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Hemispheres and Spheres. Small objects, usually of polished stone, the use of which has not been fully determined; they are therefore classed with problematical objects. The more typical forms, found in the mounds, are often of hematite and, like the cones, rarely exceed a few ounces in weight. Hemispheres are comparatively numerous, but spheres referable to this group are rare. Hammerstones and stones used as club-heads (see Clubs, Hammers) are often spherical, but usually they are not well finished, and occasionally large tail-like stones are found which can not be properly classed with the smaller polished objects. The base of the hemispheres is flat, rarely slightly hollowed out, and varies from a circle to a decided ellipse, while the vertical section departs considerably from a true semicircle. Typical objects of this group are most plentiful in the middle Ohio valley. It is surmised that they served in playing some game, as talismans or charms, or for some special shamanistic purpose. According to Grinnell (inf’n, 1906) small balls of stone are still used by some Plains tribes in a game. Little girls roll them on the ice in winter, trying to move a small stick resting on the ice in front of the opposing party, perhaps 20 ft distant. If the stick is touched and moved, the side which rolls the ball may roll it again, and a point is counted. If the stick is not moved, the ball is rolled by one of the opposing party who endeavors to move the stick which rests on the ice in front of her opponent. A small stone sphere was used by the Pima of Arizona in a kicked ball game, and numerous small spheres, usually of soft stone, are found in prehistoric ruins in Salt river valley of the same territory. Consult Rau in Smithson. Cont., xxii, 1877; Fowke (l) in 13th Rep. B. A. E., 1896, (2) Archaeol. Hist. Ohio, 1902; Hrdlicka in Am. Anthrop., viii, no. 1, 1906; Moorehead, Prehist. Impls. 1900; Gushing in Compterendu Internal. Cong. Am., vii, 178, 1890. (W. H. H.)