A mysterious large stone sphere stands on a platform of cobbles. A golden alligator holds a man in his jaws. A small jade bat becomes two sharks at the ends of its wings.
These are a few of the intriguing items in the exhibition of ''Between Continents/Between Seas: Pre-Columbian Art of Costa Rica,'' which will go on a two-year tour of the United States after its present showing at the National Gallery of Art here.
It is high time we had a look at what the people living between North and South American cultures and continents made of their situation in those times, even as we strive to understand their position now. The problem is that ever since the arrival of the Spaniards, looting has destroyed the archaeological record, making it very difficult to place artifacts in their proper context and time. But in this century, more systematic excavations have occasionally shed light on these cultures, and in the past decade or so extensive work by the Museo Nacional de Costa Rica has made it possible to establish a chronological framework for the three main geographical areas of the country.
The Costa Rican chiefdoms produced an amazing variety of pots, jewelry, and sculpture that stands comparison with that from Mexico, Panama, and Peru which is more familiar to us. Much of the work shows influences from these areas and other parts of Meso- and South America, but there is also some that seems to be specific to Costa Rica itself, including much emphasis on alligator or cayman motifs, the large stone spheres up to two meters (61/2 feet) in diameter and sometimes found in alignments suggestive of astronomical significance, and extraordinary ''flying panels'' supporting the metates, or scooped out stones for grinding.
The country has varied terrain, climate, and resources, so that people living in the northwest Guanancaste-Nicoya region were not necessarily producing the same things as those living in the Atlantic watershed and central highlands or in southwestern Diquis. The stone spheres and gold come from Diquis, for example , and the more elaborate metates from the central part of the country. Many of the jade pieces come from Nicoya and the Atlantic watershed.
So far, there is no known source of jade in Costa Rica, although it is speculated that much of it may have come by trade from Guatemala. Yet jade, though extremely difficult to work, was apparently a popular material for many centuries before its use suddenly came to an end.
Why did it end? That is one of the questions yet to be answered. Perhaps, some scholars think, trade routes to a possible jade source in Guatemala were interrupted, or gold-working methods from Panama were introduced, or some other material was introduced for items of high ritual importance.
And why are the metates so elaborately designed? The exhibition's catalog suggests a use in human sacrifice and fertility rituals, serving as visual reminders of the connection in the minds of those people between this world and what was conceived to be a next world. That catalog -- an excellent one put together by the Detroit Institute of Arts with a scientific committee of curators from that institution and the Metropolitan Museum of Art, and by the director of archaeological research at the Museo Nacional de Costa Rica -- details the work that eventually led to present knowledge and this exhibition.
The catalog interprets the creatures portrayed in the metate supports as cosmological symbols: ''Raptors and parrots are the daytime sun, felines are the night sun in the underworld, canines are the night sun's escort, and saurians are the earth's surface.'' The major theme of ''transformation through death and rebirth'' and the ''primary metaphor for all transformation (which) was the diurnal cycles of the sun'' seem to fit not only the metates but other stone sculptures and the pottery and jade as well.
Perhaps the gold pieces -- scorpions, spiders, alligators, and so forth -- also fit the metaphor. But other pieces seem less portentous, such as a beautiful crayfish, a crab pendant which is also a bell, assorted birds and frogs, and a wonderfully articulated little figure part human, part animal. Costa Rican gold is either cast by the lost-wax method or beaten into sheets and wire.
Among the ceramics are some elegant undecorated shapes, delightful representations of people and animals as well as unusual tripod containers and various pots. One pear-shaped pot on three conical feet wears a face that may be that of the rain god, but which looks to the modern viewer more like a whimsical work by Picasso. Some incense burners look almost African, as do some of the stools.
Many jade items are ax-shaped, some obviously ceremonial. Most combine the functional shape of an ax or celt with an image of some sort. In a few instances the image is reduced to abstract geometric design. Other pieces take the form of maceheads, tubular beads, pendants, and ear spools. The material itself is invariably lovely and of high quality, the designs not too complex but well executed.
Private and institutional collectors in Costa Rica have lent many delights and surprises to this exhibition, which stays in the National Gallery until May 9. From there it goes to the San Antonio Museum of Art, from June 21 through Sept. 21; the Los Angeles County Museum of Art, Oct. 29 through Jan. 16, 1983; the San Diego Museum of Art, July 4-Sept. 25, 1982; and the Detroit Institute of Arts, Nov. 7, 1983-Jan. 29, 1984.