Intersecting straight lines form the basis of the different chequered patterns in conjunction with the simple device of alternating light and dark masses. Interlacing patterns are also based on intersecting straight lines. When segmental curves are employed either the chequered or interlacing effect may be obtained. Such patterns are essentially geometric and mechanical, but some idea of the growth line is suggested by the undulating stems formed out of the arcs of circles struck from either side of the border. This effect may be used with purely artificial detail, such as arises naturally from the spaces left, or with the introduction of floral detail. It is evident that the curve of the undulating stem will vary according to the position of the centres from which the arcs are struck. [Illustration: No. 203. Brocade composed of Undulate Borders.] A fuller effect, giving more space for branching and other detail, will be obtained by basing the stem upon [Illustration: No. 204. Scroll Border based on Adjacent Circles.] [Illustration: No. 205. 14th Century Textile composed of Undulate Borders arranged obliquely.] a series of complete adjacent circles struck within the border. The latter device is the basis of the wave line, which, after all, is only the key or labyrinth with the square angles rounded. [Illustration: No. 206. French Brocade, 18th Century, composed of Borders.] Border decoration can also consist of leaves or other details symmetrically arranged on a central axis, with perhaps occasional flowers or rosettes to break the monotony. _Repetition and Alternation_ Generally speaking, the detail should preferably be of a formal character, and should consist of the repetition of units with no interest beyond that imparted by alternation. The detail must, moreover, be designed with due regard to the space to be filled, and, in any border which encloses any space, a common divisor of height and width should be found in accordance with which the unit can be designed. _Treatment of Angles_ [Illustration: No. 207. The Evolute Scroll as a Border. A. Continuous. B. Reciprocal] The meeting angles or corners of borders invariably require special treatment, and in those positions the detail should be compact and stronger in appearance than the general pattern. The simplest expedient is some form of patera or rosette, but, whatever the detail, it should always be in strong contrast to that of the run of the border. The only forms that can be continuous without any marked change in the angles, are the undulating stem, the wave, and its square form the key or labyrinth; but even with these the proportion of width to height at times needs modification. If a common divisor is not possible, the difficulty can to some extent be overcome by making the form reciprocal and letting the two sides meet in the centre of the border, so that any slight disparity in treatment and dimensions will not be noticeable. _Pilaster Treatment_