Fig. 21 is a pattern of interlacing diagonal net-work, embracing diagonal squares that are distinguished by three forms of shading or coloring.

Fig. 22 represents an embroidered pattern brought a few years ago from the East Indies. Here the forms alone can

be given, as the colors can not be represented. In the original pattern the four stars of each cross-shaped figure are white or silver, on a black ground inclosed by a silver line; and the small dark squares and the straight lines connecting them are golden.

Fig. 23 is the filling up of a mosaic pattern of Byzantine pavement. The numerous symmetrical figures that may be discerned in it show both the intricacy and at the same time the harmonious simplicity of the Byzantine style. By the aid of the ruled paper similar patterns of almost endless variety may be designed.

For free-hand drawing on the blackboard take Figs. 13, 14, 15, 16, 17, and 18. They may be shaded slightly with colored chalks, so as to make the interlacings plain.

PAGE SIX.

Fig. 24 is the simple generating form of the Grecian single fret, or meander-a species of architectural ornament consisting of one or more small projecting fillets, or rectangular bands, meeting, originally, in vertical and horizontal directions only. Although this ornament was originated by the Greeks, quite similar rudimentary forms of the fret have been found among the Chinese and the Mexicans. The Arabians extended the Greek fret to diagonal and curved interlacing bands; and the Moors afterward extended it to that infinite variety of interlaced ornaments, formed by the intersection of equidistant diagonal lines, which are so conspicuous a feature in the ornamentation of the Alhambra. In addition to the most important of the plane surface Grecian frets, here given, and some of the Moorish that are best adapted to drawing purposes, we have also shown several of them in the second number of the Drawing Series, in their more natural form in architecture, as solids.

Fig. 24 requires no directions for drawing it. Fig. 11, on

page 5, is the same as this, with the exception that Fig. 11. has an interlacing band running centrally through it. The ruler may be used for all the drawings on this page; but the shading of the darker parts (by India ink) should be lighter than the copies.

Fig. 25 is a single fret, with the band returning upon itself at regular intervals. In drawing the frets, draw the shaded portions only, and, as you proceed, trace a very faint dotted line through the central part of the fret, to distinguish it from the unshaded intermediate spaces. The frets are best shaded, mainly, by India ink; but where there are two interlacing bands, one of them should have the running dot shading.

Fig. 26 is also a single fret, a little more complicated than the former two.

Fig. 27 is a double fret, formed of two interlacing bands. A single band should first be drawn throughout, tracing it lightly at first; the spaces for the other band will then be readily apparent.

Fig. 28 is a double fret, formed by one single fret backing upon another single fret of the same form.

Fig. 29 is an interlacing double fret. Trace one of the bands throughout very lightly before beginning with the other, so as not to interfere with the crossings. The ruler should not be used (if at all) until the entire fret is clearly but lightly marked out with the pencil alone. Observe that, in all interlacing fret-work, any one band passes alternately first over and then under another.

Fig. 30 is the same as Fig. 29, but with spaces left between the bands for paneling. Observe the vertical bands marked a b in Fig. 29. These are separated in Fig. 30 for the panels, which, in Grecian architecture, were ornamented with various devices.

Fig. 31 is an interlacing double fret, similar to Fig. 30, inverted end for end, with spaces for ornamental panels. In all cases of double frets it is best to draw one of the frets throughout before beginning the other.

The fret here shown, with its panels, although strictly Grecian, was one of the forms of Roman pavement that has

been found in the ruins of Pompeii. The two bands composing the fret, which are here differently shaded, were of white marble, formed of the same number of square pieces as is designated by the ruling of the paper; and the intermediate spaces, here left unshaded, were of black marble. Fig. 32 is an interlacing double fret with panels.

Fig. 33 is a double fret with panels, but is not interlacing. Take away the panels, and the frets are doubly backed upon one another.

Fig. 34 is an interlacing double fret, formed of distinct portions connected by a rectangular link.

Fig. 35 is a diagonal and horizontal interlacing double fret; and, as its form shows, is not Grecian. It is of Moorish origin, and is one of the numerous kinds of complicated frets, painted in various colors, and on variously colored grounds, on panels of the walls of temples.

Fig. 36 is an interlacing double fret, also of Moorish origin.

For free-hand blackboard exercises take Figs. 28, 29, 34, and 36. They may be shaded lightly.

PAGE SEVEN.

Figs. 37 and 38 are borders of fret- work, formed after Moorish and Arabian patterns.

Fig. 39 is an Arabian pattern of a mosaic pavement, with some of the smaller subdivisions omitted. The peculiar star-form of ornamentation here shown, which is of Byzantine origin, was also used by the Arabians.

Fig. 40 is a diagonal double fret, which has been slightly varied from an Arabian pattern to fit it to our purpose. In copying it, either one of the bands should first be lightly traced throughout.

Fig. 41 consists of two four-pointed stars interlacing, so as to show an eight-rayed or eight-pointed star. In drawing it, first take the centre, c, then the four inner vertical and horizontal points marked 3, then the four inner diagonal points marked 2. Also take the eight ray points in a similar manner. Trace lines very faintly from the outer to the inner points; then trace an inner set of lines equidistant

from these; after which mark firmly every alternate ray border across the other border lines, when, the intersections being distinct, the whole can easily be finished. The rays may be made either longer or shorter than those in the drawing, it being considered that two diagonal spaces are nearly equal to three vertical or horizontal spaces.

Fig. 42 is copied from an Arabian pattern of a mosaic pavement in three colors; white (or cream-colored), red, and black. The groundwork may be said to consist of elongated hexagons connected by interlacing diagonal squares; then there is a central interlacing fret ingeniously varied to adapt it to the other portions, so as to make a perfectly harmonious meander. In drawing it, first trace the three parts lightly in the order here described.

Fig. 43 is also copied from an Arabian mosaic, in white, red, and black. It is taken from a pavement in Cairo. It will be seen that the diagonal lines here are all two-space diagonals; and as the drawing conforms strictly to the original, it must be true that the original pattern was formed by the aid of precisely such horizontal and vertical lines as we have used for guides on the ruled paper.

Observe how beautifully the nine small figures, in three colors, and three different forms, fill out the six-pointed star-shaped figure at the intersection of the several bands. The entire pattern is a fine example illustrating the fundamental principles of decoration; that all ornament should be based upon a geometrical construction, and that every pattern should possess fitness, proportion, and harmony, the result of all which will be a feeling of satisfied repose, with which every such decoration will impress the beholder, leaving nothing further to be desired within the scope of the ornamentation.

For free-hand blackboard exercises take Figs. 37, 38, and 41. Observe the heavy shading on those sides that would be in shade if the light came in the direction indicated by the arrow.

III. CURVED LINES AND PLANE SURFACES.

PAGE EIGHT.

A curved line is one which is continually changing its direction. If the curve be uniform, it forms part of the circumference of a circle.

A circle is a plane bounded by a single curved line called its circumference, every part of which is equally distant from a point within it called the centre. The circumference itself is usually called a circle. A straight line drawn from the centre to any part of the circumference is called a radius.

Fig. 1. At 4 are six uniform curves of five spaces' span (five inches), and a depth of one space; and at Fig. 1 this curve forms part of a perfect circle. At a and b the directions of the curves are changed; but all combined form a harmonious and equally balanced figure, because the additions a and b are uniform in position and curvature. These figures should be drawn with the compasses, using the pencil to make the connections of the curves uniform. Let the pupil find the centres from which the curves a and b are struck. Fig. 2 is formed of the same pattern curve used in different positions, but all combined to form a harmonious figure. If either of the half curves, c or d, were omitted, or changed in position, the harmony of the figure would be destroyed. At Y the same form of curve is used. Let the pupil find the centres from which the curves are struck.

Fig. 3 is also a harmonious figure, described wholly by the compasses; but the inner border lines from e to h and from g to fare described with a less radius than that used for the other curves. The curves e i and g i are, each, only half of the pattern curve, and are described from the points 1 and 2.

Fig. 4. At B is another pattern curve representing a span of six inches and a depth of one inch, described from the centre c, with a radius of five inches. In the shaded fourangled figure the pattern curve is used in four different po

D