Undoubtedly, there is something mysterious about the pre-Columbian societies of Central and South America - their pyramids and statuary, their knowledge of astronomy and their remarkably recise calendars, among other phenomena, have aroused both curiosity and wild surmise. Among the theories published in recent years there have been speculations linking various Indian peoples to Egypt, the Phoenicians, China, sub-Sahara Africa - not to mention Heyerdahl's Kon Tiki adventure which presupposed prehistoric communication between South America and the islands of the South Pacific, or the school of Von Daniken, which looked to visitors from outer space as an explanation of some hard-to-understand phenomena.

Yet another hypothesis underlies Fox's anthology. In simplest terms, he seems to believe that it might not be such a mistake, after all, to call the original inhabitants of this hemisphere "Indians." He examines, in his introduction and elaborate notes, a large body of myth and ritual from these societies and finds many parallels with elements from India, some of which have come into Western tradition by other routes. There are interesting Creation myths, stores of a universal flood that parallel those from Genesis and Gilgamesh, curious pre-echoes of the mythology we know primarily as Greek, including one story which blends, remarkably, the myths of Prometheus and Daedalus. Invoking such legens as that of the Golden Fleece, he suggests that Latin America, in prehistoric times, was "part of what amounted to a worldwide martime empire" and that "there was a regular 'route' of voyages to the New World across both the Pacific and Atlantic."

The thesis is hardly proved by the material in this book, and may not be provable. Jungian interpreters, for example, would find other explanations for the many curious parallels tracked down and examined by Fox. But this material (some of which also has considerable literary interest) suggests that what we do not know outweighs what we know - and it is healthy to be reminded of that. (Doubleday Anchor, $5.95)