and the inner and smaller curves are described from the points b, c, d, etc.

Fig. 28. While the lower portion of this bulb pattern is to be drawn with the compasses, they can afford no aid in drawing the upper portion. The outlines of the central row of bulbs are first to be drawn of uniform curves on both sides, for which the ruling will be a perfect guide.

PROBLEMS FOR PRACTICE.

1. Draw and shade Fig. 25 in full, after the enlarged outline form shown at D.

2. Draw and shade Fig. 26, according to the enlarged outline form shown at C, which is four times the size of the pattern. Why is it four times the size?

3. Draw an outline of one of the series in Fig. 27, four times its present size. 4. Draw Fig. 28 lengthwise of the paper, and four times its present size. Blackboard Exercises.-The bulb-pattern Fig., and Fig. 25, enlarged as at D.

PAGE ELEVEN.

Fig. 29 is a Grecian pattern of a painting on vases. It is still another example of conventional flower representation, in which only the general principle of the pendulous flowerbud is retained. It is drawn with the greatest regard to symmetry. The right-hand portion, left partly unshaded, shows how the forms of the pendulous buds are drawn symmetrically, and of uniform size.

Fig. 30 is a Byzantine interlaced circular pattern, sculptured in stone, from Milan, Italy. It is very easily drawn, almost wholly by the compasses. Trace the whole very lightly at first. The light is supposed to come diagonally from above, from the right hand.

Fig. 31 is a copy of one of the Assyrian painted ornaments found among the ruins of Nineveh. The central circles, a (see the end marked B), were black; the inclosing ring, 6, dark reddish brown; the winding band, c, orange; and the other winding band, d, blue; while the spaces within the borders, outside of the winding bands, had a groundwork of reddish brown. The blue winding band was separated from the orange, wherever they were contiguous, by a black

line. Thus the ancient Assyrians understood the now admitted principle that one color should never impinge upon another, and that all contiguous colors should be separated, generally by either white or black lines. The entire pattern may be easily and accurately drawn by the compasses. The same pattern is also found differently lined and colored, somewhat as shown at the end marked C.

Fig. 32 is a Byzantine pattern of interlaced ornament, to be drawn wholly by the compasses. The central points from which the several circles and semicircles are described can easily be found by the pupil.

Fig. 33 is a partially completed pattern, showing the method of putting in a series of uniform divisions that radiate from the centre of a circle. The circle is easily divided into eight equal parts by lines radiating from the centre on the vertical, horizontal, and diagonal lines, as indicated by the lettering. Each eighth of the circumference is then to be divided into three equal parts by the compasses, and the opposite points in the circumference are connected by slightly traced or dotted lines passing through the centre. The bases of the radiating white stars can then be designated with sufficient accuracy by the eye, as the points to which the sides of the stars are to be drawn, on the second circle, are intermediate between the radiating dotted lines. Figures similar to this are numerous in ancient ornamental art.

Fig. 34 is a Byzantine pattern of interlacing circles. Though seemingly intricate, it is quite easily drawn, and wholly by the compasses. It would, however, be impossible to draw it with any approach to accuracy without the aid of the ruled paper; and there can be no doubt that it was originally drawn on a ground prepared with lines such as those we have given. The ruling gives the exact centre of every circle, and renders all measuring unnecessary. Observe that the heavy shadows indicate that the light comes from above, and from the left. The background may be shaded with a uniform tint of India ink, or by the pencil, as indicated in the upper left-hand portion.

Fig. 35 is also a Byzantine interlaced ornament, a considerable portion of which may be drawn by the compasses.

Thus the three circular bands, and the projections of the interlacing loops as described from the vertical, horizontal, and diagonal centres a, a, a, etc., are all easily and accurately drawn. The connecting and interlacing of the loops centrally must be done by hand, guided by the eye alone; but after having drawn one of the connections, as from b to d, the others may be drawn in symmetrical conformity to it. Observe how the shadows are cast, the light coming diagonally from the left, and from above.

PROBLEMS FOR PRACTICE.

1. Draw a pattern similar to Fig. 29, but let the semicircular black line, from the end of which the flower-bud is suspended, be drawn with a radius of four spaces, instead of three; and let the flower-bud be two spaces longer and one space broader at the broadest part.

2. Draw a pattern similar to Fig. 31, but describe the larger circles with a radius one space greater than in the figure.

3. Draw a pattern similar to Fig. 33, but describe the outer circle with a radius of eight spaces, and divide each eighth part of the circumference into four equal parts, instead of three, thus giving to each eighth part one ray more than in the figure.

4. Draw Fig. 34 on a larger scale, having the radius of the larger circles six spaces, instead of five.

5. Draw Fig. 35 on a larger scale, at the option of the pupil.

Blackboard Exercise.-So much of Fig. 35 as there is room for on the board. It would require a board four feet square to draw it in accordance with the enlarged ruling of the board.

PAGE TWELVE.

We have given on this page a number of original designs, for the purpose of indicating the facility with which an immense variety of very pleasing patterns may be drawn almost wholly by the compasses alone.

Fig. 36 is an ornamental figure called a quarterfoil, inclosed within a circle. The quarterfoil, often used in architecture, is disposed in four segments of circles, and is a conventional representation of an expanded flower of four petals. The lettering shows with what ease and accuracy it is drawn on the ruled paper.

Fig. 37 is an ornamental figure consisting of eight seg

ments of circles, described from the eight numbered points which are at the extremities of the dotted vertical, horizontal, and diagonal lines. After drawing these dotted lines, of indefinite extent, but all passing through the centre c, equidistant points in all of them, for describing the segments, may be found by cutting the lines with the circumference of a circle described from the centre c. From the points 1, 2, 3, 4, etc., the segments are described with a length of radius that will barely allow the inner segments of circles to touch one another.

Fig. 38. The segments of circles are here drawn in a manner similar to those shown in Fig. 37; and then these segments are connected by ribs passing through the centre. The intervening spaces are then shaded, so as to give the filling-up a raised and rounded appearance, the heaviest shades being found on the lower right-hand portions-the light being indicated by the arrow A as coming diagonally from the left hand, and from above. The spaces covered by the heavy dark shade on the outside borders of the figure-the heaviest at the right and below-are marked out accurately by the compasses, by moving the fixed point of the compasses uniform distances, diagonally, from the centres 1 to the points 2. By looking at the figure through a tubular opening, it will seem to stand out from the paper as if embossed upon it-in relief.

Fig. 39 is similar in its border outlines to Fig. 38; and all of it, with the exception of the central portion, may be easily and accurately drawn, and mostly shaded, by the compasses alone. To draw the central figure accurately, first trace out lightly, in the space which it covers, the vertical, horizontal, and diagonal lines, after which the raised wedge-shaped oval figures may be drawn in between. these lines by hand. Observe how the heavy shadows are formed.

Fig. 40, drawn on the same general plan as the preceding two figures, requires no additional explanation. The shaded cross-ribs are easily drawn after making the raised circles of uniform size around their given central points. As these central points are determined by the tint lines on the draw

ing-paper, the whole figure may be drawn with the greatest ease and accuracy.

Fig. 41 is a pattern of seeming intricacy, but very easily drawn, and planned on the same general principles as the preceding figures on the same page. Every thing is drawn by the compasses from points indicated by the ruling of the paper, except the raised wedge-shaped ovals, that look as if embossed.

Fig. 42 is an interlaced pattern, drawn wholly by the compasses, with the exception of the central figure. The figures 1, 2, 3, 4, etc., show the eight central points from which the interlacing curves are described.

Blackboard Exercises.-Figures 41 and 42, omitting the central eight-leaf flower patterns.

Page 12 of this book illustrates, very happily, the great advantage which the ruled paper affords for drawing curvilinear patterns. It would be next to an impossibility to draw these designs with accuracy without this aid; but with this ruling, this kind of drawing, which is used to a great extent in all the decorative arts, becomes a very simple matter, easy of attainment by all who can describe a circle by the aid of the compasses.