In Fig. 452, let A I G H be the elevation of a" ball which it is required to construct in thirteen pieces. Divide the profile into the required sections, as shown by 0, 1, 2, 3, 4, etc., and through the points thus obtained draw parallel horizontal lines, as shown. The divisions in the profile arc to be obtained by the following general rule, applicable in all such cases: Divide the whole circumference of the ball into a number of parts equal to two times one less than the number of pieces of which it is to be composed.
In convenient proximity to the elevation, the center being located in the same vertical line A N, draw a plan of the ball, as shown by K M L N. Draw the diameter K L parallel to the lines of division in the elevation. With the square placed at right angles to this diameter, and brought successively against the points in the elevation,drop corresponding points upon it, as shown by 1, 2, 3, 4, etc. Through each of these points describe circles from the center by which the plan is drawn. Each of these circles becomes the plan of one edge of the belt in the elevation to which it corresponds in number, and is to be used in establishing the length of the arc forming the pattern of the zone of which it is the base. Extend the center line N A in the direction of O indefinitely. Draw chords to the several arcs into which the profile has been divided, which produce until they cut G A O, as shown by 1 2 E, 2 3 D, 3 4 C, 4 5 B and 5 6 A. Then E 2 and E 1 are the radii of parallel arcs which will describe the pattern of the first division above the center zone, and D 3 and D 2 are the radii describing the pattern of the second zone, and so on.
From El in Fig. 453 as center, with E 2 and E 1 as radii, strike the arcs 2 2 and 1 1 indefinitely. Step off the length on the corresponding plan line, and make 1 1 equal to the whole of it, or a part, as may be desired - in this case a half. In like manner describe patterns for the other pieces, as shown, struck from the centers D1, Fig. 454; C1, Fig. 455; B1, Fig. 456, and A', Fig. 457. The pattern for the smallest section, as indicated by F in the plan, may be struck by a radius equal to F 6 in the plan. The center belt or zone, shown in the profile by 1 0, is a flat band, and is therefore bounded by straight parallel lines, the width being 1 0 in the elevation, and the length measured upon line 1 of the plan, all as shown in Fig. 458.
Fig. 452. - Plan and Elevation.
Fig. 453. - Pattern of Zone 1 2.
Fig. 454. - Pattern of Zone 2 3.
Fig. 455.-Pattern of Zone 3 4.
Fig.456 - Pattern of Zone 45.
Fig. 457. - Pattern of Zone 5 6.
Fig. 458.-Pattern of Middle Zone.
To Construct a Ball in any Number of Zones.