1. CACTUS Linn. Sp. Pl. 466 (1753), restricted. MAMILLARIA Haw. Synop. 177 (1812), not Stackh. (1809). Usually globose to oblong plants (simple, branching or cespitose), but sometimes slender-cylindrical, covered with spine-bearing tubercles: flower-bearing areola axillary (with reference to tubercles), entirely separate from the terminal spine-bearing areola, although sometimes (Coryphantha) connected with it by a woolly groove along the upper face of the tubercle: ovary naked: seeds smooth or