In the 19th century measurements of cranial capacity by Morton and others supported a "Caucasoid>Mongoloid>Negroid" hierarchy of intelligence. This continued through most of the 20th century but was challenged by a nonhierarchical view originating with Boas. Beginning in the 1980s Rushton correlated cranial and IQ measurements and presented a hierarchy with "Mongoloids" at the top. Each of these periods relates to its social context: the 19th-century hierarchy paralleled the height of European world domination; the nonhierarchy of the 20th century reflected world wars, worldwide depression, and the breakup of empires; the "Mongoloid>Caucasoid>Negroid" hierarchy followed the economic success of several Asian nations. Morton's cranial ranking was the result of his sampling error and his acceptance of the hierarchical thinking of his time. But how is it possible for Rushton to support the M>C>N ordering while using the data of several anthropologists who have rejected racial hierarchies on empirical grounds? The answer to this question involves a critique of Rushton's use of the race concept, his aggregation of diverse populations into three traditional races, his claim to explain differences in "cultural achievements" on the basis of variation in brain size, and a number of other problems. The study concludes by noting that the major consequence of these hierarchies is the apparent justification for the exploitation of those at the bottom.