seen passing through the knee of that leg upon which the principal weight of the body is thrown. 2394. Though our object in this section is to give only a notion of the way of transferring to paper or canvas such objects as present themselves, we think it proper to hint at a few general matters which the student will do well to consider, and these relate to the balance and motion of the human figure. Geometry and arithmetic were with the painters of antiquity of such importance that Pamphilus the master of Apelies declared, without them art could not be perfected. Vitruvius particularly tells us the same thing, and, as follows, gives the proportions of the human figure:-"From the chin to the top of the forehead, or to the roots of the hair, is a tenth part of the height of the whole body; from the chin to the crown of the head is an eighth part of the whole height; and from the nape of the neck to the crown of the head, the same. From the upper part of the breast to the roots of the hair, a sixth; to the crown of the head, a fourth. A third part of the height of the face is equal to that from the chin to the under side of the nostrils, and thence to the middle of the eyebrows the same: from the last to the roots of the hair, where the forehead ends, the remaining third part. The length of the foot is a sixth part of the height of the body; the fore-arm, a fourth part; the width of the breast a fourth part. Similarly," continues our author, "have the other members their due proportions, by attention to which the ancient painters and sculptors obtained so much reputation. Just so, the parts of temples should correspond with each other and with the whole. The navel is naturally placed in the centre of the human body; and if a man lie with his face upwards, and his hands and feet extended, and from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle that the human body is thus circumscribed, as may be seen (fig. 815.) by placing it within a square. For, measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that the lines at right angles to each other, enclosing the figure, will form a square." Fig. 815. 2395. "How well," says Flaxman (Lectures on Sculpture), "the ancients understood the balance of the figure, is proved by the two books of Archimedes on that subject; besides, it is impossible to see the numerous figures, springing, jumping, dancing, and falling, in the Herculaneum paintings, on the painted vases, and the antique basso-rilievos, without being assured that the painters and sculptors must have employed geometrical figures to determine the degrees of curvature in the body, and angular or rectilinear extent of the limbs, and to fix the centre of gravity." Leonardo da Vinci has illustrated the subject in his Trattato di Pittura, a perusal of which cannot fail of being highly beneficial to the student. 2396. As in all other bodies, the centre of gravity of the human figure is that point from which, if suspended, the figure would remain at rest when turned round upon it. Flaxman, by some strange mistake, has described the centre of gravity as "an imaginary straight line, which falls from the gullet between the ankles to the ground, when it (the figure) is perfectly upright, equally poised on both feet, with the hands hanging down on each side." (Fig. 816.). The fact is, that the centre of gravity is found to be in a line so drawn, or rather removed backwards from it, in a vertical plane returning from that line. 2397. Motion implies change of position; for instance, in fig. 817., the weight of the figure is thrown on one leg, hence a line pass ing through the centre of gravity falls from Fig. 816. Fig. 817. the gullet on one leg, on which side also the shoulder becomes lowered, and that on the opposite side raised; the hip and knee sinking below those on the side supporting the weight. In fig. 818. the dotted lines terminated by the letters ABCD represent lines of motion, as also the extent of such motion. The same are also shown in fig. 819., wherein A shows the inclination of the head to the breast; B the extreme bend of the back over the legs, without changing their position; C that of the back bent backwards, the legs remaining in the same position. If the back be bent as far as D, the thighs and legs will project as far as E. 2398. Referring back to fig. 817. for comparison, as the commencement of motion, with fig. 820., we shall immediately see that the preparation for running consists in throwing the balance beyond the standing foot; and that when the centre of gravity, which is now about to take place, falls out of the common base, the hinder leg must be out, and off the ground, to Fig. 818. balance the fore part of the figure, which would otherwise fall. Fig. 819. 2399. In preparing to strike (fig. 821.), the figure is thrown back at the beginning of the action to give force to the blow: the dotted line shows the extent of the springing forward, in which the action is ended by the fall of the blow upon the object. 2400. In fig. 822., bearing a weight, the combined centres of gravity of the figure and Fig. 822. Fig. 823. Fig. 824. the weight to be borne must be found; and through it the line falls between the feet, if the whole weight rests equally on both, or on the supporting foot, if the weight is thrown upon one. Flaxman, who was a finer artist than a geometrician, has, in his lectures, fallen into another mistake on this head, by saying the centre of gravity is the centre of the incumbent weight, which is absurd; because the figure has not only to balance the weight itself, but also its own weight. 2401. In leaping (fig. 823.), the body and thighs are drawn together to prepare for the spring; the muscles of the leg draw up the heel, and the figure rests on the ball of the foot; the arms are thrown back to be ready immediately for swinging forward, and thus assisting in the impulse. When the figure alights, the arms, at the instant of alighting, will be found raised above the head; and a line dropped from the centre of gravity will be found to fall near the heels. 2402. In leaning (fig. 824.), if on more than one point, the greatest weight is about that point on which the figure chiefly rests. 2403. Fig. 825. is a flying, and fig.826. a falling figure, both whereof being in motion through the air rest on no point. In the first it will be observed that the heaviest portion of the figure is bounded by lines inclined upwards; as in falling the heaviest portion of it has a downward direction We have thought these elements would be useful, as exhibiting those leading principles without the comprehension whereof no motion or action can be well expressed. "Every change," says Flaxman, "of position or action in the human figure will present the diligent student with some new application of principles, and some valuable example for his imitation." 2404. We shall close this section with the application of the principles detailed in the management of the port crayon to the drawing of landscapes. The subject of figs. 827. Fig. 828. and 828. is from a spot a little way out of Rome, the tower of Cecilia Metella being seen in the distance. 2404a. In fig. 826. the masses are roughed in from the objects themselves; and the principal mass abc01d on the left side is first very carefully drawn by itself, being, as respects leading lines and thicknesses, corrected until the eye is satisfied of the truth of its general form. The eye is as high as E and E, which therefore show the height of the horizontal line, and are also, in fact, the vanishing points for the wall on the right-hand side of the picture, and the house on the same side a little beyond it. Holding the port crayon level, and taking on it with the thumb or forefinger the distance 01, we shall find that twice that measure in 2 and 3 will give the junction of the wall with the pler; and that a line continued horizontally from d cuts the top of the plinth of the gate pier. The picture happens to be divided into two equal parts by a vertical line drawn through the break in the city wall in the distance. dl, continued upwards, determines one side of the house on the right-hand side of the road, and from a point at a break in the foreground intersects the projecting wall at a vertical line determines the left side of the tower. The remaining horizontal lines, it will be seen, determine other points and lines; and thus it is manifest that the whole arrangement has been accomplished by making the mass abcold a measure or unit for ascertaining the size and relative position of the other parts. In fig. 828. the detail is filled in, and brought to a higher state of finish. 24046. There is a mechanical method of obtaining the exact relative sizes of objects, and their positions In making drawings from nature or casts, which we will endeavour to explain. If the draftsman take a pair of pretty large sized compasses, and, fastening a piece of string at the joint end of them, hold the points open before his eye, so as to take in the extent of space his drawing is intended to occupy; then tie a knot In the string to keep it between his teeth, so that the compasses points may be kept in any plane always equally distant from the eye; he may, for the various parts of his drawing, by opening or closing the compasses, have their exact relative heights, widths, and positions, to be at once transferred to the drawing. SECT. II. 2405. A perspective delineation is the linear representation of any object or objects, as it or they appear to the eye, and is such a figure of an object as may be supposed to be made by a plane making a section of the body or pyramid of visual rays directed from the eye to the different parts of the object. A delineation so made, being properly coloured and shadowed, will convey a lively idea of the real object, and at the same time indicate its position and distance from the eye of the observer. 2406. DEFINITIONS. — 1. An original object or objects is or are an object or number of objects proposed to be delineated: for instance, a house, a ship, a man, or all or any of them together. In fig. 829. the house ABCDFHK is the original object. 2. Original lines are any lines that are the boundaries of original objects, or of planes in those objects. The lines AB, BC, CD are original lines, being partly the boundaries of the original object ABCDFHK. 3. The ground plane is that upon which the objects to be drawn are placed, and is always considered a boundless level plane. The plane X in the figure is the ground plane, upon which is placed the object ABCDFHK. 4 The point of view or point of sight is the fixed place of the eye of the observer, viewing the object or objects to be delineated: E in the figure is such point. 5. The station point is a point on the ground plane, perpendicularly under the point of sight or eye of the observer, and expresses on the plan the station whence the view is taken. S is the station point in the figure, being a point on the ground plane vertically under the eye of the observer at E. 6. The plane of delineation or the picture is the canvas or paper whereon it is intended to draw any object or number of objects. Thus, in the figure, the plane GIKL is the plane of delineation; but, in the extensive sense of the word, the plane of delineation is considered a boundless plane, however circumscribed may be the delineation made thereon. 7. The horizontal line or the horizon is a line on the plane of delineation in every part level with the eye of the observer or point of view. VZ is the horizontal line on the plane of delineation GIKL. It is supposed to be obtained by the intersection of a plane passing through the eye of the observer, parallel to the ground plane, produced till it touches the plane of delineation. 8. The centre of the picture is a point perpendicularly opposite the eye of the observer, or point of view, and is consequently always somewhere in the horizontal line. in the horizontal line VZ is the centre of the picture, being perpendicularly opposite to the eye at E. 9. The vertical line is a line drawn through the centre of the picture perpendicular to the horizon. In the figure PR is the vertical line. It is here worthy of notice that the vertical line determines how much of the view lies to the right and how much to the left of the eye of the artist. 10. The distance of the picture is a direct line from the eye to the centre of the picture. EO is the distance of the picture, or plane of delineation, GIKL. 11. The ground line is that where the ground plane intersects the plane of delineation, as GL in the figure. 12. An intersecting point is one made on the plane of delineation, by producing a line in an original object till it touches the plane of delineation. Thus, T is the intersecting point of the original line BA. 13. An intersecting line is one made on the plane of delineation, by producing any plane in an original object till it touches the plane of delineation, or where, if produced, it would touch it. Thus WT is the intersecting line of the original plane ABCDN, being the line, where that plane, if produced, would touch the plane of delineation. 14. A vanishing point is that point on the plane of delineation to which two or more lines will converge, when they are the perspective representations of two or more parallel lines in an original object, whose seat is inclined to the plane of delineation. The point V in the figure is the vanishing point of the line AB, being found by the line EV, drawn from the eye of the spectator parallel to it, and produced till it touches the plane of delineation in the point V. For a similar reason, V is the vanishing point of the line CN; it is also the vanishing point for any other line parallel to the line CN, as BA; all parallel lines having the same vanishing point. The point Z is the vanishing point of the line AK, being obtained by a line drawn from the eye parallel to the line AK, and produced till it touches the plane of delineation. The point Z, moreover, is the vanishing point of the original lines DF and NH. And it is to be recollected by the student, that there will be as many different vanishing points of lines in the delineation of an original object as there are different directions of lines in that original object. The point Y is the vanishing point of the parallel original lines DN and FH, being found by the line EY being drawn from the eye parallel to them till it touches the plane of delineation. So also Q is the vanishing point of the line CD. In the process of perspective delineations, as we shall presently see, the plan of the object being drawn, the places of the various vanishing points are found on the ground line, whence they are transferred to the horizontal line by means of perpendiculars raised from them. 15. A vanishing line is one supposed to be made on the picture by a plane passing through the eye of the observer parallel to any original plane produced till it touches the picture. The line VZ is the vanishing line of an horizontal plane, and of all horizontal planes, being found by the intersection of a plane passing horizontally through the eye, or parallel to an horizontal plane. The vertical line YVM is the vanishing line of the original vertical plane, ABCDN being the line where a plane passing the eye of the spectator parallel to that plane would touch the plane of delineation. There will be as many different vanishing lines on the plane of delineation as there are different positions of planes in the object or objects; and |