when not represented precisely opposite to, and parallel with, the eye, will appear to converge towards some remote point, i. e. their vanishing point. Circles, when retiring in such manner, are represented by ellipses, proportioned to their distances: their dimensions in perspective are ascertained by enclosing them, or the nearest of them, where a regular succession is to be portrayed, within a square, which, being divided into any number of equal parts or chequers, will exhibit all the proportions of those more remote. 23. A bird's eye view is supposed to be taken from some elevated spot which commands a prospect nearly resembling the plane or ichnography of the places seen. Thus the view from a high tower, or from a mountain, whence the altitudes of the various objects on the plane below appear much diminished, gives nearly the same representation as is offered to a bird flying over them and hence the term. Some idea of this may be obtained by standing on any height, and observing how low those objects which are near thereto will appear when compared with those more distant; taking however the perspective diminution of the latter into consideration.

When a painter has formed a scene in his mind, and supposed, as is customary, that the principal figures of this scene lie close, or almost close, to the back of his canvas, he is, in the next place, to fix on some point on this side of the canvas from which he would choose his piece should be seen. But in choosing this point, which is called.the point of sight, regard should be had to its situation to the right or left of the middle of the canvas; but, above all things, to its distance and height with respect to the lower edge of the canvas; which edge is called the base line, and is parallel with the horizontal line which passes through the eye. For by assuming the point of sight, and consequently the horizontal line, too low, the planes upon which the figures stand will appear a great deal too shallow; as, by assuming it too high, they will appear too steep, so as to render the piece far less light and airy than it ought to be. In like manner, if the point of sight is taken at too great a distance from the canvas, the figures will not admit of degradation enough to be seen with sufficient distinctness: and, if taken too near it, the degradation will be too quick and precipitate to have an agreeable effect. Thus, then, it is evident that no small attention is requisite in the choice of this point.

When a picture is to be placed on high, the point of sight should be assumed low, and vice versa: in order that the horizontal line of the picture may be, as near as possible, in the same horizontal plane with that of the spectator; for this disposition has a surprising effect. When a picture is to be placed very high, as, amongst many others, that of the Purification, by Paolo Veronese, it will be proper to assume the point of sight so low that it may lie quite under the picture, no part of whose ground is in that case to be visible; for, were the point of sight to be taken above the picture, the horizontal ground of it would appear sloping to the eye, and both figures and buildings as ready to tumble headforemost It is true, indeed, that there is seldom

a necessity for such extraordinary exactness; and that, unless in some particular cases, the point of sight had better be high rather than low as a reason for which we may observe that, as we are more accustomed to behold people on the same plane with ourselves than either higher or lower, the figures of a piece must strike us most when standing on a plane nearly level with that on which we ourselves stand. To this it may be added that by placing the eye low, and greatly shortening the plane, the heels of the back figures will seem to bear against the heads of the foremost, so as to render the distance between them far less perceptible than it would otherwise be. The point of sight being fixed, according to the situation in which the picture is to be placed, the point of distance is next to be determined. In doing this a painter should carefully attend to three things:-first, that the spectator may be able to take in, at one glance, the whole and every part of the composition; secondly, that he may see it distinctly; and, thirdly, that the degradation of the figures and other objects of the picture be sufficiently sen

sible.

SECT. II.-GENERAL RULES.

1. Let every line which in the object or geometrical figure is straight, perpendicular, or parallel to its base, be so also in its scenographic delineations, or in the description, in all its dimensions, such as it appears to the eye; and let the lines which in the object return at right angles from the fore right side, be drawn in like manner scenographically from the point of sight.

2. Let all straight lines which in the object return from the fore right side, run in a scenographic figure, into the horizontal line.

3. Let the object you intend to delineate, standing on the right hand, be placed also on the right hand of the point of sight; that on the left hand, on that hand of the same point; and that which is just before, in the middle of it.

4. Let those lines which, in the object, are equidistant from the returning line, be drawn in the scenographic figure from that point found in the horizon.

5. In setting off the altitude of columns, pedestals, &c., measure the height from the base line upward in the front or fore right side; and a visual ray down that point in the front shall limit the altitude of the column, or pillar, all the way behind the front side, or orthographic appearance, even to the point of sight. This rule must be observed in all figures, as well where there is a front, or fore right side, as where there is none.

6. In delineating ovals, circles, arches, crosses, spirals, and cross arches, or any other figure in the roof of a room, first draw ichnographically, and so, with 'perpendiculars from the principal points thereof, carry it up to the ceiling, from which several points carry on the figure.

7. The centre in any scenographic regular figure is found by drawing cross lines from the opposite angles; for the point where the diagonals cross is the centre.

8. A ground plane of squares is alike, both above and below the horizontal line; only the

shall be.

10. Having considered the height, distance, and position of the figure, and drawn it accordingly, with its side or angle against the base, raise perpendiculars from the several angles or designed points, from the figure to the base, and transfer the length of each perpendicular, from the place where it touches the base, to the base on the side opposite to the point of distance. Thus the diametrals to the perpendiculars in the base, by intersection with the diagonals drawn to the several transferred distances, will give the angles of the figures; and so lines drawn from one point to another will circumscribe the scenographic figure.

11. If in a landscape there be any standing waters, as rivers, ponds, &c., place the horizontal line level with the farthest sight or appearance of it.

12. If there be houses, churches, castles, towers, mountains, ruins, &c., in the landscape, consider their position, that you may find from what point in the horizontal lines to draw the front and sides of them in the picture.

13. In drawing objects at a great distance, observe the proportions, both in magnitude and distance, in the draught, which appear from the object to the eye.

14. In coloring and shadowing near objects, you must make the same colors and shades in your picture which you observe with your eye in the landscape; but, according as the distance becomes greater, the colors must be fainter, till at last they are gradually lost in a darkish sky-color. SECT. III.-MECHANICAL ILLUSTRATIONS OF DRAWING IN PERSPECTIVE.

1. Suppose LLD BA, fig. 6, plate PERSPECTIVE, a square piece of pavement, consisting of twenty-five pieces of marble, each a foot square: it must be measured exactly, and laid regularly down upon paper; and for the sake of a more distinct notion how every particular square will appear when you have a true perspective view of them, mark every other stone or marble black; or else number each of them as in the figure, which is divided into squares, every other one of which may be made to appear black, like the three at the bottom marked BC D: or 1, 2, 3, 4, answering to those which are marked in the perspective with the same numbers. To lay your plan in perspective, fix your point of sight as you observe in the figure; or more or less to the right or left; then draw the line KK parallel to, and at what distance you will from LL; and raise a line on each side from L to K, to form the figure you see, as a frame; then draw a line from the corner K, which is the point of distance, to the opposite corner L; and this line will regulate your work. Now draw lines from the squares of your plan to the point, of sight, as exact as possible; and,

wherever your line of distance cuts those lines, draw lines parallel to the line LL, which will give you the squares in perspective, or the true figure of every square. Thus D, in the perspective plan, answers to B in the measured plan, and 1, 2, 3, and 4, answer to their corresponding squares in the same plan.

To raise either pillars, trees, houses, or any other bodies, according to their respective heights, at different distances and proportions, on the plan laid down, measure them out in perspective into squares of a foot or any other measure. Let one of these squares, 1, 4, in fig. 7, serve for the base of a pillar a foot thick. Mark the line L K, by the scale of the ground plan, into equal proportions or feet; a, b, c, d; which being so many feet high, and standing on the base, are uprights, not in perspective. Then draw a line, 4 5, parallel to 1 c. Join c and 5, and then you have the front of a body three feet high and one foot wide, which is the object you were to raise. From 4 draw a line with a black lead pencil, to the point of sight; and from 3 raise a line parallel to 45, till it touches the pencilled line passing from 5 to the point of sight, which will give you the side appearance of the column or body, as you will see it from the place where you stand.

Then, with a pencil, from c draw a line to the point of sight, which will determine the line 6 7 that bounds the perspective view of the column a-top. Afterwards from 2 raise a pencilled line parallel to a c or 1 c, till it touches the line drawn from c to the point of sight; then draw 67 parallel to c 5, and you will have the square of the top of the column as observed from A, which is supposed to be the place where you stand. It is to be observed that the line drawn from 2 to 6 is only imaginary, and in consequence is to be rubbed out, because, not being seen from the place where you stand, it must not appear in the drawing. The same may be understood of the line drawn from 1 to 2; but it is necessary that they appear in the draught, as they direct you how to regulate the top of your column, and to place it with certainty upon its base.

Lastly, finish your column with lines only, that is, from 1 to c, from 4 to 3, from 3 to 7, from c to 5, from 6 to 7, and from 1 to 4, whereby you will have the true representation of the column, as in fig. 8.

When this is done, you may erect other columns on the other squares in the same manner, observing to fling your shades all on one side, and being master of these few examples, which will cost very little trouble, you will find the principle of them apply to various objects.

For the construction of a camera obscura, 1. Darken the room EF, fig. 10, leaving only an aperture open in the window at V, on the side K, facing the prospect A B C D. 2. In this aperture fit a lens, either plano-convex, or convex on both sides. 3. At a due distance, to be determined by experience, spread a paper or white cloth, unless there be a white wall; then on this, GH, the desired objects A B C D will be delineated invertedly. 4. If you would have them appear erect, place a concave lens between the centre and the focus of the first lens, or receive the image on a plane speculum inclined to the

8. For example, the eye A, fig. 6, viewing the object BC, will draw the rays AB and AC, which give the angle BAC; so that an object viewed under a greater angle will appear larger, and another under a less angle smaller. That, among equal objects, those at the greatest distance appear smallest, and consequently, that in all perspective the remotest objects must be made the smallest, will be manifest from the figure: the objects BC, DE, FG, HI, and KL, being all equal, but at different distances from the eye, it is evident that the angle DAE is less than the angle BAC, that FAG is less than DA E, that HAI is less than FAG, and that KAL is less than HAI. Hence, the second, third, fourth, and fifth objects will appear smaller, though really all equal, inasmuch as the angles diminish in proportion as the objects recede. If the eye, on the other hand, were removed to M, KL would appear the largest, and BC no bigger than NO.

9. It follows that, as objects appear such as is the angle they are seen under, if several lines be drawn between the sides of the same triangle, they will all appear equal: thus all the lines comprised between the sides ON and OP, fig. 7, of the triangle NOP, will appear equal to each other: and, as objects comprehended under the same angle seem equal, so all comprehended under a greater angle must seem greater, and all under a smaller angle less.

10. This being premised, if there be a number of columns or pilasters to be ranged in perspective on each side of a hall, church, or the like, they must of necessity be all made under the same angle, and all tend to one common point in the horizon O, fig. 8. For instance, if from the points D, E, the eye being placed at A, and viewing the first object D E, you draw the visual rays DO and EO, they will make the triangle DOE, which will include the columns DE, FG, HI, KL, MN, so as they will all appear equal. 11. What has been said of the sides is likewise to be understood of the ceilings and pavements; the diminutions of the angles of remote objects, placed either above or below, following the same rule as those placed laterally. Trees, being ranged by the same law, have the same effect as the columns, &c.; for being all comprehended in the same angle, and the two rays having each its own angle, and all the angles meeting in a point, they form a third, which is the earth, and a fourth, which may be supposed the air, and thus afford an elegant prospect.

12. To exhibit the perspective of a circle, if it be small, circumscribe a square about it: draw diagonals and diameters ha and de, fig. 9, intersecting each other at right angles; and draw the right lines fg and be parallel to the diameter de through band f; as also through ƒ and g draw right lines meeting the fundamental line in the points 3 and 4. To the principal point V draw right lines V 1, V 3, V 4, V2; and to the points of distance L and K draw the right lines L 2 and K 1. Lastly, connect the points of intersection, a b, d, f, h, g, e, c, with the arches a b, bd, df, &c. Thus will a bdfhgec be the appearance of the circle.

13. If the circle be large, on the middle of the

fundamental A B, fig. 10, describe a semicircle, and from the several points of the periphery C, F, G, H, I, &c., to the fundamental line, let fall perpendiculars C1, F2, G3, H4, 15, &c. From the points A, 1, 2, 3, 4, 5, &c., draw right lines to the principal point V; as also a right line from B to the point of distance L, and another from A to the point of distance K. Through the common intersection draw right lines, as in the preceding case: thus we shall have the points e, f, g, h, c, which are the representations of these, A, C, F, G, H, I, which being connected as before give the projection of the circle. Hence it appears not only how any curvilinear figure may be projected on a plane, but also how any pavement consisting of any kind of stones may be delineated in perspective. If any complicated figure be proposed, it may not be easy to apply the practical rules to the description of every minute part; but by enclosing that figure in a regular one properly subdivided, and reduced into perspective, a person skilled in drawing may with ease describe the object proposed.

Upon the whole, where the boundaries of the proposed object consist of straight lines and plain surfaces, they may be described directly by the rules of perspective: but when they are curvilinear, either in their sides or surfaces, the practical rules can only serve for the description of such right-lined cases as may conveniently enclose the objects, and which will enable the student to draw them within those known bounds with a sufficient degree of exactness. It would indeed be a fruitless task, to seek, by the practical rules of perspective, to describe all the little hollows and prominences of objects; the different lights and shades of their parts, or their smaller windings and turnings; the infinite variety of the folds in drapery; of the boughs and leaves of trees; or the features and limbs of men and animals; much less to give them that roundness and softness, that force and spirit, that eagerness and freedom of posture, that expression and grace, which are requisite to a good picture.

It may appear a bold assertion to say that the very short sketch now given of the art of perspective is a sufficient foundation of the whole practice, and includes all the rules peculiar to the problems which most generally occur. But, the scientific foundation being simple, the structure need not be complex, nor swell into such volumes as have been published on the subject: volumes which, by their size, deter from the perusal, and give this simple art the appearance of mystery. Thus narrowing instead of enlarging the knowledge of the art; until the student, tired of the bulk of the volume, in which a single maxim is tediously spread out, and the principle on which it is founded kept out of sight, contents himself with a remembrance of the maxim, and rarely ascends to first principles.

We subjoin, however, for the information of those who would wish farther to pursue the subject an ample list of approved authors.

In the Latin language we find :-Johannis Cantuariensis, Perspectiva, Pisa, 1508, folio; an Italian translation of which, with notes was

published, by Galucci, at Venice, 1593, folio. C. Vittellionis, De Natura, Ratione, et Projectione Radiorum Visus, Luminum, Colorum, atque Formarum, quam vulgo Perspectivam vocant, libri x. Norimb. 1551, folio, with plates. Joa. Fr. Niceroni, Taumaturgus Opticus Studiosissimus Perspectiva, Paris, 1638, folio; a French translation of this appeared also at Paris, under the title of Perspective Curieuse, 1663, folio. Guido Ubaldus, Perspectiva, 1600, folio. Perspectiva Horaria, Auct. Em. Maignan, Rome, 1648. Andrea Putel, surnamed Porzi, Perspectiva Pictorum et Architectorum (Latin and Italian), Rome, 1693-1700, 2 vols. folio, with 226 engravings. This very useful work has also appeared in Latin and German, translated into the latter by J. Boxbath and G. C. Bodenner, Augsburgh, 1706-1709, folio. Strutt published likewise an edition in Latin and English, London, 1693-1707, folio. Bernard Lamy's book appeared in 1701, in 8vo.; and the ingenious work of S'Gravesande, in 1711, in 8vo., transiated into English by Stone in 1724. Ram. Rampinelli, Lectiones Opticæ, Brix. 1760, 4to., with thirty-two plates.

In Italian:-Trattato di Prospettiva di Bern. Zenale da Trevigi, Milan, 1524, folio. Prattica della Prospettiva, di M. Dan Barbaro, Venice, 1559, 1568, 1669, folio, with plates—a very serviceable publication. Dispareri in materia d' Architettura e di Prospettiva, Bresc. 1572, 4to. Le Due Regole della Prospettiva prattica, di Giac. Barozzi di Vignola, con i Comment. del P. Egn. Danti, Rome, 1583, 1611, 1644, folio, Bol. 1682, folio, Venice, 1743, fol. La Prattica di Prospettiva, del Car. Lor. Sirigati, Venice, 1596, 1626, folio. Discorso Intorno al Disegno con gl' Inganni del Occhio, Prospett. Prat. di P. Accolti, Firenza, 1625, folio. Prospettiva Prattica, di Bern. Contino, Venice, 1645, 1684. folio. Paradossi per Praticar la Prospettiva, Senza Saperla, da Giul. Troili, Bol. 1672, 1683, folio. Nuova Prattica di Prospettiva, da Paolo Amato, Pal. 1736, folio. Trattato Teoretico Prattico di Prospettiva, di Eust. Zanotti, Bol. 1766, 4to. with engravings. Della Geometrie e Prospettiva Prattica, di Bald. Orsini, Rome, 1774, 3 vols. 12mo.

In Dutch:-Het Perspectiv Conste van John Friess Vredemann, London, 1559, folio, Amst. 1633, 2 vols. folio. Marolois has given a French translation of this work, entitled La Perspective, Contenant tant la Théorie que la Pratique, Amst. 1662, folio. Onderwysinge in der Perspectiv Conste, door Henr. Hondius, La Hague, 1622, 1647, folio, of which a Latin translation was published at the same place, 1647, folio.

In French-Livre de Perspective, par J. Cousin, Paris, 1560, folio, 1587, 4to. Leçons de Perspective, par Jaques André du Cerceau, Paris, 1576, folio. La Perspective avec la Raison des Ombres et des Miroirs, par Sal. De Caux, London, 1612, folio. La Perspective of Matth. Josse, in Latin and French, Paris, 1635, folio, with fifty-five plates. La Perspective Pratique Necessaire à tous les Peintres, Graveurs, et Architectes, par un Religieux de la Comp. de Jésus, Paris, 1642, 4to., 1663, 4to., and 1679, 4to. 3 VOL. XVII.

vols.-There have appeared two English translations of this, one by Prike, 1672, 4to.-the other by Chambers, 1726, folio; and a German translation by J. C. Rembold, Augs. 1710, 4to. Manière Universelle de Gérard Desargues, pour pratiquer la Perspective par petit-pied comme géométral; ensemble les Places et Proportions des fortes et foibles Touches, Teintes, ou Couleurs, par Abr. Bosse, 1648, 2 vols. with 202 engravings. This is one of the most extensive and at the same time important of the works on perspective. It occasioned a great many other writings on the same subject, a detail of which will be found in Lettres écrites au Sieur Bosse, 8vo. The same Abraham Bosse has also given a work entitled Traité des Pratiques Géométrales et Perspectives, Paris, 1665, 12mo. with seventy engravings. Optique de Portraiture et de Peinture, par François Huret, Paris, 1675, folio. Traité de la Perspective où sont contenus les Fondemens de la Peinture, par le P. Bern. Lami, Paris, 1701, 12mo. Amst. 1734, 8vo. An English translation appeared at London in 1702, 12mo. Perspective Pratique d'Architecture, par L. Bretetz, Paris, 1706, 1746, 1752, folio. Traité de la Perspective Pratique, avec des Remarques sur l'Architecture, par le S. Courtonne, Paris, 1710, 1725, folio. Perspective Théorique et Pratique, par M. Ozanam, Paris, 1711, 8vo. Traité de la Perspective à l'usage des Artistes, par E. S. Jeaurat, Paris, 1750, 4to, with 110 engravings. Essai sur la Perspective Pratique, par Le Roy, Paris, 1757, 12mo. Raisonnement sur la Perspective pour en faciliter l'usage aux Artistes, par M. Petitot, Parma, 1758, folio, in French and Italian. Essai sur la Perspective Linéaire et sur les Ombres, par le Chevalier de Curel, Strasb. 1766, 8vo. Traité de Perspective Linéaire, par S. N. Michel, Paris, 1771, 8vo. La Perspective Aérienne Soumise à des Principes puisés dans la Nature, ou Nouveau Traité du Clair-obscur et de Chromatique, à l'usage des Artistes, par M. de St. Morien, Paris, 1789,8vo. Elémens de Perspective Pratique, à l'usage des Artistes, par Valen ciennes, Paris, 4to. Lavit, Perspective Linéaire.

In English: - Practical Perspective made Easy, by Mason, 1670, folio. Architectural Perspective, by Peake, folio. Perspective made Easy, by W. Halfpenny, 1731, 4to. Stereography, or a complete Body of Perspective, in all its Branches, by J. Hamilton, London, 1738. 1749, folio, with 130 engravings. Humphry Ditton's book, 1712, folio. Two Treatises, by Brook Taylor, one in 1715, the other in 1719. Oakley's Magazine of Architecture, Perspective, and Sculpture, 1730, folio. Perspective made Easy in Theory and Practice, by J. Kirby, London, 1755, 1768, 4to. Perspective of Architecture, deduced from the principles of Brook Taylor, and performed by two rules only of universal application, by the same, London, 1755, 1761, 2 vols. folio. The art of Drawing in Perspective made Easy to those who have no previous Knowledge of Mathematics, by J. Ferguson, London, 1755, 1778, 8vo. Practice of Perspective, by J. Highmore, 1784, 4to. Theory of Perspective in a Method Entirely New, by

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