100 3. Suppose the length of a rhomboides to be 17 feet 3, or 17 25 and the breadth 8 feet 7, or 8%, what is the content? Set one foot on the line B, to 17,25 on the line A, then again 8,58 on the line B, is 148 feet on the line A. The figure bath been represented before, and operated arithmetically, therefore it is here unnecessary. 4. Let the base of a triangle be 4 feet 1 inch, and the perpendicular 2 feet 1 inch: the half of the one is 2 feet 7 parts, and of the other 1 foot 7 parts. Set 1 on the line B to 4,15 on the line A: then against 1,07 half the perpendicular on the line B, is 4 feet and almost for the content. Or, if you set 1 on the line B, to 1,07 on the line A, against 4,15 on the line B, is 4 and almost foot on the line A. 5. If you set 1 on the line B, to 4,1 on the line A, then against 2,25 on the line B, is 8 feet (which is about 11 inches) on the line A, the half whereof is 4 feet 5 inches, which is the content of the triangle. BOOK ON MENSURATION. Hutton's Mensuration, 8vo. PART VIII.-DRAWING. DRAWING is the accurate representation of the colours or outlines of objects. Th's art forms the basis on which all the other acquirements of the artist must be built; and it is not only necessary to the student in the beginning of his career, but in proportion as the professor improves in the facility and correctness of his drawing, so much the nearer does he advance towards perfection in his art. For the sake of those who have no opportunity of receiving regular instructions, we shall endeavour to comprise in as small a compass as possible, such directions and rules as will be easily understood and applied to practice. Various are the opinions upon the best modes of beginning to learn drawing; and it is by no means an easy matter to decide upon this point, as so much must always depend upon the genius, turn of mind, and opportunities of the student. But for general purposes, and where circumstances will admit of it, we have no hesitation in recommending to begin the study of geometry and perspective. The first forms the best introduction to a knowledge of form, by giving accurate ideas respecting the most simple bodies, of which all the others may be considered as compounds and the last seems absolutely necessary not only to enable us to draw the representations of regular objects, but even to see them correctly; as it is certain that no one unacquainted with its rules, can ever attain the power of drawing without making the grossest mistakes. IMPLEMENTS USED IN DRAWING. A Drawing-board for fixing the paper upon, so that it may not shift, and also by straining it, to prevent the colours, when laid wet upon the paper, from causing it to swell up, so as to be uneven. The simplest sort is made of a deal-board, framed square, with a strong piece across each end, to prevent warping. Upon this the paper may be fixed down with pins, wafers, or sealing-wax, or strained with paste or glue. The best kind of drawing-boards, are made with a frame and a moveable pannel, upon which the paper is put wet, and then forced into the frame, where it is confined by wedges at the back. This strains equally well, without the trouble of pasting, so that you may dry it at the fire; it is proper to observe that all the angles of drawing-boards should be exactly square. Parallel rulers are for drawing parallel lines readily; they are made of two pieces of ebony fastened together by brass bars, so as to move parallel to each other. T-squares are rulers made in the form of the letter T, which are used with the drawing-boards; the short end, called the stock, being applied to the edge of the board, so as to slide forward and backward while the long part called the blade, is used for drawing lines. These are more convenient than parallel rulers, when a drawing-board is used, as by them lines are drawn at right angles to each other at once, without using the compasses. The pentagraph, this is an instrument by means of which a person may copy, enlarge, or reduce the outlines of any picture, print, or drawing. Dividing compasses are instruments of brass and steel, for dividing lines, and laying down measures, from scales, &c. They are generally sold in cases, containing also a steel pen, for drawing lines clearer than can be done by a common pen, which is useful where neatness is required and points with a black lead pencil, for putting into the compasses, when circles are to be described. These cases also contain scales of equal parts, and protractors for laying down angles. Black-lead pencils are of various qualities: the best are fine, without any grit, not too soft, and that cut easily without breaking. Indian rubber, or elastic gum, is a substance like leather, which has the useful property of erasing or defacing lines drawn with black-lead; it is therefore much used for this purpose. Indian ink. This useful substance comes from China, where it is used for writing, which is there performed with a brush instead of a pen. It is a solid substance, of a brownish-black colour; and the composition is not known, but is conjectured to be the gall of a species of cuttle-fish. When ground with water on a clean tile or plate, it may be made lighter or darker, as required, by adding to it more or less water. The best Indian ink is always stamped with Chinese characters, breaks with a glossy fracture, and feels smooth, when rubbed against the teeth. An inferior kind is made in this country, but it may be easily known by its grittiness. Hair-pencils are made of camel's hair, put into a goose or swan's quill. To choose these, moisten them a little, and if they come to a point without splitting, they are good; if not, they are not fit for drawing with. Charcoal, is used for sketching the outlines of figures, in order to get the proportions, previous to making a drawing in chalk. The best charcoal for this purpose is that of the willow; it is cut into slips, and the strokes made with it may be rubbed out with a feather of goose or duck's wing. Black-chalk, is a fossil substance, resembling slaty coal, which is cut into slips for drawing. It is generally used in an instrument called a port-crayon, which is made of steel or brass. It is much employed for drawing figures, and is the best substance for this purpose, in making drawings from plaster or after the life. It is of two kinds, French and Italian; the former is soft, the latter hard. For mellowing and softening the shadows into each other, when black chalk is used stumps are necessary. They are pieces of soft shamoy leather, or blue paper, rolled up tight, and cut to a point. White chalk is used, together with black, for laying on the lights. This is different from common chalk, being much harder. Tobacco-pipe clay is a good substitute for it. Red chalk, is a fossil substance, sometimes used for drawing, but not so much now as it formerly was, the black being preferred; however the red being cheaper, will do very well for some purposes. Drawing paper. This is made of various sizes and thickness. Middle-tint, is a paper of a brownish, or of a grey colour, and is used for drawing upon with black and white chalk. Being of a dark colour, the strokes of the white chalk are distinctly seen; and it saves time in making drawings, as the tint of the paper answers for the half-shadow, so that all that is necessary to be done is to lay in the dark shadows and the lights. Camera obscura. By the use of this instrument, any object may be drawn in its outlines, as exact as nature, without any knowledge in the art of drawing. The camera is a machine in which the images of external objects are represented distinctly, and in their genuine colours, either in an inverted or erect situation. A chamber is darkened, one of whose windows looks into a place set with a variety of objects, leaving only one small aperture open in the window shutter. In this aperture, either a plane or convex lens is fitted, or one convex on both sides. At a distance, to be determined by experience, a paper or white cloth is spread on the wall, and on this the images of the desired objects will appear inverted. In this case it is not more difficult to draw or rather copy the objects, though they are reversed, than to draw or copy several things which we see upright on the frames of transparent paper, lawn, or tiffany. To obviate the difficulty of the objects being inverted, let the paper, or what is to receive the objects, be placed against the back of a chair, and let a person look on the several objects represented thereon over it, and this will set them right to the eye. Or, if you would have the images appear erect, it may be done by a concave lens, or by receiving the image on a plane speculum inclined to the horizon under an angle of 45 degrees, or by means of two lenses included in a draw-tube instead of one. If the aperture does not exceed the bigness of a pea, the objects will be represented thereon, though there be no lens at all. To render images clear and distinct, it is necessary that the objects be illuminated by the sun. A portable camera may be thus constructed. A wooden chest must be provided, in the middle of the top of which a little turret, either round or square, open toward the object, must be raised. Behind this aperture incline a plane mirror to an angle of 45 degrees which will reflect the rays upon a lens convex on both sides, included in a tube. At the end of the focus of the lens, a table must be placed, covered with a white paper to receive the image; and lastly, an oblong aperture made to look through. By this machine, the images will be exhibited perfectly like their objects, each clothed in its different colours. Camera lucida. Dr. W. H. Wollaston has given this name to a portable instrument which he has lately invented, for drawing in perspective. COLOURS. Colours are either opaque or transparent. Opaque colours are those which, when laid on any substance, efface every other painting or stain; such as white and red lead, vermilion, &c. Transparent colours possess the peculiar property of leaving the ground, on which they are laid, visible 1 through them, and are employed for illuminating maps and charts. There is a further division into oil and water-colours. In preparing oil-colours, care must be taken to grind them extremely fine; and, when they are put on the pallet, to mix those which will not dry of themselves with drying oils; and also to mix the tinged colours in as small quantities as possible. If they are intended to be glazed, particular care must be taken to paint the under-colour strong and smooth; after which the others may be gradually added, till the whole is properly filled up. Water-colours are wrought in various ways: in distemper where the colours are prepared in size; in fresco, or painting on fresh mortar, in which case it is requisite that the colouring be quick, lest the stucco or mortar dry before it can be laid on. In agouche, where the colours are mixed with gum, and the pencil drawn along, as in paint and washings; and lastly, in miniature, for small and delicate works, in which the colours are required to be very fine and clean, to be mixed with gum, and worked in dots or points. Colouring matter is contained in almost every flower and root of vegetables, and may be extracted by a very simple process. A very fine azure-blue pigment is prepared by the Dutch, from the blossom of the corn blue-bottle. A delicate red may be obtained from the fresh leaves of roses, and a beautiful violet colour from the flowers of that name. The different pigments usually employed are black, white, red, orange, yellow, green, blue, purple, and brown. BLACK COLOURS. 1. Lamp-black is thus prepared: the impure juice collected from incisions made in pine and fir-trees is boiled down with a small quantity of water, and strained, while hot, through a bag. The dregs and pieces of bark remaining in the strainer, are burnt in a low oven, whence the smoke is conveyed through a long passage into a square chamber, at the top of which is an opening, with a large sack affixed, made of thin woollen stuff: the soot, or lamp-black, concretes partly in the chamber, whence it is swept out once in two or three days; and, partly in the sack, which is occasionally agitated, in order to take down the 'soot, and to clear the interstices between the threads, so as to admit a free current of air. 2. Ivory black is prepared from ivory, or bones, burnt in a close vessel. When finely ground, it affords a deep and beaut ful colour; but is unfit for use on account of the frequent adulteration with charcoal. An opaque deep black, for water colours, may be prepared, by grinding ivory black with gum-water, or with the aqueous liquid that settles from the whites of eggs. |