From the center e on the line e d set off e g and e h, at equal distances. From the points h g draw two arcs of different radii; if, where these arcs bisect each other, a line be drawn, it will be perpendicular to c d. By the same line e f, taking o as the center, fig. 12. To set off a walk perpendicular to the corner of a wall. - Carry out the lines a and b straight with the face of the wall, and of equal lengths; from the two ends of these lines, with equal radii, describe two arcs; from where they bisect each other, draw a line to the corner of the wall, which line will be the center of the walk, fig. 13.

Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.

Fig 12.

The annexed diagram, fig. 14, illustrates an instrument very useful in laying out mathematical figures. It consists of an upright pole two feet in length, shod with iron, upon which revolves a metallic tube with a projecting shoulder, to which is attached by a screw a wooden rod, eight, ten, or more feet in length, marked in feet and inches. Upon this rod there is a movable iron slide, with an iron sharp-pointed stud. The two-feet pole being placed in the center, or point from which the figure is to be described, the slide is moved along the rod to the proper distance, and fixed there by means of a screw. An iron handle, turned up at the end of the rod, about 18 inches in length, is taken hold of and. as it is moved round, the iron stud in the horizontal rod describes the figure intended to be formed.

Another useful instrument is a pair of wooden compasses shod with iron, the legs of which are five feet in length. To one leg a quadrant bar of iron is attached, and made to pass through the other leg. This quadrant-shaped iron rod is perforated at every three inches, and furnished with a screw-pin to keep the legs of the instrument distended to the extent required. The quadrant rod is placed exactly in the middle of the leg of the instrument, so that when the leg is moved, for example, three inches on the quadrant, it gives six inches at the points of the compasses; if moved one foot on the quadrant, it gives two feet, and so on, being always double the former extent.

The following figs., 15 to 29, which sometimes occur in flower-gardens, are given, with their centers marked to facilitate their being laid down on the ground. They are from a German work entitled Handbibliotheck fur Gartner, by Ligiler of Berlin.

Fig. 13.

Fig. 14.

Fig. 19.

Fig. 20.

Fig. 21.

Fig. 22.

Fig. 23.

Fig. 24.

Fig. 25.

Fig. 26.

Fig. 27.

Fig. 28.

Fig. 29. C. MQUENBCKC Me.