendicular is drawn from the angle of the eighth square on the base to d. Draw a line from d to the point of sight, which will give the height of the perpendiculars raised from every fourth line on the outer range of squares on both sides of the pavement ; they are taken up to the lines drawn from b to the point of MANUAL OF PERSPECTIVE. 73 sight : and the operator will be pleased to observe how beautifully they diminish in size and distance from each other as they approach the point of sight. Tig. 49. In order to obtain the centre for the arches that spring from the perpendicular lines, it will be necessary to find the centre between the two first perpendiculars ; it is marked c on the 74 MANUAL OF PERSPECTIVE. diagram. A line drawn from this point to the point of sight will give the centres for all the arches. Operation 13. — To draw a semicircular arcade in perspective. If the student wished to draw an arcade con- sisting of semicircular arches, he would find it quite easy to form the ground plane by means of squares, and also to raise perpendiculars for the piers; but if he supposed he could use the compasses for striking the semicircles, as in the preceding examples, he would find he was mistaken. Semicircles, as seen in the annexed example, must first be drawn in a square, like the semicircle drawn in elevation in the annexed diagram. The square is divided by diagonal lines drawn from the angles. Make a perpendicular line through the intersection of the diagonal lines, and it will divide the square in the centre. Place one leg of the compasses on the lower end of this short upright line, and with the pencil leg MANUAL OF PERSPECTIVE. 75 draw a semicircle, which will cross or intersect the diagonal lines. At these intersections draw lines parallel to the horizon. From this square draw all the lines that run in an horizontal direction to the point of sight, which is not shown in this diagram. If these lines are taken Fig. 50. across the perpendicular lines raised from the ground plan, the number of squares will be given. It will be necessary to find the per- spective centre of these squares, by drawing diagonal lines from their angles ; where the diagonals intersect, will be the centre. Draw a short upright line through each intersection, and the squares in perspective will be divided, 76 MANUAL OF PERSPECTIVE. like that in elevation. Observe carefully where the semicircle that was struck with the com- passes intersects the lines on the square, and it will be found very easy to draw by hand the small portions of the semicircle on the corre- sponding intersections of the squares in per- spective, no matter how many may be re- quired. In the example, only two squares are drawn, but the operation would be the same if twenty arches were required. The student will see that this is only another application of the rule for drawing a circle in perspective, as given in a former operation. Operation 14. — Pointed arches. Pointed arches are drawn from two or more centres, according to their shape. The arches in this example are triangular arches, and are drawn from the lower angles of the square, the MANUAL OF PERSPECTIVE. 77 intersection of the curved lines forming the apex, or point, of the arch. The square in elevation is divided by diagonal lines, and lines running horizontally taken Fig. 51. across them; a short perpendicular line is drawn through the intersections in the centre. This must be repeated on the squares in per- spective; and again the arches must be formed by hand; that is, without the assistance of compasses, by drawing the small part of the curved line carefully through the intersections, as seen in the diagram. The young student may say, Is there a posi- tive necessity for proceeding in this way if a 78 MANUAL OF PERSPECTIVE. ruined arch presents itself in a landscape ? If he would draw very correctly, this is the proper Fig. 52. method; but if he is thoroughly acquainted with the foregoing diagrams, he can trust a great deal to the eye and the mind. Nothing will be easier than to make the bottom of a pier the base line at any part of the ground plane, and draw a single line to the point of sight from the base and the top of the perpen- dicular line of the pier, which will be a suffi- cient guide for unconnected piers or arches. MANUAL OF PERSPECTIVE. 79 Operation 15. — Interior of a room, the point of sight in the centre. The student has by this time become so well acquainted with the points and lines used in perspective, that he will easily be able to put Fig. 53. any room in perspective by merely looking at this diagram. We have supposed the room to be about twelve feet in height, the doorway eight feet, and 80 MANUAL OF PERSPECTIVE. the horizontal line five-and-half feet. The point of sight is at b ; a a a the horizontal line ; the ground plane is formed by a line drawn from e to the point c out of the picture ; the boards of the floor are drawn up to the point of sight ; the upper line of the window, the cornice, and the ornamented panel, all run down to the point b. We may remark, that if an apartment or building is drawn to scale, the number of feet and inches are measured on the outside perpen- dicular lines c e and h e. All objects on the ground plane are measured on the base. Operation 16. — Interior of the prison in the Lollards' Tower, Lambeth Palace. The annexed drawing is inserted without the lines: it is the interior of the prison where Archbishop Chicheley confined the early Re- formers, who were at that time called Lol- MANUAL OF PERSPECTIVE. 81 lards ; and the tower, of which this room is the upper apartment, is still called the Lollards' Tower. The line hh is the horizontal line ; a the point of sight. Every line that does not run Fig. 54. parallel to the base is in this subject taken to the point of sight. The most juvenile student that has paid ordinary attention to the preceding lessons F 82 MANUAL OF PERSPECTIVE. will be able to produce this subject. The floor, the sides of the room, and the ceiling, are all boarded. Operation 17. — The Thames Tunnel. There is no structure in the Metropolis that presents so long a vista as the Thames Tunnel. The student that has an opportunity of seeing this splendid monument of human ingenuity and perseverance will, at a glance, have dis- played before him a fine example of the truth of the laws of perspective. It would require more space than could be spared in this Manual to enter into even a brief description of this magnificent work. The tunnel consists of two arcades, open to each other by spaces left in the centre wall. Only one arcade is presented in the annexed engraving. It presents an unbroken succession of semicircular divisions, as repre- sented in former operations. The point of sight is in the extreme distance, about the height of the man's head. The lamps have a most MANUAL OF PERSPECTIVE. 83 beautiful effect, and present the appearance of two lines of light meeting each other at the point of sight. Fig, 55. Any person that has made himself master of the preceding lessons would find but little difficulty in making an accurate drawing of the Thames Tunnel. It will be seen by the 84 MANUAL OF PERSPECTIVE. preceding sketch, that neither the walls nor piers in the centre are perpendicular. This pecu- liarity would present no difficulty if the points for the divisions were properly made on the ground plane; the slight curve between the semicircles and the pavement could be as easily drawn as perpendicular lines. The lines are omitted in this sketch; they would have entirely hid the picture : and the lines of the building are so simple and con- tinued, that they require no other direction. Operation 18. — Pyramidal figures and acci- dental points. Spires of churches and other pyramidal figures are frequently drawn incorrectly, even in pic- tures by artists of reputation. The true place of the apex of a spire may always be found, by drawing a line from the centre of the square on the ground plane. Fig. 1, in the annexed diagram, is a lofty MANUAL OF PERSPECTIVE. 85 spire. The square is first drawn on the ground plane, as directed in former lessons; lines are drawn within the square from opposite angles, crossing each other in the centre of the square. From this intersection a perpendicular line is drawn the height of the spire. Lines are drawn from each angle of the square on the ground plane to the upper end of the perpendicular line — and the true form of the spire is obtained. Fig. 3 is a repetition of the same process. It is a low cucumber frame. A glance at the diagram will show how the centre is found. The height of the pyramid entirely depends on the length of the perpendicular line drawn from the centre of the square on the ground plane. In describing the various points used in per- spective drawing, at the commencement of this Manual, the accidental points were purposely omitted, as it required more explanation than the student would be likely to comprehend in the preliminary remarks ; but after the number of operations he has studied it will present no difficulty. The rays from all objects on the 86 MANUAL OF PERSPECTIVE. ground plane that are placed directly before the ! spectator terminate in the points of sight or distance; but there are instances, like the block of stone in the example (Fig. 2), that may be so placed that the lines from it will not run to Fig. 56. either of the points. In that case, lines are drawn from it to the horizontal line; and where those lines terminate on the horizontal line, are called accidental points, as the point c in this diagram. MANUAL OF PERSPECTIVE. 87 Operation 19. — A cottage, according to ad- measurement. In the preceding lessons no mention is made of admeasurement ; but we will now point out the method of drawing buildings in perspective according to their true dimensions. Before the architect commences the drawing of a building, he determines the scale of feet or yards by which he desires to measure the various parts of the building: the draughtsman that wishes to draw a building in perspective, according to admeasurement, must also prepare a scale. The annexed diagram is a very simple subject, of small dimensions, so that all the lines may appear in the drawing. As in all other drawings, first draw the base and horizontal lines. In drawing this humble cottage, we are supposed to be standing op- posite the angle of the building nearest the eye; consequently, the point of sight is not 88 MANUAL OF PERSPECTIVE. visible ; all the lines are drawn to the points of distance a and b, on the horizontal line. Before proceeding with the perspective of the cottage, it will be necessary to form a scale, like that seen at d in the annexed diagram. The student will find it contains ten divisions of equal length, marked alternately black and white ; each division represents twelve inches, consequently the scale is ten feet in length, which is quite sufficient for this small drawing. Of course the scale could be extended to any length required. Commence the drawing of the cottage by raising a perpendicular line about the centre of the base line. From the end of the perpen- dicular on the base line draw lines to the points of distance a b. Then take eight divisions of the scale, and, placing one foot of the compasses on the end of the perpendicular line, from it mark off eight feet upon the base, and from this point draw a line to the point of distance b. Where this line intersects the line running to a, shows MANUAL OF PERSPECTIVE. 89 the eight feet of the ground line of the front of the cottage. Next draw a line at right angles with the base line, running through the point of dis- tance b, at some distance above and below it. The line forming the ground line of the front of Fig. 57. s the cottage running to a must be extended to the last formed perpendicular line ; and where it intersects, commence the admeasurement for the height of the upright lines of the cottage. First measure eight feet, the height of the building, and from this point draw a line to A, and it will give the true height of the two 90 MANUAL OF PERSPECTIVE. upright lines forming the front of the cottage. The side of the house must next be drawn, by ruling lines from the upper and lower ends of the centre perpendicular to b. Then on the base line c mark off eight feet from the lower end of the perpendicular towards b. From the point marking the eight feet draw a line to A ; and where it intersects the line running from the centre perpendicular to b, are the eight feet of the ground line of the side of the cottage. Draw a perpendicular line from this intersection to the line running from the upper end of the centre perpendicular line, and it will give the length of the top of the side of the cottage. The space between the angle of the cottage and the first upright line of the square window is three feet. Mark off three feet from the scale on the base line, and draw a line from it towards a till it touches the ground line of the side of the cottage. At this intersection draw an upright line, and it will give one side of the window; then on the base line mark off two feet, as seen in the diagram. From this MANUAL OF PERSPECTIVE. 91 point draw a line towards a till it intersects the ground line of the cottage ; and from the inter- section draw an upright line, and it will give the other side of the window. The eight feet of the side of the cottage are now divided into two spaces three feet wide, and a window two feet. We have obtained the width by working from the base line. The height must be measured upon the perpen- dicular line running through the point of dis- tance b. The upper line of the square of the window is six feet from the ground line of the cottage. To obtain this height correctly, six feet must be measured on the perpendicular line running through b. A line running from the point marking this distance towards a will cross the centre perpendicular of the cottage ; and lines drawn from this intersection to a and b will give the upper line of the door and win- dow. The lower line of the window is three feet from the ground line. This space must also be measured on the perpendicular crossing b ; and a line drawn from the point marking 92 MANUAL OF PERSPECTIVE. the three feet towards a will intersect the centre line of the cottage. A line drawn from this intersection towards b will give the bottom of the window. The plinth at the lower part of the cottage is about one foot in width. This is also marked on the perpendicular crossing b ; and a line from the point showing one foot taken towards a will show the width of the plinths on the front of the cottage. A line drawn from the intersection of the centre line of the cottage towards b will show the w 7 idth of the plinth on the side of the building. And we have now every part of this simple building drawn in perspective, according to admeasurement. Operation 20. — One side of the exterior of a concert-room, by admeasurement. This subject is too large to allow all the points to appear in the drawing as they were shown in the preceding operation. The base line and the horizontal line must be MANUAL OF PERSPECTIVE. 93 first drawn. Both of them are taken a con- siderable distance beyond the limits of the picture. The point of sight is seen on the horizontal line, at d, The point of distance may be easily found by placing the flat rule upon the ground line of the building, and con- tinuing the line till it intersects the horizontal line : the intersection is the place for the point of distance. The dimensions of the building are as fol- lows : — FEET. Height 30 Length 46 Pilasters 2 Space from the pilasters to windows - 4 Width of windows ------- 4 Space between the windows - - - - 6 Plinth- - - - 2 Length of pilasters, including capitals - 20 Architrave, including the parapet - - 8 Height of windows - 14 An architect may smile at the proportions of this concert-room ; but our intention is to show how to draw the various parts of a building in perspective according to admeasurement, and 94 MANUAL OF PERSPECTIVE. we will leave the architect to vary the propor- tions as he pleases. Having stated the dimensions, a scale must be drawn, as at a. The scale is generally drawn in ten divisions. Each division on this scale represents two feet: the first division is marked in the centre, to show the size of one foot. Commence the drawing with the perpendi- cular line nearest the eye raised upon the base line. Commence setting off the admeasurement from the lower end of the perpendicular line, by copying the scale on a piece of paper, and applying it to the base line, upon which all the upright lines are measured. Pilaster, two feet; space between the pilaster and the window, four feet ; window, four feet ; space, six feet. Repeat the admeasurement on the base, till the whole of the divisions of the front are marked upon the base line. All the divisions cannot be shown in this diagram, but the student will know how to continue them beyond the limits of the picture. Next draw a line from the angle on the base line to the point of sight d ; and also a MANUAL OF PERSPECTIVE. 95 line to the point of distance. This line is the ground line of the building. Place the flat rule on the points marked upon the base, and draw lines from them towards the point d, till they touch the ground line of the building. Fig. 58. Place the square upon the ends of the lines where they touch the ground line, and draw faint perpendicular lines, and the width of every object upon the face of the building will be correctly drawn. 96 MANUAL OF PERSPECTIVE. We now proceed to measure the height of the various parts, which in this drawing are measured upon the first perpendicular line. By referring to Operation 19, the student will find the admeasurement of the height of the object measured upon a perpendicular drawn across the point of distance. The same process may be repeated in this drawing ; but as we have the perspective width of two feet on the ground line given, it will be much easier to make another scale of ten divisions, taking the two feet from the ground line for the first division. This is done in the scale b ; and all the divisions on the perpendicular are measured by this scale. The width of the plinth, two feet ; space between the plinth and lower end of the windows, including the window-sill, three feet; height of windows, fourteen feet; space between the windows and frieze, one foot; the frieze, three feet; the cornice, including the parapet, five feet. All these admeasure- ments must be marked with points on the first drawn perpendicular line ; and lines drawn MANUAL OF PERSPECTIVE. from them to the point of distance, out of the picture. If the lines are correctly drawn, all the divisions of the side of the concert-room will appear in true perspective. The drawing can then be finished according to the taste of the draughtsman ; and the pencil lines showing the perspective divisions removed, by using the Indian-rubber. We might increase the size of this Manual by repeating this process a number of times, but the student would gain no increase of in- formation. Whatever building he wishes to put in perspective, according to strict admea- surement, he must proceed as in the two opera- tions here given. The rule is simple, viz. upright lines are measured on the base line : lines running parallel to the ground line of the building are measured from the same scale, on a perpendicular drawn through the point of dis- tance, or, on a reduced scale, on the perpen- dicular line of the building nearest the eye. G 98 MANUAL OF PERSPECTIVE. CHAPTER VI. FURNITURE IN PERSPECTIVE. Operation 2 1 . — Bedstead. This is a drawing of an ordinary four-post bedstead of the present fashion. We have chosen this subject in preference to a more splendid bedstead, because the lines will show more distinct ; and any upholsterer can furnish the bedstead according to his own taste, or the fancy of his customers, when he has the post and frame-work in perspective. In drawing furniture, it will be necessary to be particularly careful in having the points of station and distance in their proper places, and the horizontal line rather below than above the height of the eye of a man standing on the bed- MANUAL OF PERSPECTIVE. 99 room floor. I should advise no upholsterer to purchase this work, and think he will know how to draw furniture in perspective, unless he studies the early operations. We presuppose Fig. 59. in the following remarks, that he has done so ; and we shall therefore give no directions for finding the square upon the surface: that he has learned in the three first operations. We 100 MANUAL OF PERSPECTIVE. will therefore commence by stating that both the points of distance are out of the picture, upon the horizontal line a a. In order to make this clearly understood by the furniture draughtsman, the small diagram (Fig. 60) is annexed. The square is supposed to be the Fig. 60. size of the picture ; A is the horizontal line, drawn a considerable distance beyond each of the upright lines of the square. We have no lines in this drawing leading to the point of sight ; but the student is aware if the sight point was required, it would be exactly between the points of distance b c. The lines running to the points of distance should run from points marked on the base line, according to the scale of feet of the bedstead : MANUAL OF PERSPECTIVE. 101 but in this small diagram we merely want to show the horizontal line drawn beyond the picture, upon which is placed the points of dis- tance. The small diagram (Fig. 61) shows the bad effect of drawing an object under too small an angle of vision. Here the spectator, or rather Fig. 61. A fciiluL c the point of station, would be a short distance from the bed-post nearest the base line; and the consequence is, that though the horizontal line is drawn the same height as in Fig. 60, the points of distance are so near together that the drawing looks preposterous, a is the horizontal line ; b c the points of distance : and any person totally unacquainted with drawing 102 MANUAL OF PERSPECTIVE. could tell that this must be a false position, and that no bedstead could have that appear- ance in reality. Operation 22. — Chair, footstool, and table, in perspective. In this operation both the point of sight and point of distance are a long way beyond the boundary of the picture : a is the horizontal line; the line at o is part of the base line; two of the legs of the chair, and the leg of the table that is nearest the eye, are both supposed to be upon it. The point of sight will easily be found if the horizontal line is drawn sufficiently long. If the dotted line at I is continued till it touches the horizontal line, that will give the point of sight ; and the line from i, in the contrary direction, will give the point of distance. The dotted lines all run to these points; and, with the diagram before MANUAL OF PERSPECTIVE. 103 him, the student can have no difficulty in work- ing this operation. We might introduce numberless articles of furniture as examples for the artist and the upholsterer, but as they are all drawn by the %. 62. A same rules, the subjects introduced will be sufficient to enable them to put furniture in any part of the room in perspective. In some old works on perspective the floor is divided into squares, as in Operation 5, and the furni- ture marked on the squares. There is not the 104 MANUAL OF PERSPECTIVE. slightest occasion for this complicated method ; the student that has well practised the early operations knows how to place a square or other figure on the ground plane on any part of the surface, and he can then raise perpendicu- lars from it of any height required, always taking care to recollect the comparative height of a man and the piece of furniture. Chairs, tables, and all objects below the height of a man, must be placed at a proportionate distance beneath the horizontal line. We have, in the remarks on the horizontal line, at page 62, shown the importance of draw- ing this line the proper height. The impro- priety of placing this line greatly above or below the height of a man, is clearly seen: if drawn too high, the furniture would look as if placed on an inclined plane ; and if too low, the objects would all appear to be falling down. MANUAL OF PERSPECTIVE. 105 Operation 23. -Square monument, surmounted a circular vase. This subject is introduced to show the effect of drawing the horizontal line considerably beyond the space occupied by the picture. The square on the ground plane is first formed, and Fig. 63. perpendicular lines of the proper height raised from the angles. As the spectator is supposed to be standing opposite the angle, he can see two sides of the monument. The point of 106 MANUAL OF PERSPECTIVE. sight is in the centre of the picture, but is of course hid by the subject. The points of dis- tance must be placed on the horizontal line a a, on each side of the centre perpendicular line, and at equal distances from it. All the divi- sions on the monument must be correctly marked on the centre perpendicular, and lines drawn from them to the two points of distance, like the dotted lines in the preceding engraving. The outline of the vase must be correctly formed, and the lines drawn across it slightly curved, to show rotundity. In small round objects the rotundity is shown by the light and shade, rather than by perspective lines. Operation 24. — Greenwich and Dover Railway. The annexed engraving of the Greenwich Railway contains a great many objects that have been explained in the preceding operations; but as they have not been introduced in a real view, MANUAL OF PERSPECTIVE. 107 the detail of this drawing is given, as it will enable the student to commence and complete almost any architectural subject that may come under his notice. Fig. 64. We commence at the base line, which here also forms the lower line of the border of the picture. Next ascertain the height of the horizon: it is marked in this drawing the 108 MANUAL OF PERSPECTIVE. height of the head of the diminutive figure standing in the centre of the road near the archway. The point of sight is the head of the figure. The arch that is taken over the carriage way, and the small arches on each side of it, are in elevation. Take the horizontal line some inches beyond the drawing, on the side where the railway appears, and draw the base line a great deal longer than it appears in the picture, and upon it measure the width of the piers and the space between them. Draw a line to the point of sight, for the ground line of the piers in perspective; and from the point previously made on the base draw lines toward the point of dis- tance. Where these lines touch the ground line of the piers, draw perpendiculars. Measure the height of the first pier on the perpendicular line nearest the base, and from this point draw a line to the point of sight ; this will give the height of all the piers. Then on the perpen- dicular nearest the base measure the height of the arch ; from this point draw a line to the point of sight, and the height of all the arches MANUAL OF PERSPECTIVE. 109 will be found. Divide the squares between each pier, as directed in Fig. 50, and draw the arches. The parapet, the cornice, the heading of the piers, and the plinth, must all be measured on the same perpendicular, and the lines taken to the point of sight. The thickness of each pier will be given by the perpendicular from the ground plane. The cornice under the arches is drawn parallel to the horizon. The curves of the inner side of the arches are so little seen, and all spring from the cornice, that they can be drawn correctly by hand, without lines. The opening under the piers must be measured from the first small arch in the pier, by taking lines to the point of sight. The direction of the lines for the plinth of the piers, and the parapet of the wall above the arches, will be seen in the drawing. Mark the ground line of the iron railings upon it, and draw short upright lines at the proper divisions ; and then draw the hand- rail to the point of sight. Draw the lines for the road to the same point. Next slightly draw the figures. The whole drawing is now in true 110 MANUAL OF PERSPECTIVE. perspective, but covered with pencil lines. Ink that part of the outline forming the drawing, and take out all the perspective lines with Indian- rubber, and the drawing will be complete. The student will find it much to his advan- tage to practise this drawing twice the size of the engraving. This he can easily do, as it is only taking twice the length of the lower line of the square, and twice the height of the per- pendiculars. This increase of size will give greater facility in drawing the perspective lines, and the drawing will not be a mere tracing of the original. Operation 25. — The interior of the nave, tran- sept, and choir, of a cathedral. The student that can produce a correct copy of this operation twice the size, will have the power of drawing the interior of any cathedral that comes under his notice. The groining of MANUAL OF PERSPECTIVE. Ill the ceiling, and the arches in the nave and choir, are from Westminster Abbey. Only one shaft of the pier is drawn, as that is quite sufficient for the perspective of the church. The drawing of the architectural ornaments is another branch of art. The perspective draughtsman only raises a scaffold for the architectural and picturesque draughtsman to work upon ; but let both recollect, that how- ever beautiful and elaborate their work may appear, if they spend months upon one interior, if the perspective is incorrect, their persever- ance and skill will be thrown away, and the drawing valueless. It would be a waste of time to tell the student that has carefully practised the fore- going drawings, how to draw the ground plane of this cathedral in perspective by means of squares. The horizontal line is the height of the head of the figure in the foregound ; the point of sight is the head of the distant figure. When the squares are formed for the ground plan, take the perpendiculars as high as they 112 MANUAL OF PERSPECTIVE. are required, which is up to the springing of the groins of the ceiling. Measure the divisions of this line, if admeasurement is required, on a perpendicular raised upon the base, outside the border of the drawing. In that case you must draw to scale. From the top of the first pier draw a light line to the point of sight. Do the same for the line running above the large arches. This will give the squares ; which divide, as seen in the drawing, and then draw the pointed arches. The centre of the squares in which the arches are drawn will give the division for the arches of the triforium, which is the arched gallery between the large arches and the upper range of windows called the clerestory. This centre per- pendicular taken up to the point of the arch of the clerestory, will give the divisions on the centre line of the ceiling. Curved lines drawn from the intersections on the centre line of the ceiling to the small shafts above the triforium, will give the overhanging arches or groins of the ceiling. MANUAL OF PERSPECTIVE. 113 The work at the transept is in elevation ; all the long lines run even with the base, as do those of the organ screen, or rood loft, that separates the chancel from the nave. The author of this Manual feels assured that the student that has practised these operations will be able to meet and surmount any diffi- culty that may present itself, in producing the true perspective of any object that may come before him. It is impossible in the space of this Manual to give a greater number of examples ; nor would it benefit the student if he had them. By this time he knows that, however compli- cated the operations in engravings appear, they are but repetitions of the simple rules ; and if he keeps his mind clear, and draws so that he can distinguish the outlines of the drawing from the lines drawn to the point of sight and points of distance, he will be able to produce any drawing without being confused by its elaborate appearance during the process. A person unacquainted with art that looks at H 114 MANUAL OF PERSPECTIVE. the frontispiece of this Manual, will probably say that it is but a view of the skeleton of a cathedral: and he will be right. The perspec- tive lines form the skeleton of a drawing : the muscles and the skin, to continue the metaphor, must be furnished afterwards. The substance of the piers and arches, their roundness, light and shade, architectural decoration, and variety of surface and colour, is the province of the artist, who adds beauty to the work by his genius and taste, while he takes care it shall be bestowed upon the solid basis of mathema- tical precision, as far as it can be obtained by the rules of perspective. MANUAL OF PERSPECTIVE. ] 15 CHAPTER VII. AERIAL PERSPECTIVE — INTERIORS —LANDSCAPE PAINTING, ETC. At the commencement of this Manual a few remarks were made on the effect of air inter- vening between the spectator and distant ob- jects., and that the air through which the objects were seen was the perspective plain. In the practical lessons to which lines can be applied, we can only decrease the size of objects as they recede from the eye; but the artist has the additional advantage of decreasing the strength of colour, and making objects more indistinct the nearer they approach the horizon. The architectural draughtsman that studies aerial perspective may add greatly to the beauty 116 MANUAL OF PERSPECTIVE. and effect of the drawing of the interior and exterior of a building, by making the lines finer and of a lighter colour the nearer they approach the point of sight. In the composition of a landscape the per- spective lines cannot be applied in all cases, but the artist that has studied the rules of perspec- tive will never commit the glaring error of making human figures twice the height of the doorway of the building near which they are standing: he will know that trees and other objects on the ground plane all become smaller the nearer they approach the horizon; and, though it would be tedious to apply the per- spective lines for determining the height of every object in the picture, if he is thoroughly acquainted with the rules of the art, he will be enabled to produce a more pleasing representa- tion of natural objects than a painter unac- quainted with them can do. How often do we see, in even in other respects good pictures, ponds, rivers, and lakes, considerably above the natural horizon, and trees much below it ! It may be MANUAL OF PERSPECTIVE. 117 said that an artist must be dull indeed that could fall into such errors ; but they are to be found in pictures of the highest reputation, particularly in the productions of the old masters. In the cartoons of Raphael, the perspective in many instances is glaringly incorrect. In the cartoon of the Miraculous Draught of Fishes, all the figures in the boat are three times the size they ought to appear. Any one of them would sink the boat by his own weight ; — and all the figures are much below the horizon, and conse- quently the water is seen above their heads. Thus, however beautiful the expression and drawing of the various figures, the whole pic- ture is absurd, merely from the want of atten- tion to the rules of perspective. We shall conclude the remarks on the advan- tage of the application of perspective in the composition of pictures, by an extract from the large work on Perspective, by Mr. Brook Taylor : — tc Although the strict practical rules of per- spective are in a great measure confined to 118 MANUAL OF PERSPECTIVE. right-lined figures, yet the knowledge of the general laws of that science is of great and necessary use to inform the judgment after what manner the images of any proposed lines should run, which way they should tend, and where terminate; and thereby enables it the better to determine what appearance objects ought to present to the eye, according to their different situations and distances. It accustoms the eye to judge with greater certainty of the relations between real objects and their per- spective descriptions, and the hand to draw the same accordingly ; and directs the judgment to discover any considerable errors therein, which might otherwise escape notice. Besides that, when the ground or general plan and the prin- cipal parts of a picture are first laid down ac- cording to the rules, everything else will more naturally fall within them." These observations might be considerably extended, but enough has been stated to show the applicability of perspective to landscape painting. The rules laid down in working the MANUAL OF PERSPECTIVE. 119 operations contained in this Manual will enable the attentive reader to give the correct per- spective of every object that can come under his notice. 2 CATALOGUE OF WORKS APOCALYPTIC SKETCHES. New Edition, Vol. I. " THINGS THAT WERE." By the Rev. John Cumming, D.D. F.R.S.E. Fcap. cloth, 6s. ART-JOURNAL (The), an Illustrated Journal of the Fine Art», the Arts of Design, Manufacture, &c. &c. Published Monthly, with Two Engravings from the Royal Gallery, and between Forty and Fifty fine Engravings on Wood, &c. 2s. 6d. New Series, Vols. I. 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